Circular and Satellite Motion - Mission CG8 Detailed Help

The orbital speed of an Earth-orbiting satellite is dependent upon the ____. List all that apply ... .


 
Orbital Speed:
The orbital speed of a satellite about a planet is dependent upon the mass of the planet being orbited and the radius of the satellite's orbit. The orbital radius is measured as the distance from the satellite to the center of the planet.


 
Many students have a preconception that the orbital speed of a satellite is dependent in some way upon the mass of the satellite. The most usual idea is that a more massive satellite would need a greater orbital speed. But don't be fooled! The orbital speed of a satellite is independent of the mass of the satellite and solely dependent upon the radius of orbit and the mass of the planet being orbited.


 
The orbital speed (v) of a satellite about a planet can be derived using the equation for centripetal acceleration (a= v2/R) and the equation for gravitational acceleration (g = G•Mplanet/R2). The first step would be to rearrange the centripetal acceleration equation and then to substitute the expression for the gravitational acceleration into the equation.
 
v2 = a • R = (G•Mplanet/R2) • R
v2 = G•Mplanet/R

Taking the square root of each side yields the formula for the orbital speed of a satellite:
 
v = SQRT (G•Mplanet/R)

where Mplanet is the mass of the planet and R is the radius of the orbit.