- #1

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I'm stuck. How am i suppose to calculate the ratio. I know the that the energy to put M into orbit near the earth's surface would be a small positive energy while putting it into distant space would be a large positive energy.

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- Thread starter krypt0nite
- Start date

- #1

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I'm stuck. How am i suppose to calculate the ratio. I know the that the energy to put M into orbit near the earth's surface would be a small positive energy while putting it into distant space would be a large positive energy.

- #2

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The gravity field of a spherically symmetric celestial body (i.e.Earth) is CONSERVATIVE,which means u can apply the law of conservation of total energy.

Can u compute the energy required to put a mass into orbit near the surface of the Earth??

Daniel.

- #3

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There are no values given to me so i dont know how to compute it

- #4

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[tex]E_{binding}=\frac{Gm_1m_2}{2r}[/tex]

When a satellite is in orbit, it's total energy (total mechanical energy) is:

[tex]E_{mechanical}=-\frac{Gm_1m_2}{2r}[/tex]

So I guess the ratio would be 1:1?

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Daniel.

- #6

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I was thinking more like 1:1/r ratio would make sense.

- #7

Andrew Mason

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For near earth orbit:krypt0nite said:

I'm stuck. How am i suppose to calculate the ratio. I know the that the energy to put M into orbit near the earth's surface would be a small positive energy while putting it into distant space would be a large positive energy.

[tex]mv^2/R = F = GMm/R^2[/tex]

Which is:

(1)[tex]2KE = GMm/R[/tex]

where KE is the kinetic energy of the orbiting body, which is just -1/2 * its gravitational potential at radius R.

The condition for distant space (escape) is:

[tex]PE \ge 0[/tex]

You should see from (1) that [itex]2KE_{orbit} + PE_{orbit} = 0[/itex], which means that the kinetic energy required for escape is ______ the KE for orbit. I think that should help you answer the question.

AM

- #8

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So ratio would be 1:2?

- #9

Andrew Mason

Science Advisor

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If you mean: Kinetic energy of escape = 2 KE of orbit, then yes.krypt0nite said:So ratio would be 1:2?

AM

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