What is the speed of a satellite in orbit?

Question

The satellite has a mass of 150 kg, and it is launched into orbit at a height of 12,800 km above the earth's surface.

I got 4.558 x 10^14 m/s, but the answer is 4,558 m/s... Did I do something wrong?

Answer 1

The Force acting on a mass of m kg is

F = G M m / R^2
where G =6.673x10^ (-11) Nm^2/kg^2; M, the mass of earth =5.978x10^24kg and R, the distance of the mass from earth
= ( 12800 +6400)x10^3m.

The acceleration on the mass is

F/m = G M / R^2

This acceleration is the centripetal acceleration for the object
= V V /R.

Equating the two and canceling one R from both sides,

V V = GM / R.

---- = (6.673x10^ (-11) x 5.978x10^24) / R

---- = 3.99 x 10^ 14 / R

---- = 3.99 x 10^14 / 19.2 ^ 6

V = 4558 m/s

Answer 2

Orbital velocities of satellites which are small compared to the other body depend only on the distance from the primary (in this case the earth); the mass does not matter (ha ha).

To get the velocity at that altitude you have to know the value of g, which will be smaller than the 9.8 m/s^2 at the earth's surface.

By the way, 10^14 m/s is about one million times faster than the speed of light!

Answer 3

http://liftoff.msfc.nasa.gov/academy/rocket_sci/orbmech/vel_calc.html
Said....
The orbital velocity at 12800.00 kilometers is 4.56 km/sec! The period of the orbit is 440.52 minutes.

The calculations page is as follows
http://liftoff.msfc.nasa.gov/academy/rocket_sci/orbmech/formulas.html

I would work it myself but I am too tired... lol