PROPERTIES-OF-PLANETS-PART-1.pdf

Properties of Planets PROPERTIES 1 Orbit 2 Mass 3 Size 4 Rotation 5 Shape 6 Temperature 7 Magnetic Field 8 Surface Composition 9 Surface Structure 10 Atmosphere 11 Interior Orbit Geometry Credits: Cosmic Perspective 8th Edition ...

Properties of Planets PROPERTIES 1 Orbit 2 Mass 3 Size 4 Rotation 5 Shape 6 Temperature 7 Magnetic Field 8 Surface Composition 9 Surface Structure 10 Atmosphere 11 Interior Orbit Geometry Credits: Cosmic Perspective 8th Edition  Orbit In the early part of the seventeenth century, Johannes Kepler deduced three ‘laws’ of planetary motion directly from observations: (1) All planets move along elliptical paths with the Sun at one focus. Law of Ellipses (2) A line segment connecting any given planet, and the Sun sweeps out area at a constant rate. Law of Equal Areas (3) The square of a planet’s orbital period about the Sun, Porb , is proportional to the This Photo by Unknown Author is licensed under CC BY-SA cube of its semimajor axis. Law of Periods A Keplerian orbit is uniquely specified by six orbital elements: a (semimajor axis) – AU (Astronomical Unit) e (eccentricity) e = 0 (circle), bet 0 & 1 (ellipse), = 1 (parabola), > 1 (hyperbola) i (inclination) – tilt of the orbit (argument of periapse) or (longitude of periapse) (longitude of ascending node) f or (true anomaly)  By Lasunncty at the English Wikipedia, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=8971052 a and e fully define the size and shape of the orbit, i gives the tilt of the orbital plane to some reference plane, the longitudes and determine the orientation of the orbit and f tells where the planet is along its orbit at a given time. Alternative sets of orbital elements are also possible; for instance, an orbit is fully specified by the planet’s location and velocity relative to the Sun at a given time (again, six independent quantities), provided the masses of the Sun and planet are known. **The Titius-Bode Rule The Titius-Bode rule generates a series of numbers that appear to match the average distances of the planets from the Sun expressed in astronomical units. The rule was published in 1772 by two German astronomers named Johann Daniel Titius and Johann Elert Bode. The actual distances of the planets (i.e. the average radii of their orbits) are compared to the Titius-Bode predictions The procedure for generating this series of numbers is: 1. Write a string of numbers starting with zero: 0, 3, 6, 12, 24, 48, 96, 192, 384, 768… 2. Add 4 to each number and divide by 10. 3. The result is: 0.4, 0.7, 1.0, 1.6, 2.8, 5.2, 10.0, 19.6, 38.8, and 77.2. AU The Titius-Bode rule predicted the existence of a planet* at a distance of 2.8 AU from the Sun between the orbits of Mars and Jupiter.  The good agreement between the predicted and observed solar distances of the inner planets in suggests that they formed by a process that caused the spacing of their orbits to follow a pattern that is duplicated by the Titius-Bode rule. However, the rule does not identify this process. The discrepancies between the actual radii of the orbits of Uranus, Neptune, and Pluto and their radii predicted by the Titius-Bode rule may indicate that the orbits of these planets were altered after their formation.  All planets and asteroids revolve around the Sun in the direction of solar rotation. Their orbital planes generally lie within a few degrees of each other and close to the solar equator. For observational convenience, inclinations are usually measured relative to the Earth’s orbital plane, which is known as the ecliptic plane. The Sun’s equatorial plane is inclined by 7◦ with respect to the ecliptic plane. Among the eight major planets, Mercury’s orbit is the most tilted, with i = 7 degrees. Many smaller objects that orbit the Sun and the planets have much larger orbital inclinations. In addition, some comets, minor satellites and Neptune’s large moon Triton orbit the Sun or planet in a retrograde sense (opposite to the Sun’s or planet’s rotation). The observed ‘flatness’ of most of the planetary system is explained by planetary formation models that hypothesize that the planets grew within a disk that was in orbit around the Sun. Mass The mass of an object can be deduced from the gravitational force that it exerts on other bodies. *Orbits of moons: The orbital Credits: NASA/JPL-Caltech/Space Science Institute periods of natural satellites, together with Newton’s generalization of Kepler’s third 4πa3 M+m= law, can be used to solve for Gp2 mass. Effective when the diff bet masses is very small *What about planets without moons? The gravity of each planet perturbs the orbits of all other planets. Because of the large distances involved, the forces are much smaller, so the accuracy of this method is not high. Note, however, that Neptune was discovered as a result of the perturbations that it forced on the orbit of Uranus. This technique is still used to provide the best (albeit in some cases quite crude) estimates of the masses of some large asteroids. The perturbation method can actually be divided into two categories: short-term and long-term perturbations. *Spacecraft tracking data provide the best means of determining masses of planets and moons visited because the Doppler shift and periodicity of the transmitted radio signal can be measured very precisely. The long-time baselines afforded by orbiter missions allow much higher accuracy than flyby missions. The best estimates for the masses of some of the outer planet moons are those obtained by combining accurate short-term perturbation measurements from Voyager images with Voyager tracking data and/or resonance constraints from long timeline ground-based observations. *The best estimates of the masses of some of Saturn’s small inner moons were derived from the amplitude of spiral density waves they resonantly excite in Saturn’s rings or of density wakes that they produce in nearby ring material. Credits: NASA/JPL-Caltech/Space Science Institute *Crude estimates of the masses of some comets have been made by estimating nongravitational forces, which result from the asymmetric escape of released gases and dust and comparing them with observed orbital changes. http://solarsystem.nasa.gov/multimedia/gallery/Comet_Parts.jpg Size The size of an object can be measured in various ways: The diameter of a body is the product of its angular size and its distance from the observer. http://www.eg.bucknell.edu/physics/astronomy/as102-spr99/specials/obstri.html  206265 α= However, limited resolution from Earth results in large uncertainties in angular size. Thus, other techniques often give the best results for bodies that have not been imaged at close distances by interplanetary spacecraft.  The diameter of a Solar System body can be deduced by observing a star as it is occulted by the body. Credits: IOTA Occultation of a star by Phoebe The asteroid moves in its orbit around the Sun. Each observer in the path of the asteroid's shadow, will see the star disappear (time between less than 1s for observer #7 and several seconds for observer #4). A miss is also useful to determine the limit of the asteroid in space. The duration of this occultation is in direct relation with the size and shape of the asteroid. Source: dylanchilds.tumblr.com Euraster.net  Radar echoes can be used to determine radii and shapes. Only relatively nearby objects may be studied with radar. Radar is especially useful for studying solid planets, asteroids and cometary nuclei. An excellent way to measure the radius of an object is to send a lander and triangulate using it together with an orbiter. The size and the albedo of a body can be estimated by combining photometric observations at visible (reflected light) and infrared (IR) wavelengths (thermal radiation). Radar observation of 1999 JM8 taken on August 3, 1999 with the Arecibo radar. Credits: NASA *Additional The mean density of an object can be trivially determined after its mass and size are known. In addition to the density, one can also calculate the escape velocity using the mass and size of the object. Rotation Simple rotation is a vector quantity, related to spin angular momentum. The obliquity (or axial tilt) of a planetary body is the angle between its spin angular momentum and its orbital angular momentum. Bodies with obliquity 90 degrees have retrograde rotation.  The most straightforward way to determine a planetary body’s rotation axis and period is to observe how markings on the surface move around with the disk. Unfortunately, not all planets have such features; moreover, if atmospheric features are used, winds may cause the deduced period to vary with latitude, altitude and time.