How Much Energy Is Needed to Launch a Satellite into Orbit?

[Effective]

Homework Statement

How much energy is required to launch a 200 kg satellite from the surface of the Earth into a circular orbit with radius 8.0 * 10^6 m?

G=6.67*10^-11

Homework Equations

Ep= -GMm/r

The Attempt at a Solution

I calculated the gravitational potential energy of the object on the earth, then I calculated the gravitational potential energy of the object in the circualr orbit and then I subtracted the two and apparently that's not the correct way to tackle the problem.

 

[tiny-tim]

Welcome to PF!

How much energy is required to launch a 200 kg satellite from the surface of the Earth into a circular orbit with radius 8.0 * 10^6 m?
…
potential energy of the object on the earth, then I calculated the gravitational potential energy of the object in the circualr orbit and then I subtracted the two and apparently that's not the correct way to tackle the problem.

Hi Effective! Welcome to PF!

That will only give you enough energy to get it up there …

you need it to stay up also! ​

… you got to be practical!​

 

[thomate1]

I would like to clarify that the formula used in the attempt at a solution is correct, but it is not the most efficient way to solve this problem. The correct approach would be to use the equation for gravitational potential energy in a circular orbit, which is Ep = -GMm/2r. This takes into account the fact that the satellite is now at a distance of 2r from the center of the Earth, as it is in a circular orbit. The resulting value would be the energy required to launch the satellite into the circular orbit from the surface of the Earth. It is also important to note that this calculation does not take into account any other factors such as air resistance or the energy required for the launch itself.