# Questions tagged [celestial-mechanics]

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### Would Earth always face Sun the same way if Earth didn't rotate around it's axis?

Imagine for a second that Earth no longer rotates around its axis. It still revolves around the Sun. However, would the Earth: face the same way towards the Sun as it goes around it (permanent time ...
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### How can these two definitions of the eccentric anomaly give the same answer?

The eccentric anomaly,$E$, is defined via the equation, $$r = a(1-e \cos E) \tag{1}$$ for radius $r$, semi-major axis $a$ and eccentricity $e$. It is ALSO defined in terms of the Kepler Equation ...
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### Angular speed of Mercury [closed]

I have to calculate Mercury's angular speed ratios in the perihelion and in the aphelion $\left(\frac{\omega_a}{\omega_p}\right)$, using given eccentricity $e = 0.206$. I have no idea what ...
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### Is this a valid way to estimate the solar system's orbital velocity around the galactic center?

I know there are better ways to derive this, such as finding orbital velocities of other stars at approximately the same radius from the GC as ourselves and finding our own velocity $v_0$ as within ...
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### Vis viva equation - finding how change in velocity changes the semi-major axis distances - math trick [closed]

I'm reading about how to deorbit. I stumped upon a trick here. In the question, we wish to find how a chance in orbital speed changes the semi-major axis distances. So in the answer we start with the ...
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### Analytical proof for Kepler's first law using cartesian co-ordinates

Many detailed proofs are available for Kepler's first law, like this one. But all of them use polar co-ordinates. There is one which doesn't even use differential equations. I'm looking for a proof ...
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### Lorenz System in reference to Astrophysics / Planetary orbits

From my research I have found that there are a system of ordinary differential equations for atmospheric convection. What I am seeking are any Lorenz equations that apply to any areas of Astrophysics ...
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### Satellites orbiting around any planet's [closed]

Suppose a satellite is revolving around a planet with radius r. Now if we increase the value of r then the angular velocity and kinetic energy will decrease, but the total energy & potential ...
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### Can dark matter explain the unusual orbit of transnettunian objects? [closed]

While we are struggling to find an hypothetical planet 9 to explain the unusual orbit of transnettunian objects, I was wondering if it could be just dark matter. We know that the universe is mostly ...
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### Is space-time fabric around Uranus tilted?

I am completely new in this field, so please pardon me if I am asking something which makes no sense at all :) The Situation: According to Einstein's theory of relativity, there is a 4th dimension ...