All Questions
Tagged with newtonian-gravity celestial-mechanics
373
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Angular Momentum vs. Force Due to Gravity
I'm getting my feet wet with orbital mechanics and have a very basic question. Kepler's 2nd Law shows that 2 objects in an elliptical orbit sweep out equal areas in equal time, implying objects ...
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How to calculate Earth's speed due to moon induced orbit? [closed]
In https://stackoverflow.com/q/75297814/
the answer for the problem was that the earth like the moon had a speed due to the moon induced orbit. I don't understand how this was calculated? I have ...
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How to obtain Mercury Precession equation $\frac{d^2u}{d\theta^2}+u=a$?
Let $r=R(t)$ and $\theta=\Theta(t)$ describe the orbit of the planet. Define $$u(\theta)\equiv\frac{\bar r}{R[\Theta^{-1}(\theta)]}$$ where $\bar r=5.83\times 10^{12}$ cm be the mean value of the ...
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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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Resolving varying $ω$ in Kepler's Law's Proof
I'm having trouble understanding where $d^2r/dt^2$ comes from and what it stands for. What force is this? I'm not able to find any FBD's on google that mention any other force besides gravitational ...
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Why Saturn's rings lie in the same plane? [duplicate]
This is Saturn.
In every picture of Saturn, we can see that her rings are arranged in a perfect 2-d plane.
So the question I ask is simple, why are they arranged so? Why aren't the rings arranged in ...
- 751
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What is the condition for a body to revolve around another body? [duplicate]
For a given system consisting of two bodies, when will one body orbit another body as given by Kepler's law? Sometimes the body just gets attracted linearly and sometimes it orbits the other body ...
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Proof for equal eccentricity in a binary star system
What is the proof that the orbits of two stars orbiting around a common center of mass have equal eccentricities?
You can use: $m_1r_1 = m_2r_2,$ then say that $r_1= a(1+e_1)$, $r_2=a(1-e_2)$ and from ...
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Moon, Earth and the Sun [closed]
How to prove that the geometric locus of the points where the attractive forces of the Sun and the Moon are of equal intensity is a sphere of radius $ r = \frac{R \sqrt{Mm}}{M-m } $, where $M$ is ...
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Derive Sun's trajectory from movement of two planets in a 2D plane
Consider a solar system with 1 sun and two planets revolving around the sun in a 2D Euclidean space. While time continues, the sun moves forward, while the two planets revolve around the sun (move up ...
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How do the planets stay in their orbit? [duplicate]
The Sun has a strong gravity. The planets also have gravity. So they attract each other. But then why dont they go and mix up with the Sun?
If it is the orbit of the planets or a pre-existing motion ...
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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 ...
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Solution to two-body problem in orbital mechanics for $r(t)$ and $\theta(t)$, rather than $r(\theta)$?
I have written a simple numerical integration code to calculate the orbits of two planetary bodies orbiting a star, in order to calculate the transit-timing variation for one body due to the ...
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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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