What is the equation for finding the change in gravitational potential energy of a 64.5-kg astronaut in orbit?

[justinh8]

Homework Statement

What is the change in gravitational potential energy of a 64.5-kg astronaut, lifted from
Earth’s surface into a circular orbit of altitude 4.40 3 102 km?

The Attempt at a Solution

Ok, i know to find this i have to find the gravitational energy on Earth using Earth's radius and find the gravitational energy in orbit using the Earth's radius + the altitude. Therefore, the equation at Earth would be Eg = -GMm/re and the equation in orbit would be
Eg = -0.5(GMm/re + altitude).

However, in the solutions manual it uses the same equation Eg = -GMm/re when the object is in orbit.
I just want to know if the book is wrong or if i am wrong. I thought that when objects are in orbit you have to play in the value of kinetic energy which creates the equation of Eg = -0.5(GMm/re + altitude). Please explain

 

[Andrew Mason]

... and the equation in orbit would be
Eg = -0.5(GMm/re + altitude).

Is Eg the total energy or the potential energy?

However, in the solutions manual it uses the same equation Eg = -GMm/re when the object is in orbit.
I just want to know if the book is wrong or if i am wrong. I thought that when objects are in orbit you have to play in the value of kinetic energy which creates the equation of Eg = -0.5(GMm/re + altitude). Please explain

Why would kinetic energy affect potential energy? Potential energy is a function of r (distance from the centre of the earth) only. It looks like you may be confusing total energy with potential energy.

AM

 

[justinh8]

Ok, so the formula of -0.5(GMm/re + altitude) is for the total energy?

 

[Steely Dan]

Ok, so the formula of -0.5(GMm/re + altitude) is for the total energy?

This is correct, for something in a stable orbit. You would lose the factor of 1/2 if you just wanted the contribution from gravitational potential energy.

 

[justinh8]

So when it asks for just the gravitational potential energy, i use Eg = -GMm/r ?

 

[justinh8]

and also, does binding energy = -0.5(Gmm/r) or 0.5(Gmm/r)?

 

[Andrew Mason]

So when it asks for just the gravitational potential energy, i use Eg = -GMm/r ?

Correct. But I would suggest you use PE or U to distinguish it from total energy. This is the potential energy relative to r = ∞.

and also, does binding energy = -0.5(Gmm/r) or 0.5(Gmm/r)?

Binding energy is the work that must be done on an object of mass m to get it from R = r to R = ∞. It is positive.

AM