Calculating Energy Required to Move a Space Shuffle

[bayan]

Hi everyone.

I have a question about energy required to move a space shuffle from a radius of $$1.3*10^7 m$$ to $$2.5*10^7 m$$

I know that the area underneath the graph represents the amount of energy required and may even be able to work it using ingral laws. but is there an easy way?

 

[Dr.Brain]

May I know is the 'changing radius' that of the shuffle? or is it that you ar etaking it away from something of a particvular radius.

 

[Andrew Mason]

Hi everyone.

I have a question about energy required to move a space shuffle from a radius of $$1.3*10^7 m$$ to $$2.5*10^7 m$$

I know that the area underneath the graph represents the amount of energy required and may even be able to work it using ingral laws. but is there an easy way?

What is the gravitational potential energy and kinetic energy of the shuttle in orbits of each of these two radii? What is the energy difference?

AM

 

[nykill]

bayan the information provided in your ? is insufficient, cos the shuttle can be movied with the most least energy if its 1) of lesser mass 2) not under gravitational influence and 3) if more time can be taken

 

[Andrew Mason]

bayan the information provided in your ? is insufficient, cos the shuttle can be movied with the most least energy if its 1) of lesser mass 2) not under gravitational influence and 3) if more time can be taken

Really?
1) The Shuttle will lose mass by burning fuel, but I think the question assumes that fuel loss can be ignored. That may or may not be reasonable but since we are not given the rate of fuel consumption we have no choice. 2) how does it move in a circle (of the given radius) if there is no gravity? 3) how does the amount of time taken to change orbital radius affect the energy change?

AM

 

[bayan]

it is the radius of the orbit of space suffle. it is to be moved from $$1.3*10^7 m$$ from center of Earth to $$2.5*10^7 m$$ from the center of the earth.

They have given the graph for Gravity Vs Distance and I know that the amount of energy is the area under the graph. but how can I find it and showing any work out? I did find it using a calculator.

 

[Andrew Mason]

it is the radius of the orbit of space suffle. it is to be moved from $$1.3*10^7 m$$ from center of Earth to $$2.5*10^7 m$$ from the center of the earth.

They have given the graph for Gravity Vs Distance and I know that the amount of energy is the area under the graph. but how can I find it and showing any work out? I did find it using a calculator.

So what did you input into the calculator and what was your answer?

AM

 

[bayan]

I put it as $$y=\frac{GM}{r^2}$$ where $$r=x$$and found the area for $$1.3*10^7 m >x<2.5*10^7 m$$

my answer was $$1472360J$$