Gravitational Potential Energy in orbit

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Discussion Overview

The discussion revolves around gravitational potential energy in the context of elliptical orbits, specifically addressing a homework question about the ratio of kinetic energy to total energy in orbit. Participants explore the relationships between potential energy (U), kinetic energy (K), and total energy (E), as well as the implications of these relationships in different scenarios.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant understands the formulas for potential energy and total energy in elliptical orbits but questions the ratio of kinetic energy to total energy, suggesting that U/E could be greater than 1.
  • Another participant clarifies that K/E can be derived from the rearrangement of E = K + U.
  • There is a claim that U/E equals 2, which leads to confusion about the implications for K/E.
  • A participant expresses surprise at the integer values for ratios, questioning their acceptability in this context.
  • Discussion includes the idea that the reference point for potential energy is arbitrary, allowing for U to be less than 0.
  • Participants discuss the significance of setting U = 0 at infinite distance and its implications for total energy in relation to semi-major axis length.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the ratios of kinetic and potential energy, with some agreeing on the mathematical relationships while others question the interpretations. The discussion remains unresolved regarding the implications of these ratios and their acceptability.

Contextual Notes

Participants note that the reference point for potential energy is arbitrary, which may influence their understanding of energy relationships. There is also mention of the relationship between semi-major axis length and total energy, which remains a point of exploration.

ual8658
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This pertains to a homework question but I get the concept of PE or U = -GmM/a for an elliptical orbit. I also understand the derivation of the total energy of an object in an elliptical orbit as E = -GmM/2a. However, I have a homework question that asks for the ratio of an object's kinetic energy to total energy in orbit, and the problem states to use the relationship of K/E = 1 - U/E. However, wouldn't U/E be greater than 1 since E has a denominator of 2a while U has a denominator that is always smaller than 2a? This would force U to be greater than E, which would mean U/E is greater than 1, which leads to a K/E greater than 1. How does this make sense?
 
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ual8658 said:
and the problem states to use the relationship of K/E = 1 - U/E.
This is simply E = K + U rearranged.
 
ual8658 said:
This would force U to be greater than E, which would mean U/E is greater than 1,
That's true. U/E = 2.

ual8658 said:
which leads to a K/E greater than 1.
That doesn't follow. K/E = -1.
 
Doc Al said:
That's true. U/E = 2.That doesn't follow. K/E = -1.
Ok I'm used to having ratios that are decimals rather than integer values. So it's acceptable in this case to have 2 and -1 be ratio values?
 
ual8658 said:
Ok I'm used to having ratios that are decimals rather than integer values.
You can express an integer as a decimal if you like.

ual8658 said:
So it's acceptable in this case to have 2 and -1 be ratio values?
Why not?
 
Doc Al said:
You can express an integer as a decimal if you like.Why not?
From using the simple relationship mgh and .5mv^2 when we define total energy, U or K has always been less than the total E. But with this I guess the relationship is opposite since a U value of 0 would indicate infinite distance? Would this also mean that a planet with a larger semi-major axis has more total energy since its E value would be closer to 0?
 
ual8658 said:
From using the simple relationship mgh and .5mv^2 when we define total energy, U or K has always been less than the total E.
Note that the reference point where U = 0 (where h = 0) is arbitrary, so you can get U < 0 there as well.

ual8658 said:
But with this I guess the relationship is opposite since a U value of 0 would indicate infinite distance?
When dealing with gravity between planets and such, it is most convenient to set U = 0 when they are infinitely far apart. That is the basis of the formulas you quoted earlier.

ual8658 said:
Would this also mean that a planet with a larger semi-major axis has more total energy since its E value would be closer to 0?
Yes.
 
Doc Al said:
Note that the reference point where U = 0 (where h = 0) is arbitrary, so you can get U < 0 there as well.When dealing with gravity between planets and such, it is most convenient to set U = 0 when they are infinitely far apart. That is the basis of the formulas you quoted earlier.Yes.
Ok thank you. You've just cleared up a ton of confusion!
 

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