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Orbital Speed
The mass formula above tells you that satellites orbiting massive planets must move faster than
satellites orbiting lowmass planets at the same distance. Massive planets have stronger gravity
than lowmass planets so a satellite orbiting a massive planet is accelerated by a greater amount
than one going around a lesser mass planet at the same distance. To balance the stronger inward
gravitational pull of the massive planet, the satellite must move faster in its orbit than if it was
orbiting a lesser mass planet. Of course, this also applies to planets orbiting stars, stars orbiting
other stars, etc.
If you solve for the orbit speed,
v,
in the mass formula, you can find how fast something needs to
move to balance the inward pull of gravity:
v
2
= (G M)/r
.
Taking the square root of both sides (you want just
v
not
v
2
), you get
v =
Sqrt
[
(G M)/r
].
How do you do that?
Find the orbital speed of Jupiter around the Sun. Jupiter's distance from the Sun is 5.2 A.U., or
7.8×10
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 Fall '10
 EmilyHoward
 Astronomy

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