Gravtational Potential Energy

Lolagoeslala

1. The problem statement, all variables and given/known data

9. What is the total energy needed to place a 2.0 x 10^3-kg satellite into circular Earth
orbit at an altitude of 5.0 x10^2 km?

10. How much additional energy would have to be supplied to the satellite in question 9
once it was in orbit, to allow it to escape from Earth’s gravitational field?

3. The attempt at a solution

9. I was trying to use the equation

Wpl = (- GMem/Ro) - (-GMem/Re)
Wpl = ( - (6.67 x10^-11 Nm^2/s^2)(5.98 x10^24)(2 x 10^3 kg)/(5 x10^5m)+(6.38 x10^6m)) - (- (6.67 x10^-11 Nm^2/s^2)(5.98 x10^24)(2 x 10^3 kg)/6.38 x10^6m))

Wpl = - 11.59494186 x 10^10 + 12.50363636 x10^10
Wpl = 0.908717 x 10^10 J

IS THIS CORRECT?

and what can i do for Question 10 ?

gneill

Placing a satellite in orbit requires not only that you move it up to the required distance in the Earth's gravitational field, but also that you impart the required speed for it to orbit (otherwise it would just fall straight back down). So there's gravitational PE involved as well as KE.

One point that's not covered in the problem statement is whether or not you can take advantage of the initial speed of satellite due to it being launched from the surface of a rotating Earth; If you launch from the equator in the appropriate direction, you begin with an initial speed due to the Earth's daily rotation.

Lolagoeslala

ok so .... i am guessing you use the work of placement to find the speed?

haruspex

No, the work of placement is what you're trying to determine. How fast does a satellite in circular orbit at radius r have to be travelling to stay there?

Lolagoeslala

yes thats for number 9 .. you are completely right about that;... but for the number 10 .. second question you are finding the binding energy correct?