2
votes
3answers
74 views

How come we talk about gravitational potential energy and not gravitational potential?

With regards to gravity the equation learned is $$U=-\frac{GMm}{r}$$ And the relationship to force is $$F=-\frac{dU}{dr}$$ In electrostatics we instead talk about electric field and electric ...
0
votes
1answer
32 views

Calculating change in gravitational potential energy [closed]

A satellite mass $500\ kg$ is elevated from altitude $10000\ km$ to altitude $20000\ km$. Radius of earth is $6378\ km$. Mass of earth is $5.97 \cdot 10^{24}\ kg$. Gravity is given to be $9.81\ m/s $ ...
-3
votes
3answers
95 views

Why airports are generally near sea? [closed]

The generic way to measure the height is from the sea-level. If the airport is near the sea i.e. not at a very height from the sea, then the fuel required to make the air-plane above the sea level ...
1
vote
0answers
52 views

Gravitational potential energy and Center of Mass

I've been reading about the Nordtvedt effect, and how Gravitational Binding Energy (GBE) affects total mass. According to the WP article, experimental evidence rules out the existence of this effect. ...
1
vote
2answers
99 views

Two expressions for potential energy in the gravitational field of the earth

Let $M$ be the mass of the earth, considered as a point mass, then the potential energy of a point with distance $r$ away from the center (assume $r > \textrm{radius of earth})$ is $$ U(r) = ...
0
votes
1answer
83 views

Computing average force exerted by ground when jumping

Problem: A man of mass $m$ jumps vertically into the air from a sitting position in which his center of mass (CoM) is at a height $h_1$. When his feet are just about to leave the ground his CoM is at ...
2
votes
1answer
115 views

Loss of gravitational potential energy in an infinitely far object

Now consider I went into a rocket which goes an infinite distance far from earth. By infinite I mean very far. The gravitational attraction between me and the earth will significantly decrease and ...
0
votes
1answer
67 views

Statements about gravitational potential energy contradicting intuition?

So in my textbook I am told: two masses have gravitational potential energy because work had to be done in order to move one the masses form a position very far away (lets say infinity) to the ...
5
votes
2answers
122 views

What is the energy required to create mass of m at a height of h above the Earth?

What is the energy required to create mass of m at a height of h above the Earth? Is it $E= m c ^2$ or $E = mc ^ 2 + mgh$ ? Let's reverse the process also. If you convert mass $m$ at $h = 0$ to ...
0
votes
2answers
344 views

How does potential energy work in the context of objects in space?

It's said that potential energy is "energy of position." If an object is sitting on a shelf five feet above the floor, its potential energy can be thought of as equal to the amount of energy that ...
7
votes
1answer
542 views

Does potential energy in gravitationall field increase mass?

I was just taught (comments) that any type of energy contributes to mass of the object. This must indeed include potential energy in gravitational field. But here, things cease to make sense, have a ...
1
vote
2answers
270 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 ...
6
votes
1answer
232 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 ...
-1
votes
1answer
79 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
318 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
565 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
572 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 ...
21
votes
8answers
3k 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 ...
3
votes
4answers
2k 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 ...
1
vote
3answers
1k 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
299 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 ...
4
votes
1answer
917 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
433 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 ...