I am confused with some astrophysics stuff (esepically Q1), could anyone help me? I would really appreciate if you do. Please Register or Log in to view the hidden image! 1) Calculate the gravitational potential energy of the moon relative to the earth given that the distance between their centers is 3.94x10^8 m. Solution: Eg = -G(5.98x10^24)(7.35x10^22) / (3.94x10^8) Eg = -7.40x10^28J This is an example that I have seen. But I really really don't understand why Eg will have a negative value. (the moon is ABOVE the earth, right? So shouldn't the value of Eg be POSITIVE?) Where is the reference point of the Eg? (at the center of the earth?) For near earth surface case, Eg=mgh, and Eg of objects above the earth will be positive if you set the reference as ground level. 2) Calculate the change in gravitational potental energy for a 1.0-kg mass lifted 1.0x10^2 km above the surface of Earth. I got an answer of 9.6x10^5 J, but the answer in my textbook is 1.0x10^6J. I am having less confidence on this topic. Please Register or Log in to view the hidden image! Did I calculate anything wrong or is there a problem with the provided answer?
Consider what would happen if E[sub]g[/sub] was positive. Then the formula would read E_g = GMm/r What happens when r (the distance of the moon) increases? Eg becomes smaller, not greater, as it should. In the form given in the example, Eg becomes less negative, as r increases and thus Eg increases as r increases, just as it should as the Moon gets further from the Earth. In your second question, your answer and the textbooks are nearly the same (within 4%), so the difference is probably due to rounding choices.
Hi, 1) But the question says "Calculate the gravitational potential energy of the moon relative to the earth...", RELATIVE to the earth. Um...does that mean the zero Eg point is set on the earth's surface or the center of the earth? And why do we always want to make Eg to be negative, in general? (i.e. Eg=-GMm/r) Why don't keep it positive?
The question was worded poorly. They really only wanted to convey that you are to consider the Earth/Moon system in isolation. For any two body system, the zero potential is usually taken to be r=infinity. Then the gravitational potential represents the binding energy of the bodies.
Hi Kingwinner It sounds like you're being taught in a confusing way. Please Register or Log in to view the hidden image! First thing to realise is that energy is an observer dependent quantity in relativistic theories (including GR). This means different observers will generally not agree on energy values, and so you need to be precise in stating what your measurment is relative to. Second thing is that this very fact gives you elements of freedom. In general you're free to set zero points for potentials in any manner which suits you, as long as you are then consistent in your application. In the example provided above your reference points are set for you (the potential energy of moon relative to earth). Whether you call this potential positive or negative is again arbitrary, as long as you are consistent in your application (eg if vector quantities pointing away from earth are positive then those pointing towards earth are negative, etc). In general relativity the default convention is that zero potentials for a gravity well are set an infinite distance from the centre of mass. This is because an observer at infinity is an inertial observer and the field goes to zero there. The consequence of this convention is that gravitational potential energies are set negative relative to r=infinity, and kinetic energies are set positive. The sum of potential and kinetic energy for an object falling from infinity in the field is then zero at any point along its trajectory. Note that we could just as easily have set the potential relative to infinity as increasingly positive and the kinetic energy as increasingly negative, except that this would imply the object's velocity is complex. Setting the zero potential at infinity is counter-intuitive for beginning students, because for some reason at school you're normally taught to set the zero potential at the earth's surface. However it's neater to set the zero at infinity (and consequently set all potentials as negative) because it sums the universe's energy to zero.
Thanks for explaining! 1) So if we use the formula Eg=-GMm/r, the refernce point have to be at infinity because that's how to formual is derived, right? That is, when we use the formula Eg=-GMm/r, the gravitational potential energy becomes absolute, not relative......
Not quite. The reference point is taken at infinity by convention - sorta like a standard everyone agrees on and uses. You could change it to Eg = C - GMm/r, where C is some constant if you want a different reference point, but why bother? The formula takes its simplest form with a ref at infinity.
1) If I reword the question this way: "Calculate the gravitational potential energy of the EARTH relative to the MOON given that the distance between their centers is 3.94x10^8 m." Will the answer still be -7.40x10^28J? (i.e. same as the gravitational potential energy of the MOON relative to the EARTH?) And kevinalm suggests that the question is worded poorly, what should be the way of phrasing this question?
"Relative" usually means you're calculating the potential energy difference between two points, ie. the PE at one location minus the PE somewhere else. Where the moon is isn't the problem, but I have no idea what "relative to the Earth" would mean (I'm referring to the original question here). Compared to a point on the surface of the Earth? You weren't given its radius. Relative to the centre of the Earth? Then ΔPE would be infinite. I'm not sure how to precisely state "the moon's (conventional?) potential energy due to the moon's gravitational field." It probably wouldn't be that interesting either, since in practice its only PE differences anyone really cares about. "Absolute" potential energy doesn't really have a physical meaning.
But seeing the solution for question 1, it doesn't seem to me that they are finding the energy difference between the moon and the earth, which drives me crazy :bugeye:
If you look at the moon's "total" potential energy, you'd have to add up the potential it has due to the Earth's gravitational field + due to Jupiter's field + the sun + etc. They just meant for you to take the Earth's field into account, and that's probably what they meant by "relative to the Earth."
