Celestial Mechanics Lecture Notes PDF

Lecture 1 Celestial mechanics  Motions of objects in outer space Mechanics is the area of physics concerned with the relationships between force, matter, and motion among physical objects. Celestial mechanics deals with the motions of objects in outer space. ...

Lecture 1 Celestial mechanics  Motions of objects in outer space Mechanics is the area of physics concerned with the relationships between force, matter, and motion among physical objects. Celestial mechanics deals with the motions of objects in outer space.  Outline History – Geocentric model Observations Aristotelian physics Efbrazil, CC BY-SA 4.0, via Wikimedia Commons  Geocentric model Historically, the apparent motions of the celestial objects were described by European philosophers using the geocentric model.  Observations Two observations supported the idea that Earth was the center of the universe.  Earth First, Earth seems to be unmoving from the perspective of an earthbound observer; it feels solid, stable, and stationary.  Sun, Moon, & planets Second, the Sun appears to revolve around Earth once per day. The Moon and planets also appear to revolve around Earth about once per day. Stellarium Web Online Star Map https://youtu.be/uI2yZQOKOGk  Stars The stars appeared to be fixed on a celestial sphere rotating about once each day about an axis through the geographic poles of Earth. Geek3, CC BY-SA 3.0, via Wikimedia Commons  Celestial objects orbit Earth at the center The geocentric model describes the universe with Earth at the center. The celestial objects all orbit Earth. https://www.youtube.com/watch?v=jN4xVxKP7t4  Celestial objects have their own motions Alexey Elfimov, CC BY 3.0, via Wikimedia Commons The celestial objects have their own motions. The stars have a daily westward motion. Compared to the stars: – The Sun has a yearly eastward motion. – The Moon has a monthly eastward motion. This Photo by Unknown Author is licensed under CC BY-NC-ND  Aristotelian physics In the 4th century BC, an influential philosopher, Aristotle, wrote works based on the geocentric model. Aristotelian physics is the form of natural science or natural philosophy described in the works of Aristotle.  Celestial object is embedded in a sphere According to Aristotle, the celestial objects are embedded in concentric spheres that rotate at fixed rates. Geek3, CC BY-SA 3.0, via Wikimedia Commons  Uniform circular motion The celestial spheres are composed of the special element aether, the sole capability of which is a uniform circular motion at a given rate relative to the daily motion of the sphere of stars.  Order of spheres from Earth outward The order of spheres from Earth outward follows the decreasing orbital periods of the celestial objects. – Relative to the daily westward motion of the outermost sphere of stars: The Moon’s sphere has an eastward motion in one month. The Sun’s sphere has an eastward motion in one year. Lecture 1 – Part 2 Celestial mechanics  Outline History (cont.) – Celestial objects appear to revolve around Earth with own motions (observations) Geocentric model Aristotelian physics – Further observations Adjustments – Eccentric – Equant  Sun’s tilted path around Earth The Sun’s movement over the course of a year traces out a path along the ecliptic against the sphere of stars. The ecliptic is inclined to the celestial equator. – The Sun is north of the celestial equator for about half of the year.  Seasons On Earth, seasons are the result of the Sun’s tilted path around Earth. – The summer solstice is the time when the Sun reaches its most northerly excursion relative to the celestial equator on the celestial sphere. It is seen as the middle of summer. J.hagelüken, CC BY-SA 3.0, via Wikimedia Commons  Differences in the lengths of the seasons Astronomers observed differences in the lengths of the seasons. – Duration of the seasons of the year 2024 This is inconsistent with a premise of the Sun moving around Earth in a circle at uniform speed.  Eccentric The eccentric is generally attributed to Hipparchus (190 – 120 BC). According to Hipparchus, moving the center of the Sun’s path slightly away from Earth would satisfy the observed differences in the lengths of the seasons.  Equant Equant is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD. The Ptolemaic system predicted various celestial motions considerably better than without the equant.  Constant angular speed The equant point is placed so that it is directly opposite to Earth from the eccentric. A celestial object was conceived to move at a constant angular speed with respect to the equant.  Adjustment to Aristotelian physics The equant was an adjustment to Aristotelian physics. The moving object’s speed will vary during its orbit, faster in the bottom half and slower in the top half, but the motion is considered uniform because the object goes through equal angles in equal times from the perspective of the equant point.  Summary History – Observations Celestial objects appear to revolve around Earth with own motions – Geocentric model – Aristotelian physics » Uniform circular motion Differences in the lengths of the seasons etc. – Adjustments » Eccentric & equant » Constant angular speed  Outline History (cont.) – Observations Celestial objects appear to revolve around Earth with own motions (observations) – Geocentric model » Aristotelian physics Planetary retrograde motion – Heliocentric model – Geoheliocentric model  Copernicus’ model In the 16th century, a mathematical model of a heliocentric system was presented by Nicolaus Copernicus.  Heliocentric model In the heliocentric model, the daily-rotating Earth and the planets revolve around the Sun at the center of the universe. Only the Moon revolves around Earth.  Earth’s rotation around its axis The apparent motion of celestial objects around Earth over the course of one day is caused by Earth’s rotation around its axis.  Earth orbits the Sun Earth orbits the Sun. As seen from the orbiting Earth, the Sun appears to move with respect to the stars. Tfr000 (talk) 16:54, 15 March 2012 (UTC), CC BY-SA 3.0, via Wikimedia Commons  Planetary retrograde motion Copernicus’ system resolved the issue of planetary retrograde motion. The planets generally drift slowly eastward relative to the stars. However, a planet periodically appears to stop its eastward drift, and then drift back toward the west. Then, it appears to resume its normal motion west to east. This Photo by Unknown Author is licensed under CC BY-SA Stellarium Web Online Star Map  Earth & the planets revolve around the Sun In the heliocentric model, Earth and the planets revolve around the Sun. The heliocentric model argued that the planetary retrograde motion was apparent: a planet that Earth is passing seems to move backwards against the stars. This Photo by Unknown Author is licensed under CC BY-SA  Summary Geocentric model Heliocentric model – Planetary retrograde motion This Photo by Unknown Author is licensed under CC BY-SA  Tychonic system The Tychonic system is a model of the universe published by Tycho Brahe in 1588.  Geoheliocentric model It is a geoheliocentric model: Earth is at the centre of the universe, the Sun and Moon and the stars revolve around Earth, and the other five planets revolve around the Sun.  Mathematically equivalent to heliocentrism https://www.youtube.com/watch?v=6laRU_BzhvU At the same time, the motions of the planets are mathematically equivalent to the motions in Copernicus’ heliocentric system under a simple coordinate transformation.  Could be explained by the Aristotelian physics The Tychonic system combines what Tycho saw as the mathematical benefits of the Copernican system with the philosophical and “physical” benefits of the geocentric model. The Aristotelian physics of the time offered no physical explanation for the motion of Earth, whereas it could easily explain the motion of celestial bodies.  Summary Heliocentric model Geoheliocentric model – Aristotelian physics Celestial objects are embedded in rotating spheres  Scripture portraying Earth as being at rest Tycho also cited the authority of Scripture in portraying Earth as being at rest. – 1 Chronicles 16:30 “tremble before him, all the earth. The world is firmly established; it shall never be moved.” This Photo by Unknown Author is licensed under CC BY-SA  Summary This Photo by Unknown Author is licensed under CC BY-SA History – Observations Celestial objects appear to revolve around Earth with own motions – Geocentric model » Aristotelian physics Planetary retrograde motion – Heliocentric model – Geoheliocentric model » Aristotelian physics » Scripture  Outline History (cont.) – Tycho’s astronomical observations Kepler’s laws of planetary motion Efbrazil, CC BY-SA 4.0, via Wikimedia Commons  Tycho’s astronomical observations Tycho was also known for his comprehensive and unprecedentedly accurate astronomical observations.  Comprehensive & accurate observations He devoted many of his efforts to improving the accuracy of the existing types of instrument. – For example, a quadrant is an instrument used to measure angles up to 90. He designed larger versions of these instruments, which allowed him to achieve much higher accuracy.  Kepler’s laws of planetary motion Kepler’s laws of planetary motion was published by Johannes Kepler between 1609 and 1619. The laws modified the heliocentric theory of Copernicus, replacing its circular orbits with elliptical trajectories, and explaining how planetary velocities vary.  Heliocentric model Kepler had believed in the Copernican model.  Kepler’s religious view Much of Kepler’s enthusiasm for the Copernican system stemmed from his theological convictions about the connection between the physical and the spiritual. – The universe itself was an image of God, with the Sun corresponding to the Father, the stellar sphere to the Son, and the intervening space between them to the Holy Spirit.  Sun was the source of motive force In Kepler’s religious view of the cosmos, the Sun (a symbol of God the Father) was the source of motive force in the Solar System.  Planetary orbit Kepler introduced the revolutionary concept of planetary orbit, a path of a planet in space resulting from the action of physical causes, distinct from previously held notion of celestial sphere to which planet is attached.  Summary Tycho – Geoheliocentric model Aristotelian physics – The Sun is attached to a rotating sphere. Scripture – Earth is at rest. Kepler – Heliocentric model Kepler’s religious view – The Sun a symbol of God the Father – The Sun’s force causes Earth to move in an orbit.  Analyzed Tycho’s astronomical observations Kepler analyzed Tycho’s observations of the orbit of Mars. He could not reconcile Tycho’s highly precise observations with a circular fit to Mars’ orbit. He set about trying to fit a non-circular orbit to the data.  First law Finding that an elliptical orbit fit the Mars data, Kepler concluded Semimajor axis that all planets move in ellipses, with the Sun at one focus—his first law of planetary motion. Ag2gaeh, CC BY-SA 4.0, via Wikimedia Commons  Ellipse An ellipse is a plane curve surrounding two focal points (𝐹1 and 𝐹2 ), such that for all points on the curve, the sum of the two distances to the focal points is a constant. – It generalizes a circle, which is a shape consisting of all points in a plane that are at a given distance from the centre. The major axis of an ellipse is its longest diameter. The semimajor axis is one half of the major axis.  Second law Based on measurements of Earth and Mars, Kepler created a formula in which planets sweep out equal areas in equal times— his second law of planetary motion. Faster motion as a planet moves closer to the Sun Kepler supposed that the motive power radiated by the Sun weakens with distance, causing faster or slower motion as planets move closer or farther from it. This Photo by Unknown Author is licensed under CC BY-NC-ND  Summary History – Early astronomical observations Eccentric & equant – Geocentric model – Circular orbit – Tycho’s comprehensive & accurate astronomical observations Kepler’s laws of planetary motion – Heliocentric model – Elliptical orbit  Third law With Tycho’s data and his own astronomical theories, Kepler treated relationships between planetary orbital velocity and orbital distance from the Sun much more precisely and attached new physical significance to them. He articulated what came to be known as the third law of planetary motion: The square of a planet’s orbital period is proportional to the cube of the length of the semi-major axis of its orbit.  Further planet has a slower orbital speed The third law expresses that the farther a planet is from the Sun, the slower its orbital speed, and vice versa. https://youtu.be/3PCdNaUaYt4  Summary History – Tycho’s astronomical observations Kepler’s laws of planetary motion – Heliocentric model – Elliptical orbit https://youtu.be/3PCdNaUaYt4  Summary Celestial mechanics – History Early observations – Geocentric model – Aristotelian physics Planetary retrograde motion (observation) – Heliocentric model Tycho’s astronomical observations – Kepler’s laws of planetary motion  Summary Celestial mechanics – History (scientific inter- disciplinarity) Geocentric model (mathematics) – Observations (astronomy) – Aristotelian physics  Lecture 1 – Part 3 Celestial mechanics This Photo by Unknown Author is licensed under CC BY-NC-ND  Outline History (cont.) – Observations Celestial objects appear to revolve around Earth – Geocentric model Planetary retrograde motion – Heliocentric/geoheliocentric model Galileo’s observations with the telescope – Disproved the geocentric model Efbrazil, CC BY-SA 4.0, via Wikimedia Commons  Galileo’s observations with the telescope With the invention of the telescope in 1609, observations made by Galileo Galilei called into question some of the tenets of geocentrism. Stellarium Web Online Star Map  Moons of Jupiter Galileo could see the moons of Jupiter and stated that they orbited around Jupiter. – Galileo observed small “stars” close to Jupiter. Observations on subsequent nights showed that the positions of these “stars” relative to Jupiter were changing. He concluded that they were orbiting Jupiter: he had discovered Jupiter’s Jan Sandberg, Attribution, via Wikimedia Commons largest moons.  Not everything revolved around Earth This was a significant claim as it would mean not only that not everything revolved around Earth as stated in the geocentric model, but also showed a secondary celestial body could orbit a moving celestial body.  Venus exhibits a full set of phases Galileo observed that Venus exhibits a full set of phases similar to that of the Moon. – Galileo saw Venus at first small and full, and later large and crescent. This Photo by Unknown Author is licensed under CC BY-SA  Venus orbits the Sun This proved that Venus orbits the Sun and not Earth, and disproved the geocentric model.  Summary History – Observations Celestial objects appear to revolve around Earth – Geocentric model Planetary retrograde motion – Heliocentric/geoheliocentric model Galileo’s observations with the telescope – Disproved the geocentric model  Outline History (cont.) – Observations Celestial objects appear to revolve around Earth with own motions – Aristotelian physics Tycho’s comprehensive & accurate astronomical observations – Kepler’s laws of planetary motion Motions of objects – Newton’s laws » Provided an explanation for Kepler’s laws » Aristotelian physics was not correct Efbrazil, CC BY-SA 4.0, via Wikimedia Commons  Newton’s laws In 1687, Isaac Newton formulated the laws of motion and universal gravitation.  Laws of motion Newton’s laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it.  First law A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force.  Second law The change of motion of an object is proportional to the force impressed; and is made in the direction of the straight line in which the force is impressed.  Momentum, mass, & velocity By “motion”, Newton meant the quantity now called momentum, which depends upon the mass of a body and the velocity at which that body is moving. The momentum (𝐩) of a body is the product of its mass (𝑚) and its velocity (𝐯): 𝐩 = 𝑚𝐯  Force, mass, and acceleration Newton’s second law states that the rate of change of the momentum is the force. If the mass (𝑚) does not change with time, then the force (𝐅) equals the product of the mass and the rate of change of the velocity, which is the acceleration (𝐚): 𝐅 = 𝑚𝐚  Third law If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.  Conservation of momentum Newton’s third law relates to a more fundamental principle, the conservation of momentum. Suppose that two bodies interact. The momentum exchanged between them adds to zero, so the total change in momentum is zero. https://www.youtube.com/watch?v=hsDjzBdCTWs  Provided an explanation for Kepler’s laws Newton provided an explanation for Kepler’s laws.  Acceleration of a planet Newton computed the acceleration of a planet moving according to Kepler’s first and second laws. – The direction of the acceleration is towards the Sun. – The magnitude of the acceleration is inversely proportional to the square of the planet’s distance from the Sun (the inverse square law).  Sun is the physical cause This implies that the Sun may be the physical cause of the acceleration of planets.  Force acting on a planet Newton defined the force acting on a planet to be the product of its mass and the acceleration (Newton’s second law of motion). So: – Every planet is attracted towards the Sun. – The force acting on a planet is directly proportional to the mass of the planet and is inversely proportional to the square of its distance from the Sun.  Law of universal gravitation A force is also acting on the Sun (Newton’s third law of motion). So Newton assumed, in his law of universal gravitation: – All bodies in the Solar System attract one another. – The force between two bodies is in direct proportion to the product of their masses and in inverse proportion to the square of the distance between them.  Sun’s orbit is barely perceptible As the planets have small masses compared to that of the Sun, the Sun’s orbit is barely perceptible. Binary simulator  Aristotelian physics was not correct After the work of Newton, it became generally accepted that Aristotelian physics was neither correct nor viable. Lecture 2 Spaceflight  Fly spacecraft into or through outer space Spaceflight is an application of science and technology to fly spacecraft into or through outer space.  Outline Phases – Rocket launching – Outer space – Orbit – Orbital maneuver  Launching Spaceflight can be achieved conventionally by rocket launching, which provide the initial thrust to overcome the force of gravity (i.e. weight) and propel a spacecraft from the surface of Earth.  Rocket A rocket engine produces thrust by reaction to exhaust expelled at high speed (according to Newton’s third law). https://www.grc.nasa.gov/www/k-12/rocket/TRCRocket/rocket_principles.html  Propellant carried within User:Surachit, CC SA 1.0, via Wikimedia Commons Rocket engines work entirely from propellant carried within the vehicle. – A rocket design can be as simple as a cardboard tube filled with gunpowder. Fuel – Chemical rockets are the most Oxidizer common type of high power rocket, typically creating a high speed Combustion chamber exhaust by the combustion of fuel Exhaust with an oxidizer.  Can fly in a vacuum A rocket accelerates without using any surrounding air. A rocket can fly in the vacuum of space. Rockets work more efficiently in a vacuum and incur a loss of thrust due to atmospheric drag.  Outer space Outer space (or simply space) is the expanse that exists beyond Earth’s atmosphere and between celestial bodies.  Lacks a well-defined physical boundary The transition between Earth’s atmosphere and outer space lacks a well-defined physical boundary, with the air density steadily decreasing with altitude.  Kármán line The Kármán line, an altitude of 100 km above sea level, is a conventional definition of the edge of space. It is named after Theodore von Kármán, who calculated a theoretical limit of altitude for airplane flight above Earth. – An aircraft is a vehicle that is able to fly by gaining support from the air.  Legal & regulatory purposes The Kármán line is has no distinct physical significance in that there is a rather gradual difference between the characteristics of the atmosphere at the line. It is mainly used for legal and regulatory purposes of differentiating between aircraft and spacecraft, which are then subject to different jurisdictions and legislations.  Summary Edge of space (domain multi- disciplinarity) – Outer space is the expanse that exists beyond Earth’s atmosphere (science) – Kármán line: altitude limit of airplane flight (technology) – Legal and regulatory purposes  Orbit An orbit is the curved trajectory of an object, such as the trajectory of Earth around the Sun, or of a spacecraft around Earth. For most situations, orbital motion is adequately approximated by Newtonian mechanics.  Newtonian mechanics There are a few common ways of understanding orbits: – A force, such as gravity, pulls an object into a curved path as it attempts to fly off in a straight line. – As the object is pulled toward the massive body, it falls toward that body. However, if it has enough tangential velocity it will instead continue to follow the curved trajectory caused by that body indefinitely.  Newton’s cannonball model As an illustration of an orbit around Earth, the Newton’s cannonball model may prove useful. This is a ‘thought experiment’, in which a cannon on top of a tall mountain is able to fire a cannonball horizontally at any chosen muzzle speed. user:Brian Brondel, CC BY-SA 3.0, via Wikimedia Commons  Low initial speed If the cannon fires its ball with a low initial speed, the trajectory of the ball curves downward and hits the ground (A). https://www.youtube.com/watch?v=ALRdYPMpqQs  Sufficient speed As the firing speed is increased, the cannonball hits the ground farther (B) away from the cannon. If the cannonball is fired with sufficient speed, the ground curves away from the ball at least as much as the ball falls—so the ball never strikes the ground. It is now in what could be called a non-interrupted or circumnavigating, orbit.  Sub-orbital spaceflight A sub-orbital spaceflight is a spaceflight in which the spacecraft reaches outer space, but its trajectory intersects the surface of Earth. Hence, it will not complete one orbital revolution. This is usually because of insufficient orbital speed.  Orbital spaceflight An orbital spaceflight is a spaceflight in which a spacecraft is placed on a trajectory where it could remain in space for at least one orbit. The spacecraft reaches the minimal orbital speed required for a closed orbit.  Kepler’s laws of planetary motion When it is assumed that the spacecraft is subject only to the gravitational force of Earth (i.e. an engine thrust is not present), the orbit is described by Kepler’s laws of planetary motion.  Thrust When an engine thrust is present, Newton’s laws still apply, but Kepler’s laws are invalidated. When the thrust stops, the resulting orbit will be different but will once again be described by Kepler’s laws.  Applied at only one point in the orbit If thrust is applied at only one point in the spacecraft’s orbit, it will return to that same point on each subsequent orbit, though the rest of its path will change.  In a direction opposite to the motion Thrust From a circular (red) orbit, thrust applied in a direction opposite to the spacecraft’s motion changes the orbit to an elliptical (yellow) one. The resultant orbit will be smaller than the original circular orbit.  In the direction of the motion From a circular (blue) orbit, thrust applied in the direction of the spacecraft’s motion also creates an elliptical (yellow) orbit. The resultant orbit will be larger than the original circular orbit. Thrust  Orbital maneuver An orbital maneuver (otherwise known as a burn) is the use of propulsion systems to change the orbit of a spacecraft.  Transfer orbit A transfer orbit is an intermediate elliptical orbit that is used to move a spacecraft in an orbital maneuver from one circular, or largely circular, orbit to another. – One cannot move from one circular orbit to another with only one brief application of thrust. There are several types of transfer orbits, which vary in their energy efficiency and speed of transfer.  Hohmann transfer orbit The Hohmann maneuver is accomplished by placing the spacecraft into an elliptical transfer orbit. The maneuver uses two impulsive engine burns: the first establishes the transfer orbit, and the second adjusts the orbit to match the target. MenteMagica, CC BY-SA 3.0, via Wikimedia Commons  Bi-elliptic transfer The bi-elliptic transfer consists of two half-elliptic orbits. From the initial orbit, a first burn boost the spacecraft into the first transfer orbit. A second burn sends the spacecraft into the second elliptical orbit. A third burn injects the spacecraft into the desired orbit. AndrewBuck, CC BY-SA 4.0, via Wikimedia Commons  Energy efficiency & speed of transfer While they require one more engine burn than a Hohmann transfer and generally require a greater travel time, some bi- elliptic transfers require a lower amount of total energy than a Hohmann transfer.  Summary Spaceflight – Phases (celestial mechanics) Rocket launching Outer space – Kármán line (domain multi- disciplinarity) Orbit Orbital maneuver  Lecture 2 – Part 2 Spaceflight (cont.) – Interplanetary spaceflight – Applications Space tourism – Space pollution & atmospheric reentry  Interplanetary spaceflight Interplanetary spaceflight is travel between the planets of our Solar System. CactiStaccingCrane, CC BY-SA 4.0, via Wikimedia Commons  Sun’s gravitational pull Due to the Sun’s gravitational pull, a spacecraft moving farther from the Sun will slow down, while a spacecraft moving closer will speed up.  Extremely large amount of fuel A spacecraft desiring to transfer to a planet closer to the Sun must decrease its speed with respect to the Sun by a large amount in order to intercept it, while a spacecraft traveling to a planet farther out from the Sun must increase its speed substantially. Simply doing this by brute force – decelerating or accelerating in the shortest route to the destination – would require an extremely large amount of fuel.  More fuel is needed to put the fuel into orbit And the fuel required for producing these velocity changes has to be launched along with the spacecraft, and therefore even more fuel is needed to put both the spacecraft and the fuel required for its interplanetary journey into orbit. Fuel is Put the fuel needed into orbit  Techniques to reduce the fuel requirements Thus, several techniques have been devised to reduce the fuel requirements of interplanetary travel.  Hohmann transfer orbit 2nd burn For many years economical interplanetary travel meant using the Hohmann transfer orbit. It is an elliptical orbit which forms a tangent to the starting and destination orbits. 1st burn  Planets are moving at different speeds Earth is moving around the Sun at a different speed than the planet to which the spacecraft is travelling (in accordance with Kepler’s third law). https://youtu.be/3PCdNaUaYt4  Alignment of the two planets The alignment of the two planets in their orbits is crucial – the destination planet and the spacecraft must arrive at the same point in their respective orbits around the Sun at the same time. Phoenix7777, CC BY-SA 4.0, via Wikimedia Commons  Launch windows Launch windows for a Martian expedition This requirement for alignment gives rise to the concept of launch windows.  Synodic period Launch periods are periodic according to the synodic period. The synodic period is the elapsed time where planets return to the same kind of location. – For example, in the case of Mars, the period is 780 days (2.1 years). – 3D Solar System Viewer | TheSkyLive.com Takes ½ of the orbital period of the outer orbit The Hohmann transfer takes an amount of time similar to ½ of the orbital period of the outer orbit. – A spacecraft traveling from Earth to Mars via this method will arrive near Mars orbit in approximately 8.5 months. In the case of the outer planets this is many years – too long to wait.  Gravity assist A gravity assist is a type of spaceflight flyby which makes use of the orbit around the Sun and gravity of a planet to alter the path and speed of a spacecraft, typically to save propellant and reduce expense.  Spacecraft gains velocity The “assist” is provided by the motion of the gravitating body as it pulls on the spacecraft. This Photo by Unknown Author is licensed under CC BY-SA  Planet loses velocity The momentum gained by the spaceship is equal in magnitude to that lost by the planet, so the spacecraft gains velocity and the planet loses velocity (according to the conservation of momentum). However, the planet’s enormous mass compared to the spacecraft makes the resulting change in its speed negligibly small.  Planets are seldom in the right places The main practical limit to the use of a gravity assist maneuver is that planets are seldom in the right places to enable a voyage to a particular destination. There are years when the planets are scattered in unsuitable parts of their orbits.  Summary Interplanetary spaceflight (domain multi-disciplinarity) – Sun’s gravitational pull (science) – Techniques (economics) Hohman transfer orbit – Travel time (science) Gravity assist  Applications for spaceflight Current and proposed applications for spaceflight include: – Space tourism – Satellites (Lecture 3) – Space exploration (Lectures 4 – 9) – Protecting Earth from potentially hazardous objects (Lecture 10) – Space colonization (Lecture 11)  Space tourism Space tourism is human space travel for recreational purposes. There are several different types of space tourism, including orbital, suborbital and lunar space tourism.  Sub-orbital tourist flights Sub-orbital tourist flights will initially focus on attaining the altitude required to qualify as reaching space. The flight path will be either vertical or very steep, with the spacecraft landing back at its take-off site. https://www.youtube.com/watch?v=jbMoKbpo5tY  High-altitude part of the flight is in free fall To minimize the required fuel, the high-altitude part of the flight is made with the rockets off. A spacecraft with propulsion off is in free fall, a motion where gravity is the only force acting upon the spacecraft. – An object in the technical sense of the term “free fall” may not necessarily be falling down in the usual sense of the term. – Technically, if gravity is the only influence acting, an object is in free fall even when moving upwards.  Passengers will experience weightlessness If gravity is the only influence Same deceleration acting, then all objects (the spacecraft and passengers) “fall” (decelerate) at the same rate. The passengers will experience weightlessness. – The passengers inside the spacecraft appear to be floating. https://www.youtube.com/watch?v=TBBTJxjO-zE  Orbital tourist flights Space Adventures, a space tourism company, offers orbital spaceflight missions to the International Space Station. SpaceX, an spacecraft manufacturer, launch service provider and satellite communications company, offers paid crewed spaceflights for private individuals. Tourists visiting the International Space Station The International Space Station (ISS) is a space station maintained in Earth orbit. 13 space tourists have visited the ISS. https://www.youtube.com/watch?v=xg9R4yykvqU  Private orbital spaceflight This Photo by Unknown Author is licensed under CC BY-NC Inspiration4 was a 2021 human spaceflight operated by SpaceX. The trip was the first orbital spaceflight with only private citizens aboard. The mission spent almost three days in orbit https://www.youtube.com/watch?v=_T-exE-DRRo  Lunar tourism Lunar tourism may be possible in the future if trips to the Moon are made available to a private audience. Krückstock, CC BY-SA 3.0, via Wikimedia Commons  Natural attractions Stigmatella aurantiaca, CC BY-SA 3.0, via Wikimedia Commons Two natural attractions would be available by circumlunar flight or lunar orbit, without landing: – View of the far side of the Moon Due to gravitational locking, as the Moon orbits Earth, it always keeps the same face turned towards the planet. The far side of the Moon is never visible from Earth. – View of the Earth rising and setting against the lunar horizon https://www.youtube.com/watch?v=H1KWtG66lEQ  Environmental pollution While spaceflight altogether pollutes at a fraction of other human activities, it still does pollute heavily if calculated per passenger. – Rockets mostly exhaust greenhouse gases and sometimes toxic components. – Most rockets are made of metals that can have an environmental impact during their construction.  Space pollution Brocken Inaglory, CC BY-SA 3.0, via Wikimedia Commons Some spacecraft remain in space practically indefinitely, which has created the problem of space pollution in the form of satellite flare (light pollution) and space debris, which is a hazard to spaceflight.  Atmospheric reentry Otherwise spacecraft are terminated by atmospheric reentry.  Complete disintegration Objects entering an atmosphere experience atmospheric drag, which puts mechanical stress on the object, and aerodynamic heating—caused mostly by compression of the air in front of the object, but also by drag. These forces can cause loss of mass (ablation) or even complete disintegration of smaller objects.  Spacecraft cemetery If spacecraft do not disintegrate, their reentry is mostly controlled to safely reach a surface by landing or impacting, often being dumped into the oceanic spacecraft cemetery. – The spacecraft cemetery is a region in the southern Pacific Ocean. – The area is roughly centered on the oceanic pole of inaccessibility, the location farthest from any land.  Summary Spaceflight – Interplanetary spaceflight Domain multi-disciplinarity – Applications Space tourism – Attractions – Space pollution & atmospheric reentry  Summary History – Observations Celestial objects appear to revolve around Earth with own motions – Aristotelian physics Tycho’s comprehensive & accurate astronomical observations – Kepler’s laws of planetary motion Motions of objects – Newton’s laws » Provided an explanation for Kepler’s laws » Aristotelian physics was not correct  Lecture 3 Satellite  Object placed into Earth orbit A satellite or artificial satellite is an object, typically a spacecraft, placed into orbit around Earth.  Earth orbits Altitude classifications – Low Earth orbit – Medium Earth orbit Semi-synchronous orbit – Geosynchronous orbit Geostationary orbit – High Earth orbit  Low Earth orbit The term low Earth orbit (LEO)(cyan) region is also used for the area of space below an altitude of 2,000 km (about 1/3 of Earth’s radius). – The red dotted line represents the orbit of the ISS. According to Kepler’s third law, this corresponds to an orbit period of 128 minutes. – Stellarium Web Online Star Map  Advantages A low Earth orbit requires the lowest amount of energy for satellite placement. It provides low communication latency. Satellites and space stations in LEO are more accessible for crew and servicing.  Applications Hubble Space Telescope Space station Communications satellite Earth observation satellite  Hubble Space Telescope The Hubble Space Telescope (HST) is one of the largest and most versatile space telescope. Hubble’s orbit outside the distortion of Earth’s atmosphere allows it to capture extremely high-resolution images with substantially lower background light than ground-based telescopes. https://www.youtube.com/watch?v=0V08M1NcdJQ  Maintained by astronauts Hubble is the only telescope designed to be maintained in space by astronauts. Five Space Shuttle missions have repaired, upgraded, and replaced systems on the telescope, including all five of the main instruments. – Hubble was launched in 1990, but its main mirror had a flaw. The optics were corrected by a servicing mission in 1993.  Space station A space station is a spacecraft which remains in orbit and hosts humans for extended periods of time. Most often space stations have been research stations, but they have also served military or commercial uses, such as hosting space tourists. All space stations to date have operated within LEO.  International Space Station The International Space Station (ISS) is a large space station assembled and maintained a collaboration of five space agencies and their contractors: NASA (United States), Roscosmos (Russia), ESA (Europe), JAXA (Japan), and CSA (Canada). The ISS is the largest space station ever built.  Scientific research Its primary purpose is to perform microgravity and space environment experiments. Research is conducted in a wide variety of fields, including astrobiology, astronomy, physical sciences, materials science, and human research including space medicine and the life sciences. This Photo by Unknown Author is licensed under CC BY-NC  Tourism 13 space tourists have visited the ISS. – Dennis Tito visited the ISS in 2001, becoming the world’s first space tourist. Tito paid a reported US$20 million for his trip.  Communications satellite A communications satellite creates a communication channel between a source transmitter and a receiver at different locations on Earth. Communications satellites are used for television, telephone, radio, internet, and military applications. LEO satellites are less expensive to launch into orbit.  Relays & amplifies radio signals A communications satellite relays and amplifies radio telecommunication signals via a transponder. A satellite in LEO needs less powerful amplifiers for successful transmission.  Relay the signal around the curve of Earth The radio waves used for telecommunications links travel by line of sight and so are obstructed by the curve of the Earth. The purpose of communications satellites is to relay the signal around the curve of Earth allowing communication between widely separated Rudolfs Davis Strazds, CC BY-SA 4.0, via Wikimedia Commons geographical points. Covers a small area that moves at high velocity A single satellite in LEO only covers a small area that moves as the satellite travels at high orbital velocity.  Satellite constellation A satellite constellation is a group of satellites working together as a system. Unlike a single satellite, a constellation can provide permanent global coverage. This Photo by Unknown Author is licensed under CC BY  Earth observation satellite An Earth observation satellite is a satellite used or designed for Earth observation from orbit, including spy satellites and similar ones intended for non- military uses such as environmental monitoring, meteorology, cartography and others.  See the surface of Earth clearly by being close Earth observation satellites use LEO as they are able to see the surface of Earth more clearly by being closer to it.  Polar orbit & global coverage This Photo by Unknown Author is licensed under CC BY-NC To get global coverage with a low orbit, a polar orbit is used. Earth will rotate around its polar axis between successive orbits. The ground track moves towards the west each orbit, allowing a different section of the globe to be scanned with each orbit. https://www.youtube.com/watch?v=y_jM_BxQGvE  Medium Earth orbit A medium Earth orbit (MEO) (yellow) has an altitude above a LEO. – The green dashed line is the orbit used for GPS satellites. The edge of MEO is the particular altitude of a geosynchronous orbit (black dashed line). All satellites in MEO have an orbital period ranging between 24 hours and about 2 hours.  Semi-synchronous orbit A MEO that is particularly significant is the semi- synchronous orbit. A satellite in the semi- synchronous orbit has an orbital period of 12 hours. This Photo by Unknown Author is licensed under CC BY-SA  Reliably predictable orbit The satellite passes over the same spots every day. The orbit is reliably predictable.  Global Positioning System The Global Positioning System (GPS) is a satellite-based radio navigation system.  Four satellites in view of the receiver It provides geolocation and time information to a GPS receiver anywhere on Earth where there is an unobstructed line of sight to four or more GPS satellites. This Photo by Unknown Author is licensed under CC BY-SA-NC  Three position coordinates & time Each GPS satellite carries an accurate record of its own position and time, and broadcasts that data continuously. Based on data received from multiple GPS satellites, an end user’s GPS receiver can calculate its own geolocation and time. However, at a minimum, four satellites must be in view of the receiver for it to compute four unknown quantities (three position coordinates and the deviation of its own clock from satellite time).  Satellite constellation The current GPS consists of 24 to 32 satellites in semi-synchronous orbit, so that the satellites pass over the same locations every day. The orbits are arranged so that at least six satellites are always within line of sight from everywhere on Earth’s surface. Paulsava, CC BY-SA 4.0, via Wikimedia Commons  Geosynchronous orbit A geosynchronous orbit (GSO) has an orbital period that matches Earth’s rotation on its axis (one day).  Geostationary orbit A special case of GSO is the geostationary orbit, which is a circular GSO in Earth’s equatorial plane. A satellite in a geostationary orbit remains in the same position in the sky to observers on the surface. Lookang many thanks to author of original simulation = Francisco Esquembre author of Easy Java Simulation = Francisco Esquembre, CC BY-SA 3.0, via Wikimedia Commons Antennas are pointed permanently at a position Communications satellites are often placed in a geostationary orbit so that Earth-based satellite antennas do not have to rotate to track them but can be pointed permanently at the position in the sky where the satellites are located. Vsatinet, CC BY-SA 4.0, via Wikimedia Commons  Record the entire hemisphere continuously A weather satellite is a type of Earth observation satellite that is primarily used to monitor the weather and climate of Earth. Geostationary weather satellites can record or transmit images of the entire hemisphere below continuously. https://www.youtube.com/watch?v=ECjEHbcydDA  High Earth orbit A high Earth orbit (HEO) is farther than that of the geosynchronous orbit. One of the main benefits of HEO is that it provides a nearly unobstructed view of Earth and deep space. This makes it an ideal location for astronomical observations and Earth monitoring.  Earth monitoring Vela was a group of satellites developed by the United States to detect nuclear detonations to monitor compliance with the 1963 Partial Test Ban Treaty by the Soviet Union. – Serendipitously, the Vela satellites were the first devices ever to detect cosmic gamma-ray bursts.  Astronomical observations Transiting Exoplanet Survey Satellite (TESS) is a space telescope designed to search for exoplanets. TESS had identified 7,203 candidate exoplanets, of which 482 had been confirmed. This Photo by Unknown Author is licensed under CC BY  Summary Satellite – Earth orbits Low Earth orbit Medium Earth orbit – Semi-synchronous orbit Geosynchronous orbit – Geostationary orbit High Earth orbit – Advantages – Applications  Lecture 3 – Part 2 Satellite (cont.) – Space debris – Satellite flare  Space debris Space debris are defunct human- made objects in space – principally in Earth orbit – which no longer serve a useful function. These include derelict spacecraft (nonfunctional spacecraft) and, particularly-numerous in-Earth orbit, fragmentation debris from the breakup of derelict rocket ESA/ID&Sense;/ONiRiXEL, CC BY-SA 3.0 IGO, via Wikimedia Commons bodies and spacecraft.  Accumulate in Earth orbit Space debris began to accumulate in Earth orbit with the launch of the first artificial satellite into orbit in 1957.  Risk to spacecraft Space debris represents a risk to spacecraft. Several spacecraft, both crewed and uncrewed, have been damaged or destroyed by space debris.  First major satellite collision The first major satellite collision occurred in 2009. Two communications satellites— the active Iridium 33 and the derelict Kosmos 2251— accidentally collided. Rlandmann, CC BY-SA 3.0, via Wikimedia Commons  Creating new debris Both satellites were destroyed, creating thousands of pieces of new smaller debris. https://www.youtube.com/watch?v=6Wf4H0e9rfU&t=10s  Kessler syndrome The Kessler syndrome was proposed by Donald J. Kessler in 1978. https://www.youtube.com/watch?v=LaKz8VDkDkI&t=30s  Density of objects in LEO is high enough The LEO environment is becoming congested with space debris because of the frequency of object launches. The Kessler syndrome is a theoretical scenario in which the density of objects in LEO is high enough that collisions between objects could cause a domino effect.  Domino effect In the domino effect, each collision generates space debris that increases the likelihood of further collisions. One implication is that the distribution of debris in orbit could render space activities and the use of satellites in particular low Earth orbits difficult for many generations. https://www.youtube.com/watch?v=gjE2Kffq8Fk&t=2s  International Telecommunication Union The International Telecommunication Union (ITU) is a specialized agency of the United Nations (UN) responsible for many matters related to information and communication technologies.  Requirement on designers of a new satellite Designers of a new vehicle or satellite are frequently required by the ITU to demonstrate that it can be safely disposed of at the end of its life, for example by use of a controlled atmospheric reentry system or a boost into a graveyard orbit. – A graveyard orbit is an orbit that lies away from common operational orbits.  Summary Space debris (domain multi- disciplinarity) – Satellites (technology) – LOE (Science) – Applications (economics) – ITU requirement (legal)  Satellite flare Satellite flare is a satellite pass visible to the naked eye as a brief, bright “flare”. It is caused by the reflection toward Earth below of sunlight incident on satellite surfaces. Andreas Möller, CC BY-SA 3.0 DE, via Wikimedia Commons  Light pollution Streaks from satellite flare are a form of light pollution that can negatively affect ground-based astronomy. The Iridium constellation was one of the first anthropogenic sources of near-space light pollution to draw criticism. Larger satellite constellations, like Starlink, have received increased criticism.  Iridium satellite constellation Iridium Communications owns and operates the Iridium satellite constellation. Satellites are placed in LEO. The constellation consists of 66 active satellites in orbit, required for global coverage, and additional spare satellites to serve in case of failure.  Name Early calculations showed that 77 satellites would be needed, hence the name Iridium, after the metal with atomic number 77. It turned out that just 66 were required. Pumbaa (original work by Greg Robson), CC BY-SA 2.0 UK, via Wikimedia Commons  Reflective antennas The first-generation satellites were deployed in 1997–2002. Due to the shape of their reflective antennas, the satellites focused sunlight on a small area of Earth surface in an incidental manner. Cliff, CC BY 2.0, via Wikimedia Commons  Iridium flares Brocken Inaglory, CC BY-SA 3.0, via Wikimedia Commons This resulted in a phenomenon called Iridium flares, whereby the satellite momentarily appeared as one of the brightest objects in the night sky and could be seen even during daylight. This flashing caused some annoyance to astronomers, as the flares occasionally disturbed observations. https://www.youtube.com/watch?v=uymzXNdXwmo  New generation does not produce flares From 2017 to 2019 the satellites were replaced with a new generation that does not produce flares, with the first generation completely deorbited by 2019. This Photo by Unknown Author is licensed under CC BY-SA-NC  Summary Iridium flares (domain multi- disciplinarity) – Iridium Communications (economics) – LOE (science) – Satellite constellation (technology) – Satellite flare (environment)  Starlink Starlink is a satellite internet constellation operated by Starlink Services, LLC, a wholly owned subsidiary of SpaceX.  Satellite internet constellation It consists of over 6,000 mass- produced small satellites in LEO. Nearly 12,000 satellites are planned to be deployed, with a possible later extension to 34,400. This Photo by Unknown Author is licensed under CC BY  Small satellites This Photo by Unknown Author is licensed under CC BY Satellites can be built small to reduce the large economic cost of launch vehicles and the costs associated with construction. Miniature satellites, especially in large numbers, may be more useful than fewer, larger ones for radio relay. https://www.youtube.com/watch?v=veMts1Khido  De-orbit & avoid collisions Concerns have been raised about how the satellites will contribute to an already congested orbital environment. SpaceX has attempted to mitigate the concerns. The satellites are equipped with thrusters allowing them to de- orbit at the end of their lives. They are also designed to autonomously and smoothly avoid collisions based on uplinked tracking data.  Effect on astronomy Astronomers have raised concerns about the effect the constellation may have on ground-based astronomy. While astronomers can schedule observations to avoid pointing where satellites currently orbit, it is “getting more difficult” as more satellites come online. Egon Filter, CC BY 4.0, via Wikipedia  Reducing brightness This Photo by Unknown Author is licensed under CC BY SpaceX has attempted to mitigate astronomy concerns by implementing several upgrades to Starlink satellites aimed at reducing their brightness during operation. This Photo by Unknown Author is licensed under CC BY-ND Lecture 4 Outer space  Challenging environment Outer space (or simply space) is the expanse that exists beyond Earth’s atmosphere. It represents a challenging environment for human exploration because of the hazards of vacuum, temperature, and radiation. Weightlessness has a negative effect on human physiology.  Constitutes a near-perfect vacuum Outer space constitutes a near- perfect vacuum. The lack of pressure in space is the most immediate dangerous characteristic of space to humans.  Earth Earth is the only astronomical object known to harbor life.  Gravity The gravity of Earth is the acceleration that is imparted to objects due to the distribution of mass within Earth. Gravity decreases with altitude as one rises above Earth’s surface because greater altitude means greater distance from Earth’s centre. CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=269951  Atmosphere The atmosphere of Earth is composed of a layer of gas mixture that surrounds Earth’s surface, known collectively as air, all retained by Earth’s gravity.  Density Atmospheric density decreases as the altitude increases.  Pressure Atmospheric pressure is caused by the weight of air above the measurement point. As altitude increases, there is less overlying atmospheric mass, so atmospheric pressure decreases with increasing altitude.  Boiling point of water Water boils at 100 C at Earth’s standard atmospheric pressure. The boiling point is the temperature at which the vapour pressure is equal to the atmospheric pressure around the liquid. Because of this, the boiling point of liquids is lower at lower pressure. user:Markus Schweiss, CC BY-SA 3.0, via Wikimedia Commons  Armstrong limit The Armstrong limit is a measure of altitude above which atmospheric pressure is sufficiently low that water boils at the normal temperature of the human body. – The term is named after Harry George Armstrong, who was a major general in the United States Air Force, a physician, and an airman.  Exposed bodily liquids boil away On Earth, the limit is around 18– 19 km above sea level. At or above the Armstrong limit, exposed bodily liquids such as saliva, tears, and liquids in the lungs boil away. https://www.youtube.com/watch?v=7eX1XPhZz3M  Rupture of the lungs, etc. Out in space, sudden exposure of an unprotected human to very low pressure can cause a rupture of the lungs, due to the large pressure differential between inside and outside the chest. It can rupture eardrums and sinuses. https://www.youtube.com/watch?v=U1kEf5nh-TA&t=113s  Summary Outer space – Near-perfect vacuum Lack of pressure – Dangerous to humans  Lecture 4 – Part 2 Outer space (cont.) – Low temperature – Radiation  Outer space has a low temperature The baseline temperature of outer space is −270 C.  Sun The Sun is a sphere of hot plasma. – Plasma is a state of matter characterized by the presence of a significant portion of charged particles in any combination of ions or electrons. Roughly ¾ of the Sun’s mass consists of hydrogen; the rest is mostly helium.  Sunlight The Sun radiates energy from its surface mainly as light.  Earth’s atmosphere is a gas mixture The atmosphere of Earth is composed of a layer of gas mixture. – Dry air contains 78% nitrogen, 21% oxygen, 0.9% argon, 0.03% carbon dioxide (a greenhouse gas), and small amounts of other trace gases. – Air also contains a variable amount of water vapor (a greenhouse gas), on average around 1% at sea level, and 0.4% over the entire atmosphere.  Greenhouse gases Earth is warmed by sunlight, causing its surface to radiate heat, which is then mostly absorbed by greenhouse gases. A loose necktie, CC BY-SA 4.0, via Wikimedia Commons  Greenhouse effect The greenhouse effect occurs when greenhouse gases insulate Earth from losing heat to space, raising its surface temperature. Without the greenhouse effect, the Earth’s average surface temperature would be about −18 C, which is less than Earth’s average of about 15 C.  Summary Outer space – Low temperature Sunlight & Earth’s atmosphere – Greenhouse effect  Outer space is permeated by radiation Outer space is permeated by radiation. This includes electromagnetic radiation and particle radiation. Without the protection of Earth’s atmosphere and magnetic field astronauts are exposed to high levels of radiation.  Solar ultraviolet radiation Ultraviolet (UV) radiation is present in sunlight, and constitutes about 10% of the total electromagnetic radiation output from the Sun.  Electromagnetic radiation Electromagnetic radiation consists of waves. Shorter-wavelength electromagnetic radiation has more energy. UV light is electromagnetic radiation of wavelengths shorter than that of visible light, but longer than X-rays. This Photo by Unknown Author is licensed under CC BY-SA  Damages DNA Short-wave UV light damages DNA. For humans, suntan and sunburn are familiar effects of exposure of the skin to UV light, along with an increased risk of skin cancer. Onetwo1, CC BY-SA 3.0, via Wikimedia Commons  Filtered out by the atmosphere The amount of UV light produced by the Sun means that Earth would not be able to sustain life on dry land if most of that light were not filtered out by the atmosphere. Extremely short-wavelength UV is screened out by nitrogen.  Three categories UV radiation capable of penetrating nitrogen is divided into three categories, based on its wavelength; these are referred to as UV-A, UV-B, and UV-C.  UV-C UV-C, which is very harmful to all living things, is entirely screened out by a combination of ordinary oxygen and ozone.  Ozone-oxygen cycle Ozone in Earth’s atmosphere is created by UV light striking ordinary oxygen molecules containing two oxygen atoms (O2), splitting them into individual oxygen atoms; the atomic oxygen then combines with unbroken O2 to create ozone (O3). The ozone molecule is unstable and when UV light hits ozone it splits into a molecule of O2 and an individual atom of oxygen, a continuing process called the ozone-oxygen cycle.  Ozone layer The ozone layer is a region of Earth’s atmosphere that contains a high concentration of ozone in relation to other parts of the atmosphere, although still small in relation to other gases in the atmosphere.  Summary Ozone layer – Development of new manufactured chemicals to replace older ones (domain multi-disciplinarity) Manufactured chemicals (science, technology, economy) Ozone depletion (environment) Montreal protocol (legal)  UV-B The ozone layer is very effective at screening out UV-B. Nevertheless, some UV-B, particularly at its longest wavelengths, reaches the Vitamin D surface, and is important for the skin’s production of vitamin D in mammals.  UV-A Ozone is transparent to most UV- A, so most of this longer- wavelength UV radiation reaches the surface, and it constitutes most of the UV reaching the Earth. This type of UV radiation is significantly less harmful to DNA. This Photo by Unknown Author is licensed under CC BY-NC-ND  Summary Outer space – Solar UV radiation Earth’s atmosphere – filters out UV  Earth’s magnetic field Earth’s magnetic field extends from Earth’s interior out into space. It is approximately dipolar, with an axis that is nearly aligned with Earth’s rotational axis.  Earth’s liquid outer core The magnetic field is generated in Earth’s outer core. Earth’s outer core is a fluid layer composed of mostly iron and nickel that lies above Earth’s solid inner core.  Convection currents In the liquid outer core, there are convection currents due to heat escaping from the core. – Convection is the transfer of heat from one place to another due to the movement of fluid. User:Oni Lukos, CC BY-SA 3.0, via Wikimedia Commons  Earth’s rotation The overall planetary rotation tends to organize the flow into rolls aligned along the rotation axis. Andrew Z. Colvin, CC BY-SA 4.0, via Wikimedia Commons  Generation of the magnetic field Electric currents are created in the conductive iron alloys by the convection currents. Earth’s magnetic field is believed to be generated by the electric currents. – In an electromagnet, an electric current through a coil of wire creates a magnetic field. P.Sumanth Naik, CC BY-SA 3.0, via Wikimedia Commons  Magnetosphere The magnetosphere is defined by the extent of Earth’s magnetic field in space.  Protects Earth from the charged particles It protects Earth from the charged particles of the solar wind and cosmic rays that would otherwise strip away the upper atmosphere, including the ozone layer.  Solar wind The solar wind is a stream of charged particles released from the Sun’s outermost atmospheric layer, the corona. This plasma mostly consists of electrons, protons and helium nuclei. Earth’s magnetic field deflects most of the solar wind.  Van Allen radiation belts The Van Allen radiation belt is a zone of energetic charged particles that are captured by and held around Earth by the magnetosphere. Earth has two such belts. The belts are named after James Van Allen, who described the belts in 1958.  Charged particles held around Earth Some of the charged particles originate from the solar wind do get into the magnetosphere. They spiral around field lines, bouncing back and forth between the poles. The inner belt is mainly composed of protons; the outer belt consists mainly of electrons.  Summary Electromagnet – An electric current through a coil of wire creates a magnetic field. Van Allen radiation belts – Charged particles spiral around magnetic field lines.  Summary Outer space – Solar wind Earth’s magnetic field – Deflects most of the solar wind – Van Allen radiant belts  Summary Outer space – Low temperature – Radiation Solar UV radiation Solar wind Earth – Atmosphere – Magnetic field  Lecture 4 – Part 3 Outer space – Radiation (cont.) Cosmic rays – Weightlessness  Cosmic rays Earth’s magnetic field also deflects cosmic rays. Cosmic rays are high-energy particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light.  Two types Cosmic rays can be divided into two types: 1. Galactic cosmic rays and extragalactic cosmic rays 2. Solar energetic particles  Galactic/extragalactic cosmic rays The Sun is part of the Milky Way galaxy, which is one of many galaxies in the universe. Galactic cosmic rays and extragalactic cosmic rays are high-energy particles originating outside the Solar System. https://www.youtube.com/watch?v=MkRSmynqonM&t=270s  Supernova Ale RaFlo, CC BY-SA 4.0, via Wikimedia Commons A significant fraction of cosmic rays originate from the supernovae. The word supernova is derived from the Latin word nova, meaning ‘new’, which refers to what appears to be a temporary new bright star. – Supernovae are relatively rare events within a galaxy, occurring about three times a century in the Milky Way. NASA/ESA, CC BY-SA 3.0, via Wikimedia Commons  Powerful & luminous explosion of a star A supernova is a powerful and luminous explosion of a star. https://www.youtube.com/watch?v=aysiMbgml5g  Solar energetic particles Solar energetic particles are high- energy, charged particles originating in the solar atmosphere and solar wind. They become accelerated either in the Sun’s atmosphere during a solar flare or in interplanetary space by a coronal mass ejection.  Solar flare A solar flare is a relatively intense, localized emission (eruption) of electromagnetic radiation in the Sun’s atmosphere. https://www.youtube.com/watch?v=TujfLt9HETQ  Coronal mass ejection Image Editor, CC BY 2.0, via Wikimedia Commons A coronal mass ejection (CME) is a significant ejection (eruption) of plasma mass from the Sun’s corona. https://www.youtube.com/shorts/FusXBvPuyDE  Summary Outer space – Radiation Solar UV radiation Solar wind Cosmic rays  Ionizing radiation Outer space is permeated by radiation. Radiation is often categorized as either ionizing or non-ionizing. Ionizing radiation consists of particles or electromagnetic waves that have sufficient energy to ionize atoms or molecules by This Photo by Unknown Author is licensed under CC BY detaching electrons from them.  Health hazard Ionizing radiation presents a health hazard. Exposure to ionizing radiation causes cell damage to living tissue and organ damage. In high acute doses, it will result in radiation burns and radiation sickness, and lower level doses over a protracted time can cause cancer.  Weight The weight of an object on Earth’s surface is the downwards force on that object, given by Newton’s second law, or 𝐹 = 𝑚𝑔 where 𝑔 is the acceleration that is imparted to objects due to the effect of gravitation.  Contact force A person standing still on a platform is acted upon by gravity, which would pull him down towards the Earth’s core unless there were a countervailing force from the resistance of the platform’s molecules, a force which is named the “normal force”.  Weight-sensations The weight-sensations originate from contact with supporting floors, seats, beds, scales, and the like. A sensation of weight is produced when contact forces act upon a body.  Free fall Free fall is any motion of a body where gravity is the only force acting upon it.  Astronaut in orbit An astronaut in orbit is in free fall. – He is subject to only the force of gravity. – His orbital speed keeps him in orbit.  Weightlessness When there are no other forces, such as the normal force exerted between the astronaut and his surrounding objects, it will result in the sensation of weightlessness. – When viewed from an orbiting observer, other close objects in space appear to be floating because everything is also in free fall.  Deleterious effects on human health OpenStax, CC BY 4.0, via Wikimedia Commons Humans evolved for life in Earth gravity, and exposure to weightlessness has been shown to have deleterious effects on human health. The most significant adverse effects of long-term weightlessness are muscle atrophy and deterioration of the skeleton, or spaceflight osteopenia. Laboratoires Servier, CC BY-SA 3.0, via Wikimedia Commons  Outer space is a challenging environment Outer space represents a challenging environment for human exploration because of the hazards of vacuum, temperature, and radiation. Weightlessness has a negative effect on human physiology.  Spacecraft & spacesuit Technology such as that offered by a spacecraft or spacesuit is able to shield people from the harshest conditions. The life support system supplies air. It must also maintain temperature and pressure within acceptable limits. Askeuhd, CC BY-SA 4.0, via Wikimedia Commons  Shielding against radiation Shielding against radiation is also necessary. – Alpha () radiation consists of a fast-moving helium nucleus and is stopped by a sheet of paper. – Beta () radiation, consisting of electrons, is halted by an aluminum plate. – Gamma () radiation, consisting of energetic electromagnetic radiation, is eventually absorbed as it penetrates a dense material. Anynobody~commonswiki, CC BY-SA 4.0, via Wikimedia Commons  Regimen of exercise Muscle atrophy and spaceflight osteopenia can be minimized through a regimen of exercise.  Summary Outer space & Earth (Scientific inter-disciplinarity) – Outer space represents a challenging environment for human exploration (physics, biology) – Earth harbors life (geology) – Technology  Summary Starlink (domain multi- disciplinarity) – SpaceX (economics) – LEO (science) – Satellite constellation (technology) – Satellite flare (environment) Lecture 5 Solar System  Gravitationally bound system The Solar System is the gravitationally bound system of the Sun and the objects that orbit it.  Outline Solar System (observation) – Sun – Planets – Moons Efbrazil, CC BY-SA 4.0, via Wikimedia Commons  Sun The Sun is at the center of the Solar System. It is a nearly perfect sphere of hot plasma. Roughly ¾ of the Sun’s mass consists of hydrogen; the rest is mostly helium, with much smaller quantities of heavier elements. Matúš Motlo, CC BY-SA 4.0, via Wikimedia Commons  Large mass The Sun is by far the Solar System’s most massive component. Its mass comprises 99.86% of all the mass in the Solar System. CactiStaccingCrane, CC BY-SA 4.0, via Wikimedia Commons  Nuclear fusion of hydrogen into helium Its large mass produces temperatures and densities in its core high enough to sustain nuclear fusion of hydrogen into helium.  Releases an enormous amount of energy This releases an enormous amount of energy, mostly radiated into space as electromagnetic radiation.  Planets The planets in orbit around the Sun lie near the plane of Earth’s orbit. Planets orbit the Sun in the same direction. https://youtu.be/z8aBZZnv6y8  Mercury Mercury is the first planet from the Sun. The surface of Mercury is heavily cratered.  Venus Venus is the second planet from the Sun. Venus is notable for having a dense atmosphere with a thick, global cloud cover. The surface has been mapped in detail by using radar. The ground shows evidence of extensive volcanism.  Earth Earth is the third planet from the Sun. Earth is an ocean world, the only one in the Solar System sustaining liquid surface water. Earth has an atmosphere.  Mars Mars is the fourth planet from the Sun. Its surface is peppered with volcanoes and rift valleys. The polar regions are covered in white ice caps. Mars has a thin atmosphere. Kevin Gill from Los Angeles, CA, United States, CC BY 2.0, via Wikimedia Commons  Terrestrial planets The four terrestrial or inner planets have dense, rocky compositions. The term “terrestrial planet” is derived from Latin word for Earth (Terra), as these planets are, in terms of structure, Earth-like. CactiStaccingCrane, CC BY-SA 4.0, via Wikimedia Commons  Jupiter Jupiter is the fifth planet from the Sun. The outer atmosphere is divided into a series of latitudinal bands, with turbulence and storms along their interacting boundaries; the most obvious result of this is the Great Red Spot, a giant storm. https://youtu.be/rHwkdcppsuo  Saturn Saturn is the sixth planet from the Sun. Saturn’s atmosphere exhibits a banded pattern similar to Jupiter’s, but Saturn’s bands are much fainter. The planet has a bright and extensive system of rings.  Uranus Uranus is the seventh planet from the Sun. It is a gaseous cyan-coloured planet. – The third-most-abundant component of Uranus’ atmosphere is methane. Methane has prominent absorption bands in the red light, making Uranus cyan in colour.  Neptune Neptune is the eighth and farthest known planet from the Sun. In contrast to the featureless atmosphere of Uranus, Neptune’s atmosphere has active and consistently visible weather patterns.  Giant planets The four outer planets are called giant planets. A giant planet is a diverse type of planet much larger than Earth. CactiStaccingCrane, CC BY-SA 4.0, via Wikimedia Commons  Jupiter & Saturn are gas giants Jupiter and Saturn are gas giants. A gas giant is a giant planet composed mainly of hydrogen and helium.  Uranus & Neptune are ice giants Uranus and Neptune are ice giants. An ice giant is a giant planet significantly composed of “ice”. – The term “ice” refers to volatile chemical compounds, such as water, ammonia, or methane. Like the gas giants, the ice giants also have hydrogen and helium envelopes, but these are much smaller.  Summary Solar system (observation) – Sun – Planets  Lecture 5 – Part 2 Solar system (cont.) – Moons (observation) Saturn’s rings – Dwarf planets & small bodies (observation) – Formation Nebular hypothesis Efbrazil, CC BY-SA 4.0, via Wikimedia Commons  Moons Most of the planets in the Solar System have secondary systems of their own, being orbited by natural satellites called moons.  Earth’s moon The Moon is Earth’s only natural satellite. The lunar surface is marked by impact craters and, mostly on the near side of the Moon, by dark maria (“seas”), which are plains of cooled magma. These maria were formed when molten lava flowed into ancient impact basins. Gregory H. Revera, CC BY-SA 3.0, via Wikimedia Commons  Jupiter’s moons Jupiter has 95 known moons. The four moons discovered by Galileo Galilei are the largest moons. Io is primarily composed of Jan Sandberg, Attribution, via Wikimedia Commons silicate rock; Europa, Ganymede, and Callisto have a thick coating of ice.  Saturn’s moons This Photo by Unknown Author is licensed under CC BY-SA-NC Saturn has 146 known moons. Seven moons are large enough to have a spherical shape. Titan, Saturn’s largest moon, is the only moon in the Solar System that has a substantial atmosphere. This Photo by Unknown Author is licensed under CC BY  Saturn’s rings The rings of Saturn consist of countless small particles that orbit around Saturn.  Dwarf planets & small bodies The Solar System has dwarf planets and a vast number of small bodies. A dwarf planet is a small body that is large enough to have a spherical shape.  Asteroid belt The asteroid belt is a torus- shaped region, roughly spanning the space between the orbits of Jupiter and Mars. It contains a great many bodies called asteroids.  Asteroids Asteroids are rocky, metallic, or icy bodies. The largest are roughly spherical. The vast majority, however, are much smaller and are irregularly shaped. Kwamikagami, CC BY-SA 4.0, via Wikimedia Commons  Ceres Ceres is smaller than Earth’s moon. It is the largest asteroid and a dwarf planet.  Trans-Neptunian region Beyond the orbit of Neptune lies the area of the “trans- Neptunian region”, with the Kuiper belt and an overlapping disc of scattered objects, which reaches much further out than the Kuiper belt. The entire region is still largely unexplored. It appears to consist overwhelmingly of many thousands of small worlds composed mainly of rock and ice.  Kuiper belt The Kuiper belt is similar to the asteroid belt, but is far larger.  Pluto Pluto is smaller than Earth’s moon. It is a dwarf planet in the Kuiper belt. It is the largest known trans- Neptunian object by volume.  Summary Regions containing many small bodies – Asteroid belt – Kuiper belt  Summary Ceres – Largest body in the asteroid belt Pluto – Largest body in the Kuiper belt  Haumea, Makemake, Quaoar, & Orcus Other objects that astronomers generally accept as dwarf planets are Haumea, Makemake, Quaoar, and Orcus.  Scattered disc The scattered-disc objects have high orbital eccentricities and inclinations. These extreme orbits are thought to be the result of gravitational “scattering” by the gas giants, and the objects continue to be subject to perturbation by the planet Neptune. User: Orionist, CC BY-SA 3.0, via Wikimedia Commons  Eris & Gonggong Eris is the largest known scattered disc object and the most massive of the known dwarf planets. Gonggong is also a dwarf planet.  Extreme trans-Neptunian objects Some objects in the Solar System have a very large orbit. These bodies are called extreme trans-Neptunian objects. Tomruen, CC BY-SA 4.0, via Wikimedia Commons  Sedna Sedna was the first extreme trans-Neptunian object to be discovered. Sedna is classified as a dwarf planet. It is a large object.  Formation of the Solar System Since the 17th century, scientists have been forming hypotheses concerning the origins of our Solar System. In the 20th century, a variety of hypotheses began to build up.  Nebular hypothesis The nebular hypothesis is the most widely accepted model to explain the formation of the Solar System. – The word nebula is derived from the Latin word for ‘cloud’.  Presolar nebula The nebular hypothesis says that the Solar System formed from the gravitational collapse of a giant cloud.  Mass & composition The composition of this region with a mass just over that of the Sun was about the same as that of the Sun today, with hydrogen, along with helium, forming about 98% of its mass. The remaining 2% of the mass consisted of heavier elements.  Spun faster as it collapsed The nebula spun faster as it collapsed. – It is because of the conservation of angular momentum. https://www.youtube.com/watch?v=64t-dVtDwkQ  Center became increasingly hotter As the material within the nebula condensed, the temperature rose. – The gravitational potential energy was converted into heat. The center, where most of the mass collected, became increasingly hotter than the surrounding.  Protoplanetary disc & protosun The competing forces of gravity and rotation caused the contracting nebula to flatten into a spinning protoplanetary disc and form a hot, dense protosun at the centre. – Centrifugal force is directed radially away from the axis of rotation.  Sun Later, the temperature and density at the core of the Sun became so great that its hydrogen began to fuse, creating an internal source of energy.  Accretion The various planets are thought to have formed from the protoplanetary disc. The currently accepted method by which the planets formed is accretion, in which the planets began as dust grains in orbit around the central protosun.  Planetesimals Through direct contact and self-organization, these grains formed into clumps up, which in turn collided to form larger bodies (planetesimals).  Rocky planetesimals The inner Solar System was too warm for volatile molecules to condense, so the planetesimals that formed there could only form from compounds with high melting points, such as metals and rocky silicates.  Icy planetesimals Beyond the frost line, which is the point between the orbits of Mars and Jupiter, the material is cool enough for volatile icy compounds to remain solid.  Giant planets These icy bodies would become the giant planets. The ices were abundant, allowing the giant planets to grow massive enough to capture hydrogen and helium.  Solar wind The young Sun had a strong solar wind.  Cleared away all the gas and dust The solar wind cleared away all the gas and dust in the protoplanetary disc, blowing it into interstellar space, thus ending the growth of the planets.  Gas giants & ice giants Uranus and Neptune are thought to have formed after Jupiter and Saturn did, when the strong solar wind had blown away much of the disc material. As a result, those planets accumulated little hydrogen and helium.  Protoplanets At the end of the planetary formation epoch the inner Solar System was populated by protoplanets.  Collided & merged These bodies collided and merged.  Terrestrial planets They grew larger until the four terrestrial planets took shape. CactiStaccingCrane, CC BY-SA 4.0, via Wikimedia Commons  Small planets Metals and rocky silicates were quite rare in the presolar nebula, so the terrestrial planets could not grow very large. CactiStaccingCrane, CC BY-SA 4.0, via Wikimedia Commons  Asteroid belt The outer edge of the terrestrial region is the asteroid belt. The asteroid belt formed as a group of planetesimals. Gravitational perturbations from Jupiter disrupted their accretion into a planet.  Ceres Ceres is a surviving protoplanet.  Trans-Neptunian region Beyond Neptune, the Solar System continues into the trans- Neptunian region, a sparse population of icy planetesimals. At its distance from the Sun, initial disc lacked enough mass density to consolidate into a planet.  Pluto, etc. Trans-Neptunian dwarf planets have also been referred to as protoplanets.  Summary Pluto – Trans-Neptunian object (observation) – Protoplanet Nebular hypothesis  Moons The moons that exist around most planets originated by one of a few possible mechanisms.  Earth’s moon Earth’s moon is thought to have formed as a result of a single, large head-on collision. The impact was probably the last in the series of mergers that formed the Earth. The collision kicked into orbit some of the impactor’s mantle, which then coalesced into the Moon. This Photo by Unknown Author is licensed under CC BY-SA  Moons of Jupiter & Saturn Jan Sandberg, Attribution, via Wikimedia Commons The large moons of Jupiter and Saturn may have originated from discs around each giant planet in much the same way that the planets formed from the disc around the Sun. This Photo by Unknown Author is licensed under CC BY-SA-NC  Saturn’s rings There are two main theories regarding the origin of Saturn’s rings. 1. The rings were once a moon of Saturn. This moon disintegrated. 2. The rings are left over from the original nebular material from which Saturn formed.  Summary Solar system – Sun, planets, moons, dwarf planets, small bodies (observation) – Formation Nebular hypothesis Efbrazil, CC BY-SA 4.0, via Wikimedia Commons