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# Astrophysics orbital mechanics

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### Astrophysics orbital mechanics

1. 1. Armando Mateo
2. 2. G is an universal constant, called the constantof gravitation, and has the value 6.67259x10-11N-m2/kg2 (3.4389x10-8 lb-ft2/slug2).Earth this acceleration has the valve9.80665 m/s2 (32.174 ft/s2).
3. 3. 1. All planets move in elliptical orbits with thesun at one focus.2. A line joining any planet to the sun sweepsout equal areas in equal times.3. The square of the period of any planetabout the sun is proportional to the cube ofthe planets mean distance from the sun.
4. 4. The velocity of the satellite to stay in orbit isdetermined by1. gravity (the universal gravitational constant, actually),2. the mass of the object that the satellite is traveling around (in most cases, Earth) and3. the distance between the center of the orbit and the satellite (orbital radius) (which would be the distance from the center of the Earth to the satellite in most cases).
5. 5. Exact Satellite velocityFor a constant radius, there is onlyone speed that an object can travel tomaintain orbit. If it goes any faster orslower than this speed it will either gooff into space (faster) or crash down toEarth (slower).
6. 6. The smaller of the two answers corresponds to Rp, theperiapsis radius. The other root corresponds to theapoapsis radius, Ra.
7. 7. v= V= G = gravitational constant 6.67*10-11 mE = Mass of a planet rE = the radius of the orbit rE = h + r h = height of the orbit r = the radius of a planet from the center of the planet to its surface
8. 8. masses M and m moving in circular orbits underthe influence of each others gravitationalattraction. where P is the period of revolution
9. 9. According to the heliocentric theory, the earthis moving at about 1,000 mph at the equator. Ifthe geostationary satellites were moving, theywould have to move at a speed of about 7,000mph to maintain a stationary orbit above afixed point on the earth. That is about the samespeed as the GPS satellites that orbit the earthtwice a day. However, GPS satellites areequipped with a rocket engine tomaintain their orbit.