All Questions
4
questions
2
votes
2
answers
2k
views
How to calculate eccentricity of a planet via energy?
The relative distance of a planet moving around the sun is found to be:
$$r(\varphi) = \dfrac{\kappa}{1+\varepsilon\,\cos(\varphi)} \quad \text{where} \quad \kappa = \dfrac{L^2}{G\,{m_p}^2\,m_s} \quad ...
- 462
0
votes
0
answers
60
views
Third Kepler's Law and Collision [duplicate]
I have to solve the following problem:
Two particles of masses $m_a=m$ and $m_b=2m$ interact by gravitational forces
$$\vec{F}_{ab}=-G\frac{m_am_b\vec{r}}{r^3} \; ,\qquad \vec{F}_{ba}=-\vec{F}_{ab}$...
- 162
2
votes
1
answer
366
views
First integral of the Kepler problem
Consider the motions of a bounded particle which is under the influence of the
gravitional interaction of a second particle fixed at the origin
$$
\ddot q = -\nabla V(q)
$$
where $V(q) = - \frac{\mu}...
- 165
1
vote
3
answers
1k
views
Relationship Gravitational Potential and the Tangential Velocity of a Satellite
So gravitational potential is given by $V(r)={\frac{GM}{r}}$
and the tangential velocity of a satellite is the square root of
$V$, i.e. $\sqrt V$. So how do these two relate, if at all?
