All Questions
15
questions
-2
votes
1
answer
75
views
Potential energy with different heights [duplicate]
If system consists of earth and ball and ball is dropped from height $h_i$ to $h_f$, then:
$\Delta U = -(W_{earth} + W_{ball})$ ($W_{ball}$ can be neglected since it's small)
$\Delta U = -(-mg(h_f - ...
- 1
2
votes
0
answers
64
views
Most stable shape if Newtonian gravity was proportional to $r^\alpha$
Consider lots of mass in isolated 3D space, close to each other. Consider that only the gravitational force (Newtonian) exists. Also consider that there is no rotational motion.
It is evident that a ...
- 221
0
votes
2
answers
3k
views
Gravitational potential energy inside of a solid sphere [duplicate]
I am self-studying classical mechanics. I came across a problem which required me to calculate the gravitational potential inside of a sphere. I found in one of my textbooks that the potential energy ...
- 23
0
votes
0
answers
31
views
What's the difference between Potential energy ($mgh$) and gravitational potential energy ($-\frac{GMm}{r}$)? [duplicate]
Yeah one is for measuring potential energy between the objects of two masses $M$ and $m$
We recently started studying about gravitation and I'm really confused when swtiching back and forth, or can we ...
1
vote
3
answers
963
views
Why can gravitational potential energy be expressed both as $mgh$ and $-GMm/r$? [duplicate]
In these two different equations for the same (?) thing, not only is one directly proportional to height and one is inversely proportional to height, but they contain completely different variables, ...
1
vote
1
answer
199
views
Gravitational Binding energy of a sphere of 2 uniform densities
So I know that the gravitational binding energy of a sphere of uniform density can be given by:
$$U=-\frac{16}{3}G\pi^2\rho^2\int_0^Rr^4dr$$
Which if integrated gives:
$$U=-\frac{3GM^2}{5R}$$
As ...
- 269
2
votes
2
answers
235
views
Analogy between gravitational binding energy and the binding of Atoms
When atoms bind together, their total energy is less than each individual's energy. When planets come together, their total energy is also less (i.e. nature of attractive force). The mass of each ...
- 109
0
votes
2
answers
55
views
What is source of Earth's potential energy when an object is raised to a height from Earth?
If a ball is lifted against gravity, the work we do is stored as potential energy in it. Simultaneously earth too develops the same amount of potential energy due to the height of which the object is ...
- 662
1
vote
1
answer
2k
views
Gravitational potential at the centre of Earth [duplicate]
Why does gravitational potential at the centre of the Earth is finite i.e. $V_c=\frac{3}{2} V_s$, as at the centre $r$ becomes zero so applying $V = \frac{GM}{r}$ the result must be infinity.
- 149
2
votes
6
answers
6k
views
Does an object at the center of the Earth have potential energy?
"Potential energy: The energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors."
in other words, I think that potential ...
- 21
1
vote
2
answers
680
views
Accurate Equation for Earth's Gravitational Binding Energy
This is a relatively important question for anyone who can answer it. I am trying to find the equation that accurately solves for Earth's Gravitational Binding Energy. The information below is from ...
- 273
1
vote
2
answers
160
views
Zero-level of combination of $1/r$ and $r^2$ potential
I am solving a problem which involves a central big mass $M$ and around it a spherically symmetrically distributed mass of constant density $\rho$.
The force on a mass a distance $r$ from the centre ...
- 683
2
votes
2
answers
2k
views
What are the gravitational binding energies of giant planets?
What are the gravitational binding energies of the planets in our solar system? In particular, interested in the giant planets: Jupiter, Saturn, Uranus, and Neptune. Ideally the information would be ...
- 756
0
votes
3
answers
221
views
What is the definition of potential energy? [duplicate]
I have problems with this equation: $$U_G ~=~ G\frac{m_1m_2}{r}.$$
It's for potential energy of say something placed on Earth.
But it intrigues me. $r$ is the distance from the very center of the ...
- 1,361
18
votes
2
answers
1k
views
Is it possible to prove that planets should be approximately spherical using the calculus of variations?
Is it possible to use the Lagrangian formalism involving physical terms to answer the question of why all planets are approximately spherical?
Let's assume that a planet is 'born' when lots of ...
- 4,747