The discussion revolves around the concept of potential energy in the context of a spacecraft in circular orbit around the Earth. The original poster seeks to specify the reference state for potential energy, particularly in relation to gravitational forces and the position of the spacecraft.
The discussion is active, with various interpretations being explored regarding the reference level for potential energy. Some participants have provided clarifications about the nature of potential energy and its dependence on the chosen reference point, while others continue to question the implications of these choices.
There is an ongoing examination of the assumptions regarding the distribution of mass within the Earth and how this affects the calculation of potential energy. Participants are also considering the implications of using different reference points, such as the center of the Earth versus infinity.
Infinitum said:Reference state/level is the one relative to which you measure the potential energy. So in this case it would be _______?
charmedbeauty said:well potential energy is really the distance from the centre of the Earth to the space ship, r in this case.
so the reference level is on Earth which is r- the distance from the spaceship to surface of the earth?
Infinitum said:Um, no. Let me be more clear. The reference state, in other words, is where the potential energy is taken to be 0. So, where is the potential energy 0?
charmedbeauty said:at the centre of the Earth assuming that all the mass in the Earth is evenly distributed.?
Not if you're using this formula for PE:charmedbeauty said:at the centre of the Earth assuming that all the mass in the Earth is evenly distributed.?
Using that expression for PE, where is the zero point?charmedbeauty said:the total energy is
E=K+U
= 1/2mv2-GmM/r
Doc Al said:Not if you're using this formula for PE:
Using that expression for PE, where is the zero point?
charmedbeauty said:r→∞
but it's seems strange to me. does that mean that all matter can never have 0 potential energy?
Right. Using that formula implies that you are taking PE = 0 as r → ∞.charmedbeauty said:r→∞
The place you choose to call PE = 0 is arbitrary. (But using that formula is very convenient for some purposes.) What physically matters is the change in PE as you go from one point to another, which is independent of the arbitrary PE = 0 reference point.but it's seems strange to me. does that mean that all matter can never have 0 potential energy?
Doc Al said:Right. Using that formula implies that you are taking PE = 0 as r → ∞.
The place you choose to call PE = 0 is arbitrary. (But using that formula is very convenient for some purposes.) What physically matters is the change in PE as you go from one point to another, which is independent of the arbitrary PE = 0 reference point.
Right. The PE never quite equals zero for finite r. PE goes to zero as r goes to infinity. But it's perfectly OK as a reference point.charmedbeauty said:ok, but doesn't P.E only →0 since r can only ever→∞
from PE=-GmM/r
PE→0 as r→∞
Since r can never = ∞
how can it be that PE can =0
??
Doc Al said:Right. The PE never quite equals zero for finite r. PE goes to zero as r goes to infinity. But it's perfectly OK as a reference point.
On what basis would you say that a particle at the center of the Earth would have zero PE? What are you using as your reference point? Just because the gravitational force is zero doesn't mean that the PE is zero.charmedbeauty said:Ok thanks, but if the Earth is perfectly spherical with the mass evenly distributed, what would be the PE of a particle in the centre of the earth? I thought it should be zero, but are you saying that it does have a discrete amount of PE?
Doc Al said:On what basis would you say that a particle at the center of the Earth would have zero PE? What are you using as your reference point? Just because the gravitational force is zero doesn't mean that the PE is zero.
charmedbeauty said:the centre of the earth. using -GmM/r when r→0 i.e. as a particle gets closer to the centre of the earth. what does this mean its PE→?
is it undefined...or should PE→∞..for a point particle can it not be exactly in the centre of the Earth so that PE≠-GmM/0..ie PE≠∞?
You cannot apply the formula PE = -GmM/r for points within the surface of the earth. Instead, think in general principles: How much work against gravity would be required to raise a particle from the center of the Earth to an arbitrary point?charmedbeauty said:the centre of the earth. using -GmM/r when r→0 i.e. as a particle gets closer to the centre of the earth. what does this mean its PE→?
is it undefined...or should PE→∞..for a point particle can it not be exactly in the centre of the Earth so that PE≠-GmM/0..ie PE≠∞?
Doc Al said:You cannot apply the formula PE = -GmM/r for points within the surface of the earth. Instead, think in general principles: How much work against gravity would be required to raise a particle from the center of the Earth to an arbitrary point?