Calculating Energy for Orbital Deployment

[ashvuck101]

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

Ep=-Gm₁m₂/r

w=fd

f=Gm₁m₂/r²

The Attempt at a Solution

using

f=Gm₁m₂/r²

= 9.83*10²

w=fd
= 9.83*10²*100000
= 9.83*10⁷


b)

im not sure if a is right and i don't know how to get the answer for b

somebody at least tell me i am going in the right direction here

 

[alphysicist]

Hi ashvuck101,

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

Ep=-Gm₁m₂/r

w=fd

f=Gm₁m₂/r²

The Attempt at a Solution

using

f=Gm₁m₂/r²

= 9.83*10²

Okay, this is the force of gravity on the object at the Earth's surface.

w=fd
= 9.83*10²*100000

You seem to be missing a zero here for the distance.

But more importantly, this approach is what you would use if the gravitational force were constant over the entire 1000 km. (Because to find the minimum energy, you would set the pushing force to be equal to the gravitational force.) However, gravity decreases with height. How do you find the work of a force that is not constant?

As an alternative, what is the definition of potential energy? How can that help you find the work done by gravity?

= 9.83*10⁷


b)

im not sure if a is right and i don't know how to get the answer for b

somebody at least tell me i am going in the right direction here