So who can do this?

[manxy1]

A spherical planet with a diameter of 1600 km with a uniform density of 5200 kilograms per metre
If a space station is in a circular orbit 630 km above the surface of the world
What is its orbital velocity in metres per second?

Believe it or not, this is a question found on a kids site and my son has asked ME! to do it for him.
I haven't a clue, but would appreciate some help here and an explanation as to the answer would be First Rate. Thanks

[zaza]

Welcome to the Forums

When an object is in orbit, the gravitational force is balanced by the centrifugal force (centripetal, to be technically correct).
Newton's law of gravitation states that the gravitational force between two masses is:

F = GMm/r^2 where G is the Gravitational Constant, M and m are the two masses and r is the separation of their centres of gravity.

The centrifugal force is given by mv^2 /r (that's m*v*v/r) where m is the mass of the object, v is its velocity and r is its orbital radius. So, for a satellite orbiting a planet, GMm/r^2 = mv^2/r, which can be rearranged to give:

v^2 = GM/r

In other words, the velocity does not depend on the mass of the satellite, just on the mass of the planet and the orbital radius.

In your case, you can get the mass of the planet because you know the diameter, so the volume is 4/3 * Pi * r^3, where radius r is half the diameter. And since density = mass / volume, the mass is simply density * volume. You're given the radius, and you can Google for the exact value of G (approx 6.67*10^-11 m^3 kg^-1 s^-2).

And Bob's your Uncle.


BTW, your "kid" must be of a reasonable age. In the UK, this is A-level physics and I was asked a similar question at my Oxford Uni interview.


zaza

[manxy1]

Much obliged zaza for your help. I'm still struggling to understand any of this, but my 13 year old son will no doubt appreciate telling his schoolmates in the Isle of Man what this means.
Manxy