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### Course: High school physics>Unit 7

Lesson 8: Gravitational potential energy at large distances

# Gravitational potential energy at large distances

Learn how to calculate gravitational potential energy when we can no longer assume the gravitational field is uniform.

## Want to join the conversation?

• I read somewhere that aboslute gravitational potential energy is negative because it is workdone against gravity and that energy of an object in bound state is negative so is it the reason or we just take it as negative for our own convenience?
• confused: r^2 in newtonian definition is earth radius. but r @ is height or distance. So these are differnt things--how do they cancel out??
• r is often approximated as earth's radius for situations happening close to the surface but it is really the distance between the two centres of mass
• Energy can't have a negative value. How come Ug= -(G*m1*m2)/r ?
• Hello there, Ryunah Kang,
It is a common misconception that energy cannot have a negative value. You see, when we refer to the object that Sal talked about at we do so by refering to its to total gravitational energy with respect to the space—time continuum.
Ideally, Space-time when there exists no mass around a space-time continuum, there should be no deformation. If we consider mapping this plane, we can make its displacement (height or in the case of Sal's example at , r) 0. So at this point r=0.
But when mass is introduced on to the continuum, it bends the fabric of space time. This allows for a gravity well to be produced. When an object experiences the force of this gravity well, it moves in its direction: downwards (with respect to the point where r=0) hence the Ug value is negative with respect to space—time.
• Crap so does like everything we know bout friction and other physic things just go out the window now bescause the gravity feilds arent uniform
• the value of g=9.8 m/s2, does it include any air resistance?
(1 vote)
• The minuscule mass of the air on Earth could add to the overall mass of the planet when considering gravitational acceleration at large distances, but no, air resistance does not play a factor with gravity in this case.
• Does variation of g happen with respect to altitude ?
(1 vote)
• Yes, but the change in the gravitational acceleration is so miniscule and very rarely do you need to be more precise than 3 significant figures with this value. It'll take heights bigger than the peak of Mt. Everest to change the value of g even by 1e-2m/s^2.
• g=GM/R^2

here g is inversely proportional to the R square. That means if radius will increase then acceleration due to gravity will decrease. But how is it possible?
(1 vote)
• The farther you get from the Earth, the less force you experience and therefore the less acceleration you experience. Hope this helps!
• @ Is mgy considered a negative force?
(1 vote)
• First off, mgy is not a force. It is the energy of gravitational potential on the object. This value is not negative as it is in reference to the height above the planet. Usually, the value of Ug is negative because the height of an object suspended in space-time is always negative due to the bending of space-time due to mass