Physics Help Forum speed of space station

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 Sep 8th 2017, 01:23 PM #1 Junior Member   Join Date: Aug 2017 Posts: 4 speed of space station After watching the interstellar movie I have a question: which solution will consume less fuel? The space station moves in a circular orbit and has too slow speed. To increase it has two possibilities: 1. Increase the orbital speed, 2. Increase the height of the orbit, and thus reduce the first space velocity.
 Sep 8th 2017, 11:31 PM #2 Senior Member   Join Date: Apr 2017 Posts: 157 I'll assume you want to change orbit ....Imagine a rocket in orbit , it's nose is pointing in the direction of it's travel .... to increase the distance from Earth you fire the rocket ... as if to increase the speed ... This will push the rocket away from earth into a higher orbit ... but paradoxically the speed of the rocket will be reduced !! energy from the rocket firing ,and from the reduction in speed (kinetic energy) , has gone into increased potential energy( greater distance from earth) ...
 Sep 9th 2017, 01:46 AM #3 Junior Member   Join Date: Aug 2017 Posts: 4 For example, if you have 5tonnes of fuel and the orbital speed of 7km/s, but you need 8km/s (on the altitude of 500km above the Earth) what are you doing? 1. You direct the engine nozzle tangentially to the current track (to get these 8km/s) 2. Or direct the engine towards the Earth so that the station gets a non-zero radial speed (the station will, for example, be at an altitude of 800km and will no longer need to orbit 8km/s but 7km/s)
Sep 12th 2017, 11:00 PM   #4
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 Originally Posted by Kamil19991 After watching the interstellar movie I have a question: which solution will consume less fuel? The space station moves in a circular orbit and has too slow speed. To increase it has two possibilities: 1. Increase the orbital speed, 2. Increase the height of the orbit, and thus reduce the first space velocity.
I don't know the answer off the back of my hand. Simply determine the energy in each case. The one requiring the lesser energy will require less fuel.

The energy is the sum of the gravitational potential energy U = -GMm/r^2 and the kinetic energy K = mv^2/2. The orbital requirement is for the centripetal force to be equal to the gravitational force in magnitude.

Sep 20th 2017, 10:09 AM   #5
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 Originally Posted by Pmb I don't know the answer off the back of my hand. Simply determine the energy in each case. The one requiring the lesser energy will require less fuel. The energy is the sum of the gravitational potential energy U = -GMm/r^2
That's gravitational force. The potential energy is GMm/r.

 and the kinetic energy K = mv^2/2. The orbital requirement is for the centripetal force to be equal to the gravitational force in magnitude.

Sep 20th 2017, 12:17 PM   #6
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 Originally Posted by HallsofIvy That's gravitational force. The potential energy is GMm/r.
Really? Gee. I never knew.

Last edited by Pmb; Sep 20th 2017 at 12:23 PM.

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