The Solar System PDF

The Solar System By: Muhammad Afzal Alvi Learning Outcomes By the conclusion of this chapter, you should be able to: Explain modern view of the solar system. Describe the composition and internal structure of the Sun and its surface features. Identify nuclear fusion as the s...

The Solar System By: Muhammad Afzal Alvi Learning Outcomes By the conclusion of this chapter, you should be able to: Explain modern view of the solar system. Describe the composition and internal structure of the Sun and its surface features. Identify nuclear fusion as the source of the Sun’s energy, and describe how that energy travels from the core to the surface. Outlines the properties of Sun and other stars. Explain how gravity holds planets in orbits around the Sun. A Survey of the Solar System Our solar system currently consists of the Sun, eight planets, five dwarf planets, nearly 200 known moons, and a host of smaller objects. The inner planets called the terrestrial planets.— Mercury, Venus, Earth and Mars They have weak magnetic fields; Venus and Mars do not. Earth and Mars have moons; Venus and Mercury do not. The terrestrial planets are small, and solid with iron cores. The inner, terrestrial planets have high densities and moderate atmospheres.  The outer worlds called Jovian planets. They are also known as gas giants. Two gas giants -Jupiter and Saturn Two ice giants -Uranus and Neptune The Jovian planets have many moons each and all have rings, a feature unknown on the terrestrial planets. The Jovian planets rotate more rapidly, and have stronger magnetic fields. The Jovian planets are larger and more massive, and have no solid surfaces. The Jovian planets, have low densities and thick atmospheres.  The orbits of the planets are nearly circular and in one plane. Apart from Mercury. In order of distance from the Sun Dwarf planets are: Ceres, Pluto, Haumea, Makemake, and Eris. Ceres is the only dwarf planet in the asteroid belt. The rest are beyond Neptune in the Kuiper Belt. The Sun rotates counterclockwise on its axis, planets also orbit the Sun counterclockwise as viewed from above Earth’s North Pole. A planet revolves around the Sun but rotates on its axis.  The asteroids, or “minor planets,” orbit in a broad band called the asteroid belt which lies between the orbits of Mars and Jupiter. The Kuiper belt is a band of icy bodies orbiting beyond the orbit of Neptune. Comets, meteoroids, and asteroids are other important objects in the solar system. 99.80% of the Solar System's mass is in the Sun and nearly 90% of the remaining mass are in Jupiter and Saturn. The Solar System developed 4.6 billion years ago. Comets and meteoroids A comet is a small body of ice, dust and rocky matter that revolves about the Sun in its own elliptical orbit. When a comet comes near the Sun, some of its material vaporizes, forming a large head of tenuous gas and a tail. Sometime comets break up after they have passed close to the Sun many times. These pieces of dust, rock or metallic body along with those derived from other sources in outer space, are called meteoroids. N.B. If the size of meteoroid is larger than 1 m in diameter then it is called asteroid. A comet consists of a nucleus, a coma, a dust tail, and an ion tail. Meteor Sometimes the path of a meteoroid crosses the position of Earth, and it enters Earth’s atmosphere at varying speed of 15 km/s to 70 km/s. Most meteoroids are so small that they completely burn up in Earth’s atmosphere. A meteoroid that burns up in Earth’sAburns meteoroid that up in Earth’s atmosphere is atmosphere is called a meteor, called a meteor. A meteor is the streak of light shown in Figure 19. Meteorites When a meteoroid is large enough, it might not burn up completely in the atmosphere. If it strikes Earth, it is called a meteorite. Meteorites occasionally strike Earth’s surface. A large meteorite struck Arizona, about 50,000 years ago, forming a crater about 1.2 km in diameter and about 200 m deep.  Asteroids An asteroid is a piece of rock (size 1m to 1000 km) similar to the material that formed into the planets. Most asteroids are located in an area between the orbits of Mars and Jupiter The asteroid belt lies called the asteroid belt. between the orbits of Other asteroids are scattered throughout the solar system. Mars and Jupiter. They might have been thrown out of the belt by Jupiter’s gravity. The total mass of all the asteroids combined is less than that of Earth's Moon. Some of these asteroids have orbits that cross Earth’s orbit. Scientists continuously monitor asteroids, whose paths intersect Earth's orbit. However, it is unlikely that an asteroid will hit Earth in near future. Mass of members of the Solar System: Question Which two planets have no moons? Mercury and Venus. Kepler’s First Law of Planetary Motion Kepler’s first law of planetary motion has to do with the shapes of the planetary orbits: This law is also called the “Law of orbits”. Kepler’s first law: Each planet moves around the Sun in an orbit that is an ellipse, with the Sun at one focus of the ellipse. FIGURE Ellipse An ellipse can be drawn with the aid of a string, a pencil, and two thumbtacks. Kepler’s Second Law of Planetary Motion The second law addresses the speed at which a planet traverses different parts of its orbit: This law is also called the “Law of Equal Areas”. Kepler’s second law: The straight line joining a planet and the Sun sweeps out equal areas of ellipse in equal A line joining a planet to the Sun sweeps out equal areas in equal intervals of time. intervals of time. The three shaded regions A, B, and C are equal in area. Kepler’s Third Law of Planetary Motion Kepler’s Third Law tells us that planets on larger orbits take longer to complete one trip around the Sun. This law is also called the “Law of Periods”. Kepler’s third law: The square of a planet’s orbital period is directly proportional to the cube of the semi-major axis of its orbit. Kepler’s Third Law of Planetary Motion P^2 ∝ a^3 P^2 = ka^3 Where k is some constant number. We find k = 1. When we measure ‘P’ in year and ‘a’ in A.U. are used: P^2 = a^3 Question An asteroid is found and its orbital semi-major axis around the Sun is measured to be 4 A.U. What is the period of its orbit round the Sun? Solution: P^2 = a^3 with P in years and a in A.U. Since a = 4 A.U, P^2 = a^3 = (4)3 = 64. So P = 8 years. Newton’s law of gravitation The force of gravitational attraction between two masses, M and m, is proportional to the product of the masses and inversely proportional to the square of the distance between them. The constant G is the gravitational constant, r is the distance between the masses from their centres. The negative sign means that the force is attractive.  Gravity The surface gravity of any large, spherical body such as a moon or planet is the acceleration due to gravity on that body.  Question: Ganymede is the largest moon in the solar system, with a mass of 1.48×10^23 kg and a radius of Ganymede 2630 km. What is the surface gravity on Ganymede? Give your answer to two decimal places.  Orbital Velocity or Circular Velocity In this formula, M is the mass of the central body (Earth in this case) in kilograms, r is the radius of the orbit in meters, and G is the gravitational constant, 6.67 x 10 ^- 11 N m^2/kg^2.  Question How fast does the Moon travel in its orbit? Earth’s mass is 5.97 x 10 ^24 kg, and the radius of the Moon’s orbit is 3.84 x 10 ^ 8 m. Therefore, the Moon’s orbital velocity is:  Calculating Escape Velocity Escape velocity is a fundamental concept in astrophysics and aerospace engineering, crucial for understanding the mechanics of space travel and celestial mechanics. Escape velocity is the minimum speed an object must reach to break free from the gravitational pull of a body without further propulsion. Escape velocity, Ve , is given by a simple formula:  k.e. = g.p.e 1/2mv2 = GMm/r mv2 = 2GMm/r v2 = 2GM/r v = (2GM/r)1/2 In this formula, M is the mass of the central body (Earth in this case) in kilograms, r is the radius of the orbit in meters, and G is the gravitational constant, 6.67 x 10 ^- 11 N m^2/kg^2. (Notice that this formula is similar to the formula for circular velocity; in fact, the escape velocity is square root of 2 times the circular velocity.  Application of Escape velocity Space Travel: To determine the initial speed required for spacecraft to leave a planet or moon. Astrophysics: To understand the behavior of celestial objects, like the conditions necessary for an atmosphere to remain bound to a planet. Planetary Science: To study the gravitational fields of planets and moons, which is crucial for landing and takeoff of space missions. Question You can find the escape velocity from Earth by again using its mass, 5.97 x 10 ^24 kg , and the value of Earth’s average radius, 6.37 x 10 ^6 m. The escape velocity from Earth’s surface is: How the Solar System Formed? We believe that the solar system was formed from a nebula. A nebula is a large cloud of gas and dust in space The cloud started collapsing under its own gravity. The cloud began to rotate and formed into a disk. As it contracted, its temperature and pressure increased. As nuclear fusion reaction began at its center and the Sun was born. N.B. As the cloud continues to contract, the conservation of angular momentum accelerates the rotation, just as the skater who brings her arms in close will send herself into a dazzling spin.  Fusion of nuclei lighter than iron into heavier ones – this is called Nuclear fusion reaction. Splitting/breaking of nuclei heavier than iron into lighter ones – this is called Nuclear fission reaction. In order to make nuclear fusion reaction occur, the mutual repulsion of nuclei must be overcome, and this requires ✓very high temperatures (approximately 15 million K) and ✓very high density of matter.  If the temperature of a star drops, the outward pressure will also decrease. This will cause the star to contract. If the temperature of a star increases, the outward pressure will also increase. This will cause the star to expand. If gravity were not balanced by pressure, the Sun would collapse. If pressure were not balanced by gravity, the Sun would blow itself apart.  Hydrostatic Equilibrium Gravity wants to collapse the Star, and pressure, wants to blow it apart. Figure The structure of the Sun is determined by The structure of the Sun is a the balance between the result of balance between the forces of pressure and gravity and the balance between the outward force of pressure and energy generated in its core and the energy radiated the inward force of gravity: this from its surface. balance is known as hydrostatic equilibrium.  The Sun Is Stable. The Sun, like the majority of other stars, is stable; it is neither expanding nor contracting. In the interior of a star such as the Sun, the outward push of pressure of hot gas balances the inward pull of gravity. This is true at every point within the star, guaranteeing its stability. Some of the basic characteristics of the Sun are listed in Table. Intensity : The amount of solar energy reaching surface area of 1 square meter each second is a quantity known as intensity. I = E/tA = P/A ; (W/m2). It’s value is 1370 ~ 1400 watts per square meter (W/m2). This value is known as the Solar Constant. Luminosity: Luminosity—The total amount of energy emitted per second is called Luminosity or radiant power. The luminosity of a star is a measure of how bright it really is and is expressed in watts. Its value is independent of an observer’s distance. The power radiated by a black body (Sun or any other star) per unit surface area is σT4 To calculate the total luminosity of a star multiply σT4 with surface area = 4πR2  According to the Stefan-Boltzmann law, the luminosity (L) of a star is proportional to its surface area (A) and the fourth power of its absolute temperature (T), L = A × σ × T4 L = 4πR2 σT4 It means luminosity of a star depends on The size of the star: The temperature of the star: Where σ = 5.67 x 10^-8 W/m^2 K^4, is the Stefan-Boltzmann constant. Lsun = 3.9 x 1026 W We use the symbol Lsun to denote the Sun’s luminosity; hence, that of Sirius can be written as 25 Lsun. Q. What properties determine the intrinsic power output or luminosity of a star? A. Temperature and size of the star Q. If two stars A and B have the same effective temperature but one is larger than the other then what is the radiated power per unit area? A. same, and is equal to σT4 Q. If two stars A and B have the same effective temperature but one is larger than the other then which star has greater luminosity? A. Star B; because it has greater surface area The Brightness of light depends on the Luminosity and distance of the light source. The amount of a star’s energy that reaches per unit area per second here on Earth its apparent brightness or just brightness. It’s unit is W/m2. Brightness depends on luminosity and distance of the light source. Brightness (B) = Luminosity (L) /4πd2 The apparent brightness of a star observed from the Earth is called the apparent magnitude. If the star was at a distance of 10 parsecs (32.6 light years )from us, then its apparent magnitude would be equal to its absolute magnitude.  m = apparent magnitude M = absolute magnitude d = distance measured in parsecs (pc) https://shiken.ai/physics/absolute-magnitude To get values for d, "un-log" (d), or "10 to the power of ------------". Apparent Brightness Question: A Cepheid has an apparent magnitude of +15.2. For a star with its pulsation period it should have an absolute magnitude of -4.2. How far away is it? Solution: m - M = -5 + 5 log (d) 15.2 - (-4.2) = -5 + 5 log (d) 15.2 + 4.2 = -5 + 5 log (d) 19.4 = -5 + 5 log (d) 19.4 + 5 = 5 log (d) 24.4/5 = log (d) 4.88 = log (d) To "un-log" (d), take 10 to the power of 4.88 d = 10 4.88 = 75,857.76 pc Question: A type II supernova just went off in the Andromeda galaxy. These supernova usually reach an absolute magnitude of around -17 when they are their brightest. The Andromeda galaxy is 730,000 pc away. How bright will the supernova be in the night sky (or what is its apparent magnitude)? Solution: m - M = -5 + 5 log (d) m - (-17) = -5 + 5 log (730,000) m + 17 = -5 + 5 x 5.86 (the log of 730,000 = 5.86) m + 17 = -5 + 29.3 m + 17 = 24.3 m = 24.3 - 17 m = 7.3 Composition of the Sun’s Atmosphere What the solar atmosphere is made of? About 73% of the Sun’s mass is hydrogen, and another 25% is helium. All the other chemical elements (such as carbon, oxygen, and nitrogen) make up only 2% of our star. In fact, the Sun is so hot that many of the atoms in it are ionized, that is, a large quantity of free electrons and positively charged ions in the Sun, making it an electrically charged environment—(Scientists call such a hot ionized gas a plasma. Plasma is a fully or partially ionized gas.) The Sun—An Average Star The Sun is an average star. It is middle-aged, It shines with a yellow light. The Sun is unusual in one way. It is not close to any other stars. Most stars are part of a system in which two or more stars orbit each other. When two stars orbit each other, it is called a binary system. When three stars orbit each other, it is called a triple star system.  The Sun: A Nuclear Powerhouse The fusion process occurs in the Sun and in all main sequence stars, is that hydrogen atoms fuse to form helium. At the same time lots of gamma-photons γ and electron-neutrinos νe are produced. Parts of the Sun: This illustration shows the different parts of the Sun, from the hot core where the energy is generated. The Sun’s Layers The Sun’s interior has layers that include the core, radiative zone, and convective zone. The Sun’s Atmosphere The Sun’s atmosphere includes the photosphere, chromosphere, and corona.  Above the core is a region known as the radiative zone. The light generated in the core is transported through the radiative zone very slowly, since the high density of matter in this region. The convective zone is the outermost layer of the solar interior. The plasma at the bottom of the convective zone is extremely hot, and it bubbles to the surface where it loses its heat to space. Once the plasma cools, it sinks back to the bottom of the convective zone. The Atmosphere of the Sun Beyond the convective zone lie the outer layers of the Sun, which are collectively known as the Sun’s atmosphere. These layers, shown in Figure , include the photosphere, the chromosphere, and the corona. We can observe these layers of the Sun directly using telescopes and satellites.  The Photosphere The effective temperature of the photosphere is calculated from the Sun’s luminosity and radius using the Stefan-Boltzmann law. The photosphere has an effective temperature of 5780 K ~ 5800 K. Above the photosphere is the chromosphere. Corona is the largest layer of the Sun’s atmosphere and extends millions of kilometers into space. Temperatures in the corona are as high as 2 million K.  Charged particles (mainly protons and electrons) continually escape from the corona and move through space as solar wind. These particles flow outward from the Sun into the solar system at a speed of about 400 kilometers per second. (i.e. with this high speed that they cannot be held back by solar gravity). At the surface of Earth, we are protected to some degree from the solar wind by our atmosphere and Earth’s magnetic field.  The magnetic field lines come into Earth at the north and south magnetic poles. Here, charged particles can follow the field down into our atmosphere. As the particles strike molecules of air, they cause them to glow, producing beautiful curtains of light called the auroras, or the northern and southern lights (Figure). Produce auroras and can disrupt power grids and damage satellites. Surface Features Sun’s surface has many features, including sunspots, prominences, flares, and CMEs. Areas of the Sun’s surface that appear dark because they are cooler than surrounding areas are called sunspots. Sunspot usually consists of two parts: an inner darker core, the umbra, and a surrounding less dark region, the penumbra. Many spots become much larger than Earth. Like storms on Earth, sunspots are not fixed in position.  Sunspots Sunspots are caused by increased magnetic activity. Dark regions called umbra is at a temperature of about 3800 K, whereas the bright regions that surround them are at about 5800 K. Sunspots aren’t permanent features on the Sun. They appear and disappear over a period of several days, weeks, or months. The number of sunspots increases and decreases in a fairly regular pattern called the sunspot, or solar activity, cycle.  The differential rotation of the Sun: Sun doesn’t rotate as a solid body, as Earth does. It rotates faster at its equator than at its poles. Sunspots at the equator take about 25 days to complete one rotation. Near the poles, they take about 35 days. This is known as differential rotation. Prominences and Solar Flares: Sunspots are related to several features on the Sun’s surface. The intense magnetic fields associated with sunspots might cause prominences, which are huge, arching columns of gas. Some prominences blast material from the Sun into space at speeds ranging from 600 km/s to more than 1,000 km/s. Gases near a sunspot sometimes brighten suddenly, shooting outward at high speed. These violent eruptions are called solar flares. You can see a solar flare in Figure. Prominences and Solar Flares: The End