Transcript Chapter 1
Chapter 2 Orbits and Gravity What causes one object to orbit another? What is the shape of a planetary orbit? What general laws govern orbits? 17 January 2006 Astronomy 2010 1 2.1 The Laws of Planetary Motion • Kepler used Tycho Brahe’s observations to deduce three laws on planetary orbits: 1. Planets move around the Sun on an ellipse, with the Sun at one focus. 2. The line joining a planet and the Sun sweeps out equal areas in equal time. 3. The square of a planet’s period is proportional to the cube of its semi major axis. 17 January 2006 Astronomy 2010 2 The Ellipse is a Conic Section 17 January 2006 Astronomy 2010 3 Drawing an Ellipse 17 January 2006 Astronomy 2010 4 17 January 2006 Astronomy 2010 5 Equal Areas in Equal Time 17 January 2006 Astronomy 2010 6 17 January 2006 Astronomy 2010 7 Kepler’s Third Law • The third law is easy if we measure the period of a planet in Earth years and the semi major axis in astronomical units (AU): – (period)2 = (semi major axis)3 • We will usually treat orbits as circles – For most planets, this is nearly true. – The semi major axis of a circle is its radius. – (period)2 = (radius)3 Mars: (1.88 years)2 = 3.53 and (1.52AU)3=3.51 17 January 2006 Astronomy 2010 8 2.2 Newton’s Great Synthesis • • Newton invented the calculus. Newton’s Laws of Motion: 1. Unless acted on by an external force, a body remains in uniform motion along a straight line. 2. The change of motion of a body is proportional to the external force acting on it and is made in the same direction as the force. 3. For every action there is an equal and opposite reaction. 17 January 2006 Astronomy 2010 9 Interpretation of Newton’s Laws 1. Conservation of momentum. 2. A force must be applied to change momentum. 3. If object A pulls on object B with a force F, then object B pulls on object A with the same force, F. 17 January 2006 Astronomy 2010 10 Mass, Volume, and Density • Mass is the measure of the amount of material. On Earth’s surface, we experience mass as weight, but even a weightless object can still have mass. • Volume is the measure of how much space something occupies. Objects with the same mass can have completely different volumes, like a penny and a balloon. • Density is mass/volume. Solids and liquids have roughly constant volumes, and constant densities. The density of a gas changes with pressure. 17 January 2006 Astronomy 2010 11 2.3 Universal Gravity • Newton proposed that the same force that makes an apple fall to the ground also keeps the Moon in orbit around the Earth! • Universal force every object attracts all other objects. – M1 and M2 are the masses of the objects – R is their separation – G = 6.673 10-11 Nm2/kg2 is a universal constant 17 January 2006 Astronomy 2010 12 Weightlessness Why does an astronaut in orbit, 300km above the Earth’s surface feel weightless? Strength of gravity changes by only a few percent! 1. Both the shuttle and astronaut are “falling” around the Earth. Everything “falls” together so gravity is neutralized. 2. The acceleration of the shuttle and astronauts towards the Earth cancels the gravity of the Earth. (Einstein’s equivalence principle) 17 January 2006 Astronomy 2010 13 2.4 Orbits in the Solar System • • • • • The orbit is the path an object follows through space. Characterize orbits by size (semi major axis), shape (eccentricity), and period of revolution (see Table 2.2). Perihelion is the closest point on an orbit to the Sun. Aphelion is the farthest point. Perigee and apogee are defined similarly for an orbit about the Earth. 17 January 2006 Astronomy 2010 14 Solar System Orbits Red lines for Comets (very elliptic) Blue lines for Asteroids (little elliptic) Black lines for Planets (nearly circular) 17 January 2006 Astronomy 2010 15 2.5 Motions of Satellites and Spacecraft • The law of gravity, Kepler’s laws, and Newton’s laws apply to man-made spacecraft and satellites. • Once boosted to orbit, spacecraft coast in orbits just like the Moon does. • However, in low orbit, satellites experience drag with the upper atmosphere, and eventually fall out of orbit. 17 January 2006 Astronomy 2010 16 17 January 2006 Astronomy 2010 17 17 January 2006 Astronomy 2010 18 Satellites in Earth Orbit 17 January 2006 Astronomy 2010 19 Interplanetary Spacecraft • We have sent spacecraft to every planet, except Pluto, and to comets and asteroids. • To escape Earth’s gravity, a spacecraft must achieve escape velocity. • Small rockets adjust and correct the path of the spacecraft. • To orbit another planet, the spacecraft must be slowed with additional rocket thrusts. • To return to Earth, another rocket is needed. 17 January 2006 Astronomy 2010 20 Voyager Spacecraft 17 January 2006 Astronomy 2010 21 2.6 Gravity with more than Two Bodies • Two bodies is relatively easy. • Three or more bodies is hard – Requires difficult calculations – Today we use computers to perform the calculations • In the mid-1800’s, the existence of Neptune was predicted by Adams and Leverrier based on small deviations of the orbit of Uranus. 17 January 2006 Astronomy 2010 22