Gravitational potential energy problem.

Click For Summary

Homework Help Overview

The discussion revolves around a gravitational potential energy problem involving a satellite transitioning between two circular orbits around Earth. The original poster presents calculations for the gravitational potential energy in each orbit and explores related concepts such as work done and orbital speed.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to calculate the gravitational potential energy using the formula Ep = -GMm/r for two different orbital radii. They express uncertainty about their calculations and seek feedback. Other participants confirm the use of the correct equation and share their own calculations for both orbits, raising questions about the relationship between gravitational potential energy and work done. Additionally, there is a query regarding the calculated speed needed for the new orbit, with concerns about the magnitude of the result.

Discussion Status

Participants are actively sharing their calculations and reasoning, with some confirming the correctness of the original poster's approach. There is ongoing exploration of the implications of their findings, particularly regarding the relationship between gravitational potential energy and work done. The discussion reflects a collaborative effort to clarify concepts without reaching a definitive conclusion.

Contextual Notes

Participants note the need to consider energy conservation principles and the implications of their calculations on work done during the satellite's transition between orbits. There is an acknowledgment of potential uncertainties in the calculations presented.

Tyyoung
Messages
7
Reaction score
0

Homework Statement


A satellite with a mass of 5.00 x 10^2 kg is in a circular orbit, whose radius is 2re, around Earth. Then it is moved to a circular orbit with a radius of 3re.

a) Determine the satellite's gravitational potential energy in each orbit.


Homework Equations



Ep= -GMm/r

The Attempt at a Solution



Ep= -GMm/r
= -(6.67*10^-11)(5.98*10^24)(5.00*10^2)/2(6.38*10^6)
Ep= -1.56*10^10

I'm uncertain about that answer, I don't necessarily have a reason to believe it is wrong but I don't trust my judgment on this one. Any feedback as to what I may have done wrong would be greatly appreciated.
(I answered for only the 2re orbit.)
 
Last edited:
Physics news on Phys.org
Ep= -GMm/r is the right equation, so that answer is right.
 
So I got the answer for both 2re and 3re which are
Ep = -1.56*10^10
Ep = -1.041969697*10^10

and then for the next question it asks to determine the change in gravitational potential energy which I'm pretty sure is (Delta)Ep=Ep2-Ep1 which I got 5180303030 J ( I just subtracted the two answers above to arrive at that)

now in the third question it asks me to determine the work done in moving the satellite from the first orbit to the second orbit (2re to 3re) apply energy conservation. Isn't the change in gravitational potential energy also the work?? (Delta)Ep=W=F*d
 
Last edited:
also d) for the same problem asks me to Calculate the speed it would need in order to maintain its new orbit.

I did v = sq.root of Gme/r

so I got v = sq.root of (6.67x10^-11)(500)/3(6.38x10^6)
v = sq.root of 1.742424242x10^-15
v = 0.000000042 m/s
that seems way to small to me, can someone show me where I went wrong pleasezzz.
 

Similar threads

Replies
5
Views
3K
Replies
8
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 7 ·
Replies
7
Views
1K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 43 ·
2
Replies
43
Views
4K
Replies
5
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
6
Views
3K