# Problem using Newtonian Gravity... Will you check my work?

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1. Mar 18, 2017

### sunnnystrong

1. The problem statement, all variables and given/known data
The space shuttle is in a 300 km-high circular orbit. It needs to reach a 520 km - high circular orbit to catch the Hubble Space Telescope for repairs. The shuttle's mass is 6.5 E4 kg. Mass of the Earth = 5.98 E24 kg. Radius of Earth = 6.37 E6 m.

How much energy is required to boost it to the new orbit? Express your answer with the appropriate units.

2. Relevant equations
The specific orbital energy of an object in a circular orbit is:
-epsilon = (1/2) (mu/r)

E = epsilon * m
E = -GMm/2r

Also can use:

E = GMm/2 * (1/ri - 1/rf)

3. The attempt at a solution

E(300,000m) = -GMm/2r = -1.943 E12 J
E(520,000m) = -GMm/2r = -1.881 E12 J
E(520,000m)-E(300,000m) = 6.20566 E 10 J

Last edited: Mar 18, 2017
2. Mar 18, 2017

### Staff: Mentor

Your problem statement doesn't actually state what it is you need to determine...

3. Mar 18, 2017

### sunnnystrong

How much energy is required to boost it to the new orbit? Express your answer with the appropriate units.

4. Mar 18, 2017

### Staff: Mentor

Okay! Your work method looks good. You might want to check that you don't quote more significant figures than is warranted by the given data.

5. Mar 18, 2017

Thank you :D