Cost of setting up a sattelite?

[Zaros]

Homework Statement

A scientist wants to put an 100kg experimental package in orbit around the Earth. The cost of deployment depends on the amount of extra energy it takes to get it into the required position i.e. how much more energy is used than just sending the rocket up there.
a) Determine the amount of work that must be done to get the package to 1 000km above the Earth’s surface.
b) Determine the amount of extra work needed to put the package into a circular orbit at this height.

Homework Equations

W=F*d
F=(G*m₁m₂)/r²

The Attempt at a Solution

a) W=F*d
F=FG
=(Gm1m2)r²
=(6.67 * 10^-11 * 100 * ME)/(RE + 1000000)²
= 731 N
W= F*d = 730 * 1000000
= 7.31 *10⁸

 

[D H]

W=F*d

That is true only for a constant force.

You need to use something else. Hint: What is the relation between work and energy?

 

[Zaros]

Work is equal to kinetic energy i.e. W= ¹/₂ mv²
Is that what your getting at?

 

[D H]

What about potential energy?

 

[Zaros]

W = KE + PE = 1/2 mv² + mgh
Is that right?

 

[D H]

No. That mgh term is assuming a uniform gravity field.

 

[Zaros]

then should i use the F= (G*m₁*m₂)/r² instead so that would lead to
F= 1/2 mv² + h((G*m₁*m₂)/r²)

Now is this correct?

 

[Pengwuino]

then should i use the F= (G*m₁*m₂)/r² instead so that would lead to
F= 1/2 mv² + h((G*m₁*m₂)/r²)

Now is this correct?

Stop just throwing equations at the problem. You equated F, Force, with an energy. Not good. You need to stop and think about the problem.

What would your change in potential energy be if you were to take the package on the ground with 0 kinetic energy and put it up into space at the height required and still not let it have any kinetic energy?