A 1000 kg space craft is orbiting the moon at a height of 50 km. If it has a total energy of -1.5 x 10^9 J, how fast is it going?

Question

A 1000 kg space craft is orbiting the moon at a height of 50 km. If it has a total energy of -1.5 x 10^9 J, how fast is it going?

What equation do I use? I'm so confused.

Answer 1

In circular orbit, the total energy equals negative kinetic energy

E = - K

Since E = - 1.5*10⁹

-1.5*10⁹ = -K

1.5*10⁹ = K

Which becomes

1.5*10⁹ = ¹/₂ m v²

Now you can solve for v