I came across this website and I intend to find out more about work done by gravity and derivation of gravitational potential energy (Sorry, the thread name is too long, so I abbreviate it as G.P.E.) Ok, here is the problem. I am quite confused with the calculation of work done against gravity and work done by gravity. Suppose I have a spacecraft at a distance r1 from the Earth's center. Then, I move the spacecraft to a distance r2 from Earth's center. I want to calculate the work done by gravity on the spacecraft. Here is what I do (Sorry, I don't know how to use LaTeX): In the above case, I assume that: In the second case, which is following the link to the website is this: I bring the S/C from a distance r2 to r1. And here is my calculation: Questions: 1. In the first case, work done by gravity is negative. But I remember there should be a negative sign when calculating work done in my equation (because Force, F and displacement, dr are in opposite direction), why is it that now I don't have to put it but I can get the right answer? Why 2. In the second case, I follow the website link as shown above but the same question pops up, now Force, F and displacement, dr are of the same direction but remember that I define F is opposite in direction to dr, so supposedly there should be a negative sign as well in the formula since now, F is of same direction as dr. Can anyone tell me my mistake? Thank you. The negative signs are frustrating... Best regards, Zheng Tien.