A satellite orbits the sun (mass Ms = 1.99x10^30 kg) with a period of 1 day. What is the radius of its orbit?


Please Help!

Ans) 2.9 x10^6 km

The following derivation of the formula for orbital mechanics is probably in your text book:
From Newton's law of gravity:

F = GMm/r^2

From Newton's 3rd law:

F = ma

For an object in circular motion its acceleration is w^2r (where w = "omega" = rotational velocity in radians/second).

Set them equal:

GMm/r^2 = mw^2r

Rearrange:

GM = w^2r^3

You now need to convert the orbital period of 1 day into radians/second, and solve for r. Post back if you still have difficulties.