# Finding min amount of energy to move a satellite from its orbit using EnergyPrinciple

#### enchanteuse

1. The problem statement, all variables and given/known data

You will need to use the Momentum Principle to do the first part of this problem, and the Energy Principle to do the second part.

A satellite of mass 6000 kg orbits the Earth in a circular orbit of radius of 7.4 106 m (this is above the Earth's atmosphere).The mass of the Earth is 6.0 1024 kg.
What is the speed of the satellite?

What is the minimum amount of energy required to move the satellite from this orbit to a location very far away from the Earth?

2. Relevant equations

Momentum Principle: deltap = Fnet*deltat or pf = pi + Fnet*deltat
Energy Principle: deltaEsystem = Wsurr + Q

3. The attempt at a solution

I got the first part of the problem, which is v = sqrt(G*Mearth/r) = sqrt ((6.67*10^-11)(6*10^24)/(7.4*10^6)) = 7353.98 m/s

I'm having problems with the second part. Here is my attempt: E = GMm/r = (6.67*10^-11)(6*10^24)(6000)/(7.4*10^6)) = 3.24*10^11 J

What am I doing wrong?

#### D H

Staff Emeritus
Re: Finding min amount of energy to move a satellite from its orbit using EnergyPrinc

Your attempt would be correct if the vehicle was at a dead stop. It's not at a dead stop. It is moving at 7.3 km/sec.

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