All Questions
13
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Why doesn't the centre of mass of the solar system move away from the sun? [duplicate]
Consider our solar system, in the frame of the sun (i.e. "the sun is stationary"), with a simplified 5 planets and nothing else. Suppose that for a brief moment, all of the planets aligned (...
- 535
0
votes
2
answers
149
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How to actually plot the Kepler Problem?
As far as I understand the Kepler problem tries to predict the motion of two bodies under the influence of gravity.
Here the trajectory of each particle is chosen to be:
$$\vec{r}_1 = \vec{R}+\dfrac{...
- 462
1
vote
0
answers
54
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Confusion regarding 2-body problem [duplicate]
I'm new to 2-body problems, especially the case of binary stars, or a planet around a star system, and I'm facing this small doubt. I know, that in order to solve this, we mostly reduce this 2-body ...
- 1,791
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votes
4
answers
2k
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Can the Sun orbit the Earth?
You know how the earth orbits the sun because of gravity?...well if the sun were the right distance from the earth and it had the perfect tangential velocity...could it orbit the earth?
In other words....
- 1,189
0
votes
2
answers
83
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What's the nicest proof that two isolates masses orbit their center of mass? [duplicate]
Although it seems intuitive, I haven't found proof of this fact in my textbooks from a purely mathematical standpoint. I was wondering if anybody knows of a particularly elegant proof of this fact, ...
-1
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3
answers
1k
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Why does planet's mass affect it's speed around sun?
Let's assume that planet orbits sun with a perfect circular orbit. If force by which sun pulls planet is $\frac{GM_1m_2}{r^2}$, and $F=ma$ than $a = \frac{GM_1}{r^2}$. Now we also know that for ...
2
votes
3
answers
622
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Why is the pull from the Sun a central force if it is not at the centre of an elliptical orbit?
Closed Kepler orbits are ellipses with the Sun at one focus.
The force felt by the planet points in the direction of the Sun. As such, it is not a central force, since the focus is not the center.
I ...
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1
vote
1
answer
203
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Kepler's 3rd law/law of periods
Kepler's 3rd law of planetary motion is
The square of the time period of a planet orbiting a sun is proportional to the cube of the semi major axis of the elliptical orbit.
$$(T_1)^2 = (A_1)^...
- 49
7
votes
1
answer
3k
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Kepler's third law for binary systems
We all know that Kepler's third law for a system of two bodies which one of them have much greater mass than the the other is like this:
$\frac{{T_B}^2}{{a_B}^3}=\frac{4\pi ^2}{Gm_A}\;\;\;\;(m_A\gg ...
- 872
2
votes
2
answers
273
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Question about elliptical orbits
For two bodies attracting to each other, we use the reduced mass and distance between them (r) to solve the equation of motion. The final result is an elliptical obit under certain conditions.
My ...
- 890
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votes
1
answer
4k
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If two stars of mass $M$ and $2M$ move about their common centre of mass, then they have same angular velocity [duplicate]
Two stars of masses $M$ and $2M$ move in circular motion about their common centre of mass. Which of the following statements is true?
A. Both stars move with the same radius.
B. Both stars move ...
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-1
votes
1
answer
1k
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Why do the stars in a binary system, revolve diametrically opposite to each other?
I encountered this question, as I was reading up on Gravity. The author of my textbook says that the stars orbit a common centre which is their center of mass. I somehow think that this fact might ...
- 1,082
0
votes
0
answers
878
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3-body system centre of mass
I have a three body system of point masses that represent mercury, earth and the sun. I want them to orbit about a common centre of mass, but I think the centre of mass will move. I need the centre of ...
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