What is Gravitational potential: Definition and 388 Discussions

In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move an object to that location from a fixed reference location. It is analogous to the electric potential with mass playing the role of charge. The reference location, where the potential is zero, is by convention infinitely far away from any mass, resulting in a negative potential at any finite distance.
In mathematics, the gravitational potential is also known as the Newtonian potential and is fundamental in the study of potential theory. It may also be used for solving the electrostatic and magnetostatic fields generated by uniformly charged or polarized ellipsoidal bodies.

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1. Time slows down at lower gravitational potential

Common interpretation is that time slows down at lower potential. I wonder if people are simply saying for the time interval between two events at lower potential, it's smaller than what would be measured at greater potential ##d \tau < d t##. i.e. Clock at lower potential shows a time interval...
2. B Analogy to binding energy

Can I understand the relationship between binding energy and mass by comparing it to the relationship between kinetic energy and potential energy? When an object falls, its gravitational potential, a scalar value, decreases, and its energy is converted into kinetic energy. Even when a nuclear...
3. B Time dilation in a planet-moon system

In Wikipedia time dilation is considered: As far as I know, in a planet-moon system, the difference in elapsed time between a clock on the planet and a clock on its moon is calculated using GR/proper time, so it's not very obvious if/how the movement/velocity of the moon around the planet...
4. I Conservation of Energy in GR: A-B System Analysis

Assume you have a two particle system, A, which has a mass and gravitational pull of g, and B, an object with low mass, The system starts at time 0 with the distance between A and B being 0, A being at rest and B having enough kinetic energy to move it a distance r away from A, until time t all...
5. B Gravitational Potential Energy & Mass Change: Andrew's Question

If I start with two, otherwise isolated, masses M and m initially together and do work to separate them then the work done, I assume, goes into the gravitational binding energy between them. Will the system of mass M and m have increased in mass due to this in accordance with e=mc^2? I...
6. I Gravitational potential energy

Hello everyone! I noticed in the derivation of potential energy, Mr Lewin defined the gravitational potential energy of a mass m at point P relative to a much larger mass M. He says the potential energy of m at point P is equal to the work he would have to do to move the mass m from infinity to...
7. Gravitational potential energy traveling from earth to mars

My attempt: Let ##M_e## be the mass of the Earth and ##M_m## be the mass of the person. Let ##D_{EM}## be the distance from Earth to Mars and let ##R_e## be the radius of the earth. Defining these constants (leaving off units for brevity): Masses in Kilograms (G is not a mass but I'll leave...
8. I Image for increase in gravitational potential energy in radial field

A question to physicists: What sort of real world scenario / image would *best* depict the increase in gravitational potential energy in a radial field? Would a rocket traveling through the Earth's atmosphere suffice or are there better alternatives? This image would have to be relevant to the...
9. Misunderstanding of Gravitational Potential Energy

Here is my solution, which is correct. The tilt of the water at the top can be described in terms of ##x## and ##y## as ##y = \frac{2y_0}{L}x##. The height of the water at any given x is then equal to ##h + \frac{2y_0}{L}x## where ##x \in [-\frac{L}{2}, \frac{L}{2}]##. So the potential...
10. I Gravitational potential of an ellipsoid

There is a formula for the potential ##\varphi## outside of a homogenous ellipsoid of density ##\mu## in Landau\begin{align*} \varphi = -\pi \mu abck \int_{\xi}^{\infty} \left(1- \dfrac{x^2}{a^2 + s} + \dfrac{y^2}{b^2 + s} + \dfrac{z^2}{c^2+s} \right) \frac{ds}{R_s} \ \ \ (1) \end{align*}where...
11. Gravitational Potential In the Field Caused by Two Masses

I got (a) but have no idea about b. Potential fields aren't just additive all the time are they?
12. Gravitational potential energy question - normal force on us

Hi, If we are standing on the ground, the Earth applies a force equal to our weight to us, but why do we feel a greater force when we fall to the ground from a certain height? Our weight is the same along this small height because our mass and acceleration are the same and, even so, the normal...
13. Gravitational potential energy question -- Ojbect sitting on the Earth

Good day, If I consider my system to be an object and the earth, and the object is on the surface of the earth, then the system will have gravitational potential energy. Why couldn't I say that only the object (considering it as my system) has gravitational potential energy? Thanks
14. A Gravitational Potential Energy & the Equivalence Principle

First, in section 20.4, after listing all the things gravitational potential energy does not do, they say the equivalence principle forbids it being localized. I thought I understood the equivalence principle, but maybe I don’t. Any comments explaining that would be appreciated. Second, they...

16. Gravitational Potential Energy on an Incline

Hi, When regarding Gravitational Potential Energy, I know the formula is U=mgh. However, when the object is on an incline (say at an angle of 52 degrees) would it still be mgh or something else? (This isn't homework I simply was just curious).
17. A non-spherical Earth's gravitational potential?

hi guys i was reading a book on astrodynamics and was trying to understand the mathematical treatment of the Earth gravitational potential . i kinda understand the main idea , after reaching the following equation of the potential in terms of the Legendre polynomials : ##\alpha = r_{Q}/r##...
18. Gravitational Potential Energy

I know I just have to replace in the equation, I just want to know, is d=r=0.5 m or is d=2r, so r = 0.25 m ?
19. Gravitational Potential & Gravitational Potential Energy

Hi, I am confused about the negative aspect of these quantities. The definition in my book for gravitational potential is: "The work done to move a unit mass from infinity to a point in a gravitational field" I understand that the work done is negative because gravity is doing the work if you...
20. Difference in Gravitational Potential on the Moon

1. Since the gravitaional field strength is 1/6 of that on Earth: W=mg W=90*9.81/6 W=90*1.635 W=147.15 ~ 147 N 2. ∆Ep=mg∆h ∆Ep=90*1.635*50 ∆Ep=7357.5 J I do not now whether this method would be suitable and if I should have instead used the formula for gravitaional Potential, V grav=-Gm/r? 3...
21. Question about gravitational potential energy and angular motion

hello I would like some help with the first part of this homework. for the moment i have done this: E initial=m*g*h Efinal= 1/2 m*v ^ 2+1/2I*ω ^ 2 Ei=m*g*h+1/2I*ω ^ 2 Ef=1/2*m*v ^ 2 my doubt is with the potential energy since it confuses me when there is or not...
22. B Does E=mc^2 apply to gravitational potential energy?

I'm reading Schutz's A First Course In General Relativity and in chapter 5 he discusses an idealized experiment in which an object is dropped from a tower, then turned into a photon and sent back up to its original height. In classical mechanics we would say that as the object falls it loses...
23. Gravitational potential energy -- Why is it always negative?

the gravitational potential energy of a body at any point is defined to be negative of the work done by the conservative force(gravity in this case) from bringing it to that point from a given reference point. if the reference point is taken to be at infinity and the potential energy at this...
24. Gravitational potential energy formulas

m.g.h = (GMm)/r how can we prove that mgh is potential energy and both equal to that?
25. Why gravitational potential energy is a system property?

Spring has more potential energy when it is compressed or stretched from its initially balanced state. As external work is done, it stores energy in the form of potential energy. Here, we know energy is stored in spring but For the Earth-ball system, where the energy stored?
26. Work done to reach the point where the gravitational potential is zero

Hi there I have been attempting the parts to this question and I'm finding some trouble on how to answer the last part which is d)iii Here is what I have done for the rest of the parts and what I think I should start off with in part d)iii Thanks!
27. Calculating Gravitational Forces and Potential Energy Using Newton's Laws

For the first part, I considered the Force acting on it by all charges as given by $$\vec {F} = \Sigma_{j} \frac{m_{i} m_{j}}{\left(r_j - r_i \right)^{1.5}} \vec{r_j} - \vec {r_i} = \Sigma_j m_i \vec {g_j}$$ Where ##\vec{g_{j}}## represents gravitational acceleration of ##m_i## due to jth mass...

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29. How to relate the gravitational potential energy zero to the axes?

(Throughout all my post, I will refer to “gravitational potential energy” just as “potential energy”) Hi! I have this confusion about when is potential energy positive/negative and how it is related to how we define our axes. I think it is easier to understand my confusion with the following...
30. How does gravitational potential energy work?

Gravitational energy is the potential energy a physical object with mass has in relation to another massive object due to gravity, so, does an object outside a gravitational field have no gravitational potential energy? For example, the Earth is 4.5 billion years old, so it's gravity stretches...
31. I Gravitational potential gradient in accelerated reference frames?

Hi, Could you please help me to clarify the following problem? In the gravitational field of a mass, the force on a body in steady state comes from the gradient of the gravitational potential - or the gradient of speed of time. But what about accelerated reference frames? I assume that there is...
32. Gravitational Potential: How to know where the max GP is located?

By using the equation for the Gravitational Potential -GM/R. It is understand that the max Gravitation Potential would be at infinity point. - G(100M)/22R-(-GM/22R) would be the maximum Gravitational Potential... I guess... Then what would be the next step to find the distance?
33. I Relativistic mass and gravitational potential

Hello everyone, Any object has a gravitational potential energy as a function of the distance from the Earth (R). Does this energy depend only on the rest mass of the object; or one must take into account it's relativistic mass? In other words, if we imagine two identical bullets on the top...
34. Gravitational Potential Energy questions near the surface of a planet

Homework Statement The change in gravitational potential energy of a mass m as it moves from the surface to a height h above the surface of a planet of mass M and radius R is given by: ΔPE= GMmh/R(R+h) a) show that when h is very small compared to R , this approximates to the more familiar...
35. Does the gravitational potential energy affect the burning of two logs?

Homework Statement Let's consider two wooden logs. We burn the first one at the base of the mountain and the second one on the peak. Which one is releasing more energy? Do they release the same amount of energy? Does the potential energy affect the burning Homework Equations ## \Delta H =##...
36. Gravitational Potential Reference Point

Can someone please show that calculation of gravitational potential energy at a point R+h from the centre of the Earth by choosing the centre of the Earth to be at zero potential. Here R is the radius of the Earth and h is not very small wrt to R
37. I Gravitational time dilation - acceleration vs potential

What I know gravitational time dilation (based on GRT) is dependent on gravity potential and not on gravitational acceleration. That would mean, that for example in center of Earth is the gravitational acceleration zero, but the gravitational potential is bigger than on the surface of Earth...
38. Gravitational Potential Energy Project Thor

Homework Statement Project Thor is a proposed (and terrifying) weapon system where a cylindrical tungsten rod (19600 kg m3 ) about the size of a telephone pole (6.10 m long and 0.300 m in diameter) is dropped from Earth orbit. Imagine you dropped one of these from an orbit 10,000 km above the...
39. I A minus sign in the gravitational potential

So we have the Newtonian gravitation potential given by ##\phi_M(r)=-GM/r##, and in class the teacher said that the Newtonian force is given by ##F_m = -m\nabla \phi_M(r)##. Now, I was thinking about what was taught in UG or high school, isn't the force should be ##F_m = GmM/r^2##, if I plug...
40. Deriving gravitational potential energy -- mistake

Homework Statement Hi I'm attempting to derive the gravitational potential energy of a point mass (##m##) that's moving from infinity to a point r' inside a gravitational field produced by a another mass ##M##. For simplicity I treated it as a one dimensional case. The problem I get is that the...
41. Velocity needed to escape gravitational potential

I am solving a problem where I need to decide if an asteroids velocity is high enough to escape the planets gravitational pull. The way I did it was use conservation of energy and angular momentum to find an expression for the radial velocity and show that it remains positive as r tends to...
42. Gravitational potential energy of a coupled pendulum

Homework Statement I'm trying to solve problem a problem of complete energy of doubled pendulum (2 mathematical pendulums connected by a string). For a kinetic energy I would get (1/2) J(w_1)ˆ2 + (1/2) J(w_2)ˆ2 and for a potential energy of a spring (1/2) k (ϕ_1-ϕ_1) What about gravitational...
43. Where is the gravitational potential energy?

I am confused on where the gravitational potential energy is in this solution. Thank you
44. Gravitational potential energy and continuous matter

The gravitational potential energy of two massic points ##P_1## and ##P_2## with respective masses ##m_1## and ##m_2## is given by $$U = -G \frac{m_1 m_2}{|| P_2 - P_1 ||}$$ Now I was wondering how this formula could be applied to continuous matter. Let us imagine a very simple case where we...
45. Calculating Gravitational Potential

Homework Statement I was going through a worked example in my textbook to gain a better understanding but after I had a go myself it is the opposite to what I have calculated. I have attached the worked example which asks you to calculate the gain in gravitational potential moving from a point...
46. Gravitational potential for various matter configurations

Homework Statement Consider the Earth as 1. with a constant density of matter, 2. as a thin shell empty sphere and 3. with a constant linear density of matter ##\rho(r) = \rho_{0}r##. In all cases, calculate the gravitational potential and the gravitational field everywhere and make a...
47. GCSE Physics : Temperature & Gravitational potential energy

Homework Statement Q7. Some lead shot with a mass of 50 grams is placed into a card board box the distance from one end to the other being 1m. The ends are sealed with rubber bungs in order to prevent the lead shots from falling out, the tube is rotated so the lead shots fall down from one end...
48. Work, Gravitational Potential and Kinetic Energy, Spacecraft

Hi guys. I'm new to this forum so I'm not sure if I'm posting this in the right place or correctly, but I was totally stumped on a Physics 12 question as I was studying for my exam. The question is: An explorer spacecraft is descending towards Mars using a rocket engine for braking. The...
49. Gravitational Potential Energy-Work (ΔU) Question

Homework Statement The string (in the pic) is L=120 cm long,has a ball attached to one end,and is fixed as its other end.The distance d from the fixed point end to a fixed peg at point P is 75.0cm.When the initally stationary ball is released with the string horizontal as shown,it will...
50. Change in gravitational potential below the surface of the Earth

Homework Statement Hi, Infinitely far away from a mass-->gravitational potential is zero. As get closer-->becomes negative. At surface-->it is the smallest value of r, i.e. the radius of the mass, hence the most negative value for gravitational potential. But as you go below surface of Earth...