Tagged Questions
7
votes
2answers
171 views
No closed orbits for a Newtonian gravitational field in 4 spatial dimensions
We are supposed to show that orbits in 4D are not closed.
Therefore I derived a Lagrangian in hyperspherical coordinates
$$L=\frac{m}{2}(\dot{r}^2+\sin^2(\gamma)(\sin^2(\theta)r^2 \dot{\phi}^2+r^2 ...
0
votes
1answer
108 views
Non-relativistic Kepler orbits
Consider the Newtonian gravitational potential at a distance of Sun:
$$\varphi \left ( r \right )~=~-\frac{GM}{r}.$$
I write the classical Lagrangian in spherical coordinates for a planet with mass ...
2
votes
2answers
150 views
Is the gravitational constant G a minimum value in some sense?
Assume a central body of mass $M$, and call $a$ the acceleration of a test
body at a distance $r$ due to any interaction whatsoever with the central
body. Is is correct to say that the ratio $a r^2/ ...
2
votes
1answer
172 views
Do Lagrangian points actually maintain a fixed distance?
I was reading on up Lagrangian points and the restricted three-body problem.
From what I was able to tell, the Lagrangian points are 5 points in a two-body system such that a third body would be ...
4
votes
3answers
607 views
Hanging chain in a planet's gravitational field
The curve for a chain hanging between two poles in a uniform gravitational field is known as the catenary.
Is there known an expression for the curve of a hanging chain on a planet of mass $M$ which ...
