How do I calculate the additional energy needed to escape Earth's orbit?

[decamij]

1. How can i prove that Eg = mgh

2. What is the total energy needed to place a 2.0x10^3-kg satellite into circular Earth orbit at an altitude of 5.0x10^2 km?

For number 2, the answer is apparently 6.7x10^10J. However, shouldn't Total Energy = 1/2 (Eg)? If that is the case, the answer would be 5.8x10^10J.

(P.S. in the question after this, i must calculate the additional energy required to allow the object to escape Earth's orbit, and the answer is 5.8x10^10J).

 

[cepheid]

1. Remember that the work done by a conservative force such as gravity is defined as the negative of the change in the potential energy. You can easily prove it from the definition of work as force X distance, in the simplest scenario in which you consider a constant gravitational force applied to an object that happens to be moving vertically upward in a straight line.

 

[pack_rat2]

For the energy to put the satellite in orbit, how are calculating it? I get 9.36 X 10^9 J. (I might have made a mistake...) Also, what is "Eg"? I'm not familiar with that term.

 

[Tide]

Don't forget that most of the energy required to put a satellite into orbit goes into kinetic energy! Merely lifting it 500 km won't get you very far.

 

[decamij]

1. Eg is gravitational potential energy

2. I learned the following equations:


Etotal = -(GMm)/r

 

[decamij]

1. Eg is gravitational potential energy

2. I learned the following equations:


Etotal = -0.5(GMm)/r
Ek = -Eg


Ek is kinetic energy, G is the grav. constant, m is the mass of the satellite, is the mass of the Earth and r is the distance of the satellite from the centre of the Earth.

 

[pack_rat2]

OK, I got 6.77 X 10^10 J by adding the KE ((G*m1*m2)/(2*d)) to the PE. I got the PE (9.36 X 10^9 J) by integrating the force of gravity (G*m1*m2/d^2) with respect to the distance from the Earth's surface to the height of the orbit.