Insufficient Data: Calculating Orbital Energy Gain

[Parth Dave]

Came across another question during my exam review. Seems to me like there is insufficient data again.

When the space shuttle delivers a crew to the international space station, it usually boosts the orbit of the station from about 320 km to 350 km. How much energy does the shuttle add to the stations orbit?

Orbital energy is given as:
E = -GMm/(2r)

The energy gain would be the difference from the initial energy and final energy. But how can you solve it without being given the mass (ans is 1.48E10 J)?

 

[vincentchan]

yes, you can't solve this without the mass... try google it...see if you have luck...

 

[dextercioby]

Whose mass??The satellite's??Or the Earth's?

Daniel.

P.S.Set the equations properly and see what data is missing.

 

[Parth Dave]

Energy the shuttle added = change in potential energy
Therefore,

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

Where m = mass of the space station, M = mass of earth

Everything is given except m.

 

[BobG]

The current mass of the ISS is 187,000 kg. Don't count on that giving you the right answer. The question will only work out if you know what the mass of the ISS was on the date the question was written. That's going to take quite a bit of googling. Granted, with the halt in shuttle flights, the mass has stayed reasonably constant for awhile, now, but the mass will start increasing again as soon as they start taking more major components up to it.

When all the segments have been completed, launched, and assembled, it will have a mass of 417,000 kg (down from about 470,000 kg thanks to a few canceled projects).

Of course, no matter how many segments are added, the specific energy per unit of mass will stay the same. If you want to analyze the motion of the ISS, the specific energy will do since the acceleration due to gravity is the same regardless of the mass (but the specific energy won't match your answer, either).

(This question is almost as challenging as determing the amount of potential energy gained by taking Oprah up Mt Everest, isn't it?)

 

[Parth Dave]

Thx a lot! Although I'm not concerned about the question. I just wanted to make sure I was correct in assuming the mass was necessary. No exam question will ever require you to know the mass of the ISS. Btw, the 187,000 kg gives an answer pretty close to what they wanted.