Tagged Questions
1
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2answers
105 views
Negative potential energy of gravity
Does the negative potential energy in the gravitational field have to be considered in calculating the total mass of the system in question (because of $E=mc^2$)?
If so it seems to me that the ...
4
votes
1answer
68 views
Orbital mechanics and rocketry: Is it ever a good idea to intentionally lower periapsis?
tl;dr: Hohmann Transfer appears to be the optimal way to achieve a circular-to-circular orbit, but is it possible to lower the periapsis in order to achieve a more elliptical orbit with apoapsis at ...
0
votes
1answer
45 views
Gravitational potential energy
Consider two places next to each other: Place 1, where there is a gravitational field whereas Place 2 - there's no field.
Now if we lifted a box in place 1, it gains potential energy. Then, we move ...
0
votes
2answers
122 views
Measuring work done by gravity over non-constant gravitational acceleration
A question from an example from a MIT Classical Mechanics Lecture on Work.
Here's the given definition for gravitational potential energy (~32:00): "The ...
1
vote
1answer
302 views
Derivation of the self gravitational potential energy of a sphere
I have been searching on the Internet but have not found a derivation of the formula for the self gravitational potential energy of a sphere. Can someone show how to do this? I assume it involved 6 ...
2
votes
2answers
252 views
Lever Mechanics - How to formulate an ideal lever launch
Let's say I have a simple lever as shown below, and the lever is massless and the pivot is frictionless and there is no air resistance. I'm thinking the cradle for the projectile would have to have a ...
1
vote
3answers
253 views
What is the most efficient machine for translating gravitational potential energy of one mass into kinetic energy of a different mass?
As the question states, what is our current best machine for translating falling gravitational potential energy, such as a large weight, into launching a smaller projectile vertically? A lever? A ...
17
votes
8answers
994 views
Why are L4 and L5 lagrangian points stable?
This diagram from wikipedia shows the gravitational potential energy of the sun-earth two body system, and demonstrates clearly the semi-stability of the L1, L2, and L3 lagrangian points. The blue ...
4
votes
4answers
672 views
Does the mass of an object change as it moves away from the earth?
The mass of a helium nucleus is less than the mass of two isolated protons and two isolated neutrons. When the component hadrons are assembled, this mass is lost as energy ($E=mc^2$). This makes it ...
0
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3answers
553 views
Still trying to understand gravitational potential and Poisson's equation?
A week or so back I asked a question about the gravitational potential field
$$\phi=\frac{-Gm}{r}, \qquad r\neq 0, $$
and how to show the Laplacian of $\phi$ equals zero for $r\neq 0$? Eventually, ...
1
vote
2answers
160 views
Why no basis vector in Newtonian gravitational vector field?
In my textbook, the gravitational field is given by$$\mathbf{g}\left(\mathbf{r}\right)=-G\frac{M}{\left|\mathbf{r}\right|^{2}}e_{r}$$
which is a vector field. On the same page, it is also given as a ...
3
votes
1answer
409 views
Trying to understand Laplace's equation
I'm struggling here so please excuse if I'm writing nonsense.
I understand that the gravitational potential field, a scalar field, is given by $$\phi=\frac{-Gm}{r}$$
where $\phi$
is the ...
2
votes
1answer
277 views
Potential energy in a gravitational field
I've seen the following formula for the potential energy of a body in a gravitational field ($\rho$ is the density, $g$ is the gravitational acceleration):
$$ \rho g \int_E z dV $$
Can you please ...
4
votes
1answer
4k views
Why is gravitational potential energy negative, and what does that mean?
I usually think of gravitational potential energy as representing just what it sounds like: the energy that we could potentially gain, using gravity. However, the equation for it (derived by ...
