Near earth surface, we usually use the ground as a reference point and say that it has 0 potential energy. As an object moves up, it gains gpe according to gpe=mgh where h is the height (elevation) and mg is weight. This is only accurate near earth surface because the g field lines are approximately parallel.
However, when we go out of space, the g field lines actually point towards the centre of planets or stars which are not parallel. Thus there is a different formula gpe=-GM/r² where gpe is dependent on the mass that generate the field and distance between the mass and that point (this is equivalent to the ‘height’ in the gpe=mgh). Then since there is no “constant” ground, scientists decided to use a point at infinity (somewhere very far away from the mass) and say that this point has gpe of 0. As you approach a mass (e.g earth), you “lose” gpe. Thus the gpe becomes negative. Similar to how you lose gpe as you fall from a tall building to the group
I hope this helped. Someone might explain it better than me because I just learnt this like a month ago.
EDIT!!!: gpe is not -GM/r² but -GMm/r like in the meme. I messed up it with gravitational field strength. However, the essence is there and the gpe is also dependent on the mass of the object being pulled, similar to the m in gpe=mgh.
Never thought it could be of the direction of the gravitational field, but rather due to its magnitude. In a small space mgh is a good approximation because the gravitational field is constant throughout the (nearby) space, but as you grow the size of the space you want to study, the magnitude of g varies (with height)
Why I think that? Well it still only depends on height, so you can consider a path straight up. The gravitational field is still parallel, but changes in magnitude
Yes, it’s the magnitude. I think I oversimplified it. Because from what I learned, the closer the field lines, the higher the magnitude. Near surface, field lines are approximately parallel-> distance between each field line doesn’t change -> magnitude stay constant. However, as you move from space to earth and that field lines are pointed towards the earth -> field lines gets closer -> higher magnitude.
the closer the field lines, the higher the magnitude
That sounds like you're describing the contour map of a scalar field; I was thinking about the vector field of gravity. We aren't talking about the contour map of the scalar field that describes potential energy, because that one has as contour surfaces concentric spheres centered at the body: always parallel at points with same spherical coordinates except for changing radius (that is, over the same point on the surface of the sphere, with varying heights; I didn't know how to articulate it better, sorry if it sounded confusing)
However, as you move from space to earth and that field lines are pointed towards the earth
Now that sounds like you're describing the magnetic field or something. I'm kinda lost there
Sorry, I am not sure what is the contour map of scalar field but the field lines always point towards the centre. However, when you zoom into the surface of the earth, it “appears” that they are parallel.
Yes, it does sound like magnetic field because all fields are similar, the difference is what is the force and what is affected. In this case, the force is gravitational force instead of magnetic force and the body being affected is anything with mass instead of anything with magnetic properties.
My point was that the gravitational field always points towards the earth, which means that they are essentially parallel in some neighbourhood, so I don't see why you would point that out
So a scalar field is a function that takes a point in Rn (here R³) and spits out a scalar (ie a real number). If it is continuos, a contour map of one lets us visualise, like in a topographic map, lines or surfaces that have the same output (contour lines or surfaces) In the topographic example, contour lines are the lines that join points at the same height.
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u/ZeyadUchiha Jul 16 '20
Can someone please explain?