Astrophysics-Orbital mechanics

Armando Mateo

Newton’s law of universal gravitation

Earth this acceleration has the valve 9.80665 m/s2 (32.174 ft/s2).

G is an universal constant, called the constant of gravitation, and has the value 6.67259x10-11 N-m2/kg2 (3.4389x10-8 lb-ft2/slug2).

Newton’s law of universal gravitation is:

Kepler's laws of planetary motion.

1. All planets move in elliptical orbits with the sun at one focus. 2. A line joining any planet to the sun sweeps out equal areas in equal times. 3. The square of the period of any planet about the sun is proportional to the cube of the planet's mean distance from the sun.

The velocity of the satellite to stay in orbit is determined by1. gravity (the universal gravitational

constant, actually),2. the mass of the object that the satellite is

traveling around (in most cases, Earth) and

3. 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).

For a constant radius, there is only one speed that an object can travel to maintain orbit. If it goes any faster or slower than this speed it will either go off into space (faster) or crash down to Earth (slower).

Exact Satellite velocity

The smaller of the two answers corresponds to Rp, the periapsis radius. The other root corresponds to the apoapsis radius, Ra.

ORBITAL MECHANICS

Orbital Velocity of space vehicle is derived that Fc = Fg

v = v =

V=

G = gravitational constant 6.67*10-11

mE = Mass of a planetrE = the radius of the orbitrE = h + rh = height of the orbitr = the radius of a planet from the center of the planet to its surface

masses M and m moving in circular orbits under the influence of each other's gravitational attraction.

where P is the period of revolution

Launch of a Space Vehicle

Satellite drag

Satellite kick motor

According to the heliocentric theory, the earth is moving at about 1,000 mph at the equator. If the geostationary satellites were moving, they would have to move at a speed of about 7,000 mph to maintain a stationary orbit above a fixed point on the earth. That is about the same speed as the GPS satellites that orbit the earth twice a day. However, GPS satellites are equipped with a rocket engine to maintain their orbit.