Gravitational potential Definition and 389 Threads

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. M

    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...
  2. U

    Density and circumference relationship? From Example in book

    Homework Statement Example 5.3 from The Marion Thornton book (fifth edition) of Classical Dynamics states the following problem: Consider a thin uniform circular ring of radius a and mass M. A mass m is placed in the plane of the ring. Find a position of equilibrium and determine whether it...
  3. R

    Gravitational potential between two massive particles....

    If my understanding is correct, all particles are sources of gravitational fields (albeit minor ones), and the gravitational potential energy between two bodies is given by: U = -GMm/r So, if we have two Z bosons (or any other bosons with mass but no repulsion due to charge) which are traveling...
  4. Pratik89

    Elastic and gravitational potential energy

    X has a mass of 55 kg and hangs from a rope. As a result of this the rope stretches by 0.6 m. Calculate the energy stored in the rope as a result of stretching. Solution: F = kx and E = 0.5x^2. Using this fetches the answer as 161.5 However, the change in potential energy (calculated using mgh )...
  5. B

    Gravitational potential energy problem

    Homework Statement Question :- Two stars, each of a solar mass and radius ##10^7 m## are at a distance of ##10^{12} m## from each other. Find the speed of each star before collision if initial speed is negligible. Homework Equations $$V(r) = {-G Mm \over r}$$ The Attempt at a Solution...
  6. B

    What does gravitational potential mean ?

    Gravitational potential energy between 2 objects is ##-{G\times M\times m\over R}.## My question is, does the value of this equation of this equation mean total gravitational potential energy of both objects ? i.e, say the gravitational potential energy of object with mass ##M## is ##p## and...
  7. Elvis 123456789

    Gravitational Potential due to spherical shell

    Homework Statement What is the gravitational potential both inside and outside a spherical shell of inner radius b and outer radius a? Homework Equations φ = ∫g⋅da = -4πGMencl g = d∅/dr in the r hat direction The Attempt at a Solution I can get as far as getting the gravitational field for...
  8. L

    Gravitational potential energy

    Homework Statement A teeter toy is composed of a massless central stick of length L and two massless sticks of length l attached at angles α, each with a mass m at the end (see the figure). We imagine tilting the toy by an angle θ from the upright position. a) Find an expression for the...
  9. victorhugo

    Gravitational Potential Energy & L.C.E. Questions

    1. A comet that passes by Earth has GPE, which will be all lost if it begins to fall towards Earth. If it's shot back up, it will now start with Ek and finish with a higher GPE. Now, what exactly is this GPE? if energy cannot be created or destroyed, but transformed, where does it get stored at...
  10. ThinkerCorny

    Understanding gravitational potential due to spherical shell

    I know that gravitational potential due to uniform sherical shell at a point outside the shell is equivalent to the potential due to particle of same mass situated at the centre and got proof here http://m.sparknotes.com/physics/gravitation/potential/section3.rhtml. But I was looking for more...
  11. donaldparida

    Gravitational potential energy conflict

    I know that when an object A a does positive work on another object B, object A loses energy and object B gains energy(there is transfer of energy from object A to object B) and when object A does negative work on object B, it gains energy and object B loses energy(there is transfer of energy...
  12. t_r_theta_phi

    I Gravitational Potential Energy: 1/2 Factor Explained

    I am currently reading Gravitational Curvature by Theodore Frankel. In the derivation of Einstein's equations in chapter 3, he states that the gravitational potential energy of a blob of fluid is ∫B½p0U√gVdx where the integral is a volume integral, p0 is the rest energy density and √gvdx is...
  13. T

    What Is the Work Done on a Body Taken from Earth's Surface to Infinity?

    Homework Statement A body of mass m is taken at a constant speed from the surface of the Earth (radius = Re) to infinity. (a) What is the work W1 done on the body in the process? (b) If m is taken from a distance r > Re to infinity, how much work W2 is required? (c)Which quantity is larger, W1...
  14. B

    I Multiple time derivatives of gravitational potential

    Hello! Let's say our gravitational potential is (as usual for 2 body), $$a = -\frac{\mu}{r^3} \mathbf{r}$$. Then the gradient of this is G, $$\frac{\partial G}{\partial \mathbf{r}} = G = \frac{\mu}{r^3} [3 \hat{\mathbf{r}} \hat{\mathbf{r}}^\top - I] $$ Now if we take two time derivatives of...
  15. e2m2a

    I Gravitational potential energy and rest mass

    Does the rest mass of an object increase when it acquires gravitational potential energy, and if so, is this the reason why Einstein believed that the inertia of a mass increases in the presence of other masses?
  16. S

    Kinetic energy and Gravitational Potential Energy

    Hi Guys,When we are finding the wasted energy when something is dropped a tower, we do this: mgH-0.5mv^2 My question is, does the velocity of the kinetic energy have to be vertical component, or can it be the impact velocity when it hits the ground? Thanks
  17. A

    Gravitational Potential Energy

    Hello, I do not quite get this. Can anyone provide examples? " We may feel that it takes a force greater than the weight of the object being raised to lift it upwards, but it is not so. Provided the force is equal to the weight, the object will move upwards at a steady speed. "
  18. C

    Distance in Electric versus Gravitational potential energy

    Homework Statement Consider the equations for electric potential energy: and gravitational potential energy: GPE=m*g*h In the case of GPE, the potential energy increases as the distance between the two objects increases. This makes sense (to me), as the greater distance between the Earth...
  19. A

    Gravitational potential energy

    Suppose the mass of planet is" M" and there is body in its surface whose mass is "m" and the field strength is "g" . If the body is thrown 1800 m then Gravitational Potential energy = mg(1800). My question is why can't we use formula GPE= GMm/x ? This is also the formula for gpe but why...
  20. R

    Gravitational Potential Energy of a Sphere

    Homework Statement Homework Equations ΔPE = G × M₁ × M₂ (1/Ri - 1/Rf) where G = gravitational constant M₁ = mass of one object M₂ = mass of the other object Ri = initial distance Rf = final distance ΔPE = -ΔKE The Attempt at a Solution My solution is v = 2√(GM/d). I am making sure it is...
  21. S

    Simple gravitational potential energy

    Homework Statement A 400-N child is in a swing that is attached to a pair of ropes 2.00 m long. Find the gravitational potential energy of the child-Earth system relative to the child’s lowest position when (b) the ropes make a 30.0° angle with the vertical Homework Equations Ug=mgy The...
  22. A

    Graphs of Gravitational Potential and Field Strength

    Hi all, I am very confused about the graphs of gravitational potential and gravitational field strength... I know that both gravitational field (g) and electric field strength (E) are negative gradient of their corresponding potential (Vg and Ve). If so, shouldn't g and Vg graph look very much...
  23. iamazombie911

    Gravitational Potential Energy

    Homework Statement Two neutron stars are separated by a distance of 4.80 E 10 m. They each have a mass of 3.60 E 30 kg and a radius of 1.30 E 5 m. If they are initially at rest... How fast is each star moving when their separation has decreased to half its initial value? How fast is each star...
  24. U

    Gravitational Potential Energy in orbit

    This pertains to a homework question but I get the concept of PE or U = -GmM/a for an elliptical orbit. I also understand the derivation of the total energy of an object in an elliptical orbit as E = -GmM/2a. However, I have a homework question that asks for the ratio of an object's kinetic...
  25. N

    What is the gravitational potential energy of the box relative to the floor?

    Homework Statement An 18.5kg box is slid up a 5.6m long ramp that makes an angle of 33 degrees with the floor. What is the gravitational potential energy of the box relative to the floor? Homework Equations Ek = 1/2mv2 The Attempt at a Solution My teacher gave me an answer of 550J, but I'm...
  26. N

    How to prove V=-(GM)/r without applying calculus?

    In my textbook, gravitational potential , V=-(GM)/r, has been evaluated by applying calculas. I want to evaluate it with another simple way except calculas. I want to learn the simplest way to evaluate it in such a way that even a boy of 12 years old can understand it without facing any difficulty.
  27. Gian Lukmana

    Gravitational potential energy of a cylinder to a particle

    Hi everyone I'm kinda new here, your support will really be appreciated ! :D 1. Homework Statement Let's say the cylinder has radius R, and height T. Homework Equations U = ∫GmdM/x The Attempt at a Solution My attempt is shown in the picture, I took a tiny element of the cylinder with...
  28. M

    What is a potential? Specifically, an electrostatic potential

    Homework Statement How do we define an electrostatic potential? My teacher tried to explain it through teaching us gravitational potentials, and I have presented what I came up with under '3.The attempt at a solution'. Please see below and thanks in advance for any help in clarifying whether my...
  29. B

    Gravitational potential energy

    Homework Statement Why is the gravitational potential energy of a ball a distance r from the center of the Earth negative? Homework Equations U_\text{grav}(r) = - GMm/r [/B] (To me, this makes sense because gravity is an attractive force and bodies will want to minimize the distance between...
  30. F

    Good values for gravitational potential

    In the context of a project, I had to solve numerically Poisson equation with cylindrical coordinates. I put here results for z = 0 on a 3D mesh 256x256x256. Below 1 figure representing the final solution (in absolute value) in the case of a galaxy; I use the CGS units for the potential. I...
  31. K

    Hydrostatic pressure and Gravitational Potential Energy

    So say I had a glass of water on a table ,with the glass filled to the top. The bottom of the glass, the water would have a higher pressure than the top of the glass. This is the concept of hydrostatic pressure etc. But how does GPE fit into all of this? Does the water at the top of the glass...
  32. C

    Question: Gravitational Potential Energy in a Ball-Earth-Moon system?

    Hello, here's a questions I was wondering if any of you could solve. I don't have the exact numbers, but the scenario is this: a guy standing on the Earth throws a ball upwards and catches it a few seconds later. How does would affect the potential energy and/or mechanical energy of the...
  33. E

    Thin Rod Gravitational Potential and Field Vector

    Homework Statement I am having a hard time understanding where to begin with this problem. Here it is: Consider a thin rod of length L and constant density n that lies on the x-axis with endpoints at x=0 and x=L. (i) Find a formula for the gravitational potential Φ = Φ(x) at the (variable)...
  34. T

    Calculating Gravitational Potential

    Homework Statement :[/B] "Calculate gravitational potential at point Z, which is 8.10 x 107m away from a planet of mass 1.08 x 1023. " (This point is between the planet and a moon, where the gravitational field strength is zero. I'm not sure if that makes a difference. The moon's mass is 4.8 x...
  35. S

    Dot product in the Gravitational Potential Energy formula

    This is the gravitational potential energy formula $$U = -\int_\infty^r\vec{F}_\text{field}\cdot d\vec{r}$$ If r vector's direction is form infinity to r, then it means it has same direction as Gravitational Force. So cos0=1 But after multiplication there is a negative sign here: "-GMm" $$U =...
  36. H

    Dependence of gravitational potential

    I am reading a textbook about potential theory, it mentions that a uniform sphere has 'dependence' on its gravitational potential, in terms of spherical harmonics. [ite I don't understand the term dependence? What does this mean exactly? Cheers
  37. C

    E=mc^2, Gravitational Potential & Energy Balance

    If two masses that are separated by a distance are created from pure energy using the equation E=mc^2, where did the gravitational potential energy between them come from? Does this mean the speed of light isn't really constant, and must be changed very slightly to accommodate it? Could it be...
  38. NotZakalwe

    Gravitational Potential of Hanging Cord

    Homework Statement A uniform cord of length .25 meters and mass .015 kg is initially stuck to a ceiling. Later, it hangs vertically from the ceiling with one end still stuck. What is the change in gravitational potential energy of the cord with this change in orientation?Homework Equations Ug...
  39. SnakeDoc

    Gravitational Potential energy Problem

    Homework Statement A projectile is fired vertically from Earth's surface with an initial speed of 3.1 km/s. Neglecting air drag, how far above the surface of Earth will it go? Homework Equations KF+UF=KI+UF U=-G(M1m2)/r2 K=1/2mv2 mass of Earth = 5.972E24 radius of Earth = 6371km G=6.673E-11...
  40. R

    Definition of gravitational potential

    Homework Statement The definition of gravitational potential at a point in my textbook is "the work done per kg to move a small test mass from infinity to that point" I am having difficulty grasping this concept, how is work done bringing an object closer to earth?? shouldn't work be done...
  41. Calpalned

    Gravitational potential energy

    Homework Statement For a satellite of mass ##m_s## in a circular orbit of radius ##r_s## around the Earth, determine its kinetic energy K. Homework Equations ## K = \frac {1}{2}mv^2 ## Gravitational potential energy ## U(r) = - \frac {GmM_E}{r}## The Attempt at a Solution My answer is ## K...
  42. W

    Gravitational Potential Energy Question

    Homework Statement [/B] Calculate the gravitational potential energy of the interacting pair of the Earth and a 23kg block sitting on the surface of the Earth. You would need to supply the absolute value of this result to move the block to a location very far from the Earth (actually, you...
  43. M

    Gravitational potential energy: derive expression for energy

    Homework Statement Part A: Derive an expression for the energy needed to launch an object from the surface of Earth to a height h above the surface. Part B: Ignoring Earth's rotation, how much energy is needed to get the same object into orbit at height h? Express your answer in terms of...
  44. D

    Gravitational potential energy problem

    Homework Statement A broken spaceship is located h=10 km above the center of a large circular thin sheet of unknown dust. The sheet has a radius of R=106 km and a density of σ = 7*1011 kg/m2. The spaceship and the dust attract each other due to the gravitational force. a) Find the initial...
  45. julianwitkowski

    Gravitational Potential Energy of a fall

    In this case the height of the fall is far to high above Earth to be use PE=mgh. So I'm trying to integrate the inverse square gravitational force over distance. ##\int \frac{GmM_e}{r^2}dr## So I'm confused with respect to another object, specifically the moon, if the max height of the fall...
  46. J

    Gravitational Potential Energy Sign

    I understand that GPE is negative, but it does not come out this way when i try to derive it. I took the change in potential energy in bringing a particle from an infinite distance to a distance of b from another particle. ## \Delta U = - \int \vec F \cdot d \vec r ##. Since the...
  47. V

    Integration constants, gravitational potential of sphere

    Homework Statement So I'm calculating the gravitational potential of a sphere at at point P. R = radius of sphere, r = distance from center of sphere to point P. I'm looking at two scenarios; r > R (1) and r < R (2). So I have the following integral: \begin{equation} V(r) = \int...
  48. N

    Gravitational potential energy of a retaining wall

    Homework Statement Forty 2.0kg blocks 20.0cm thick are used to make a retaining wall in the backyard. Each row of the wall will contain 10 blocks. You may assume that the first block is placed at the reference level. How much gravitational potential energy is stored in the wall when the blocks...
  49. C

    Gravitational Potential (problems with definition)

    I tried to get the potential from the potential energy and I get a positive sign for potential...! I cannot find what I did wrong. - Gravitational force is conservative so its work W is symmetrical to the change in potential energy U. - Potential is the work done by gravitational force, per unit...
  50. pyman999

    Gravitational Potential at a Midpoint: What is the Solution?

    Homework Statement Homework Equations g = G*M / r^2, where g is the gravitational field strength, G is the gravitational constant, M is the mass of the attracting body, r is the distance from the center of mass of the body. V = -G*M / r, where V is the gravitational potential. The Attempt...
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