Calculating Gravitational Potential

[Jimmy87]

Homework Statement

I was going through a worked example in my textbook to gain a better understanding but after I had a go myself it is the opposite to what I have calculated. I have attached the worked example which asks you to calculate the gain in gravitational potential moving from a point that is 3800km away from the Earth's surface to a point that is 2250km away.

Homework Equations

V = - GM/R (where V is gravitational potential) using G as 6.67 x 10^-11 and M as 5.97 x 10^24 kg

The Attempt at a Solution

I thought as you move further away the gravitational potential increases as it is inversely proportional to the negative of 'R'. So how can moving closer to the Earth be a GAIN in gravitational potential. When I calculated it I added the radius of the Earth to the distances from the Earth. I don't see how yo can leave that out like they do in the worked solution? So I did:

Potential at A = -GM/R = - 3.92 x 10^7 J/kg
Potential at B = -GM/R = - 4.62 x 10^7 J/kg

I used the radius of the Earth as 6.371 x 10^6 m

So I thought any change in physics is always the final minus the inital. So if we are going from point A to point B it would be:

change in gravitational potential = -4.62 x 10^7 - (-3.92 x 10^7) = -0.7 x 10^7 J/kg

I thought this made sense to me as I thought gravitational potential energy and gravitational potential always increase as you move away from the gravitating object. Since B is closer to the Earth I expected my answer to be negative meaning the gravitational potential has decreased as you have got closer to the gravitating object - which is has! However, the worked example is the complete opposite to what I have done so now I am confused. Please help!

 

[kuruman]

You are correct and I agree that the example is confusing. The gravitational potential decreases as one moves nearer the center of the Earth. It seems that this textbook has defined "gain" as the absolute value of "change", the latter always being final minus initial value.

On Edit: The question would make more sense if it asked, "What is the gain of gravitational potential between the two points?"

 

[Jimmy87]

You are correct and I agree that the example is confusing. The gravitational potential decreases as one moves nearer the center of the Earth. It seems that this textbook has defined "gain" as the absolute value of "change", the latter always being final minus initial value.

On Edit: The question would make more sense if it asked, "What is the gain of gravitational potential between the two points?"

Thanks. Would I get it right in an exam though? As my answer and the textbook answer are completely different.

 

[kuruman]

Thanks. Would I get it right in an exam though? As my answer and the textbook answer are completely different.

Since your instructor will be grading your exam, I think you should get a clarification of what "gain" means from him/her. Then you will be sure to get it right.