All Questions
58
questions
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Find eccentricity of orbit given the velocity and the semi-major axis
Is it possible to calculate eccentricity of orbit knowing only the semi-major axis and the velocity of both celestial bodies? If not, what other additional information is required.
Does the fact that ...
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0
votes
1
answer
48
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Speed of satellite in elliptical orbit [closed]
A satellite $S$ orbits a planet of mass $M$ in an elliptical orbit. At perihelion, $S$ has a tangential velocity of $v_1$ and is distance $r_1$ from the planet. At aphelion, $S$ has a velocity of $v_2$...
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1
vote
1
answer
78
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Two bodies orbiting around barycenter
There are two bodies with masses $m_1$ and $m_2$ orbiting around barycenter. Distances to both bodies from barycenter are $r_1$ and $r_2$ . First body has known velocity $v_1$ as on the picture :
My ...
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1
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46
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How to add kinetic energy to gravitational energy to obtain total energy?
Cambridge Pre-U 9792/03/M/J/22
Examination question: What is the total energy E of the binary star system?
Given: The kinetic energy of star X is $E_x = \frac {2GM^2}{9D}$
Working:
$E_Y = \frac{GM^2}{...
5
votes
3
answers
249
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What am I doing wrong? An easy gravity problem
The following problem is giving me a headache:
Halley's comet follows an elliptical orbit around the sun. At perihelion, its distance from the sun ($r_P$) is $8.823 \cdot 10^{10}$ metres. At aphelion,...
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1
answer
39
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Angular Momentum or Gravitation question [closed]
Question: If the earth suddenly shrinks to $\frac{1}{64}$th of its original volume keeping mass same, the period of rotation of earth becomes $\frac{24}{x}$ hours, what is $x$?
So basically, why can’...
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-1
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1
answer
92
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1
vote
1
answer
77
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Kepler third law for circular orbits [closed]
This question may be uber trivial, but it has been stuck in my head for a while.
Kepler's third law states that the period of the orbit $T$ is related to the semi-major axis $a$ though
\begin{equation}...
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3
votes
3
answers
2k
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Deriving energy for elliptical orbit
So I wanted to derive the total energy for an elliptical orbit, $E = -GmM/2a,$ and while I was doing it, I ran into this hurdle. So at the closest point to the focus, the orbiting object is at a ...
0
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49
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How does this trick work in solving the 2-body central force equation of orbit?
I am working on understanding the derivation of Kepler orbits via section 8.5 of John R. Taylor's classical mechanics textbook, and one small detail has been tripping me up.
The equation being solved ...
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1
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54
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Circular motion of planet around star
The question says that the planet moves in a circular orbit around the massive star. But the graph says that velocity of the star wrt the COM of star-planet system varies with time. But my confusion ...
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1
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Can I please get the proofs for different trajectories of a satellite when projected at different velocities? [duplicate]
I recently came across a question about the trajectories of satellites, I have tried many resources for the proofs but couldn't find them.
For example, a satellite will have an elliptical orbit if (...
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votes
1
answer
97
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Free fall and the period in keplerian motion [closed]
What is the time it takes for a free fall compared with keplerian time period?
Is it half the orbital period or a quarter?
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-1
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1
answer
66
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How to find equatorial orbit pericenter position in 2D if I know $\mu$, $a$, $e$, excentricity anomaly, focus pos and current position and velocity?
How to find equatorial orbit pericenter position if I know $\mu$, $a$, $e$, excentricity anomaly (observed at current moment), force focus position (but don't know empty focus position) and body ...
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1
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66
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Sudden change in central potential
I was wondering what would happen to the path of a mass in a central force $F=-K/r^2$ if $K$ is suddenly reduced by a factor 2. Let's say the initial orbit is circular.
Would the planet stay in a ...
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