Questions tagged [celestial-mechanics]

Questions regarding the motions of celestial objects.

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36 votes
1 answer
9k views

Why do the planets in our solar system orbit in the same plane?

(Yes I'm excluding Pluto from this the same way it was excluded for not being a planet) Observing the planets orbit of the Sun they all seem relatively planar and roughly all orbit along the same ...
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34 votes
3 answers
7k views

Is Venus in some way tidally locked to... Earth?

The video here demonstrates how Earth sees the same face of Venus every inferior conjunction (i.e., two planets are the closest to each other): https://www.youtube.com/watch?v=4m_ouMC61-w (or https://...
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27 votes
2 answers
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Where do we have it from that the Moon is migrating away from Earth?

I know Neil Armstrong placed a mirror on the Moon and people shoot lasers there which get reflected, thus measuring the time the light needs they can conclude the current distance of the Moon. But the ...
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25 votes
2 answers
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How can Io be tidally heated while it is in tidal lock?

According to its Wikipedia page: Rotation period: synchronous Eccentricity: 0.0041 But also ...extreme geologic activity is the result of tidal heating... How is it possible? It should not be ...
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21 votes
3 answers
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Why won't the Sun set for days at N66.2 which is below the arctic circle?

Correct me if I am wrong, but if we count sunsets by the center of the Sun apparently crossing the horizon then the Sun is supposed to set every day at latitudes under the arctic circle. (Yes if you ...
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14 votes
4 answers
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Is there any way for a planet orbiting a red dwarf in the habitable zone to not be tidally locked?

Is there any way to avoid the tidal locking of a planet orbiting a red dwarf in the habitable zone? For example, could a planet with a 90° obliquity and large moon avoid such a situation?
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14 votes
1 answer
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How does the gravitation of Jupiter or other big planets affect Kepler's third law?

Does anyone know a good reference for this? I once read how Jupiter's gravitation can be treated as a perturbation. I think they expanded Jupiter's gravitation as an infinite sum of one of the special ...
11 votes
2 answers
3k views

The deduction of the Hill Sphere formula

This question may be a little lazy, but can anybody give me a proof of the Hill sphere formula? Acording to wikipedia, the formula for the radius, $r$, is $$r\approx a(1-e)\left(\frac{m}{3M}\right)^{...
10 votes
3 answers
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What's the meaning of virial in Astronomy, and in particular the expression "a virialized cluster of galaxies"?

The virial theorem relates the kinetic energy of a system to the total potential energy of the system: $ \Delta K = -\frac{1}{2}\Delta V $ so it has lots of uses in mechanics, thermodynamics and ...
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9 votes
2 answers
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Spotting the booster rocket of the Chinese space station?

SpaceWeather.com's newsletter states Sky watchers are reporting two new objects in the night sky: China's new space station and an out-of-control booster rocket that helped launch it. The tumbling ...
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9 votes
2 answers
986 views

clarification of the Kozai mechanism

As Wikipedia says, In celestial mechanics, the Kozai mechanism, or the Lidov–Kozai mechanism, is a perturbation of the orbit of a satellite by the gravity of another body orbiting farther out, ...
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9 votes
1 answer
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If Saturn's rings cannot coalesce into a moon because of tidal forces, then how are shepherd moons able to exist?

From Wikipedia: In celestial mechanics, the Roche limit, also called Roche radius, is the distance within which a celestial body, held together only by its own force of gravity, will disintegrate due ...
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9 votes
2 answers
743 views

Is Io's orbit or rotation affected by its volcanism?

The rotations of comets and asteroids are affected by outgassing volatilities. Io is very volcanically active. Does this give Io a varying orbit and a slow rotation? Tidal forces should take longer ...
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8 votes
2 answers
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Is Pluto a "proto-planet"?

My question is this : could the Charon-Pluto system becomes in the coming few millions years a full fledged planet, as in the IAU classification ? I ask this because there are two facts that bother ...
8 votes
1 answer
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Why is Uranus able to support a regular satellite system?

Uranus has an obliquity of 98° which means that the mutual inclination between a satellite orbiting in its equatorial plane and the orbit of Uranus around the Sun would exceed the critical angle for ...
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7 votes
4 answers
280 views

Apsides Calculation

I’m trying to calculate the precise moment of Earth’s apsides (perihelion and aphelion). The only formulas I find are in Astronomical Algorithms by Jean Meeus (1998). However, they give erroneous ...
7 votes
4 answers
3k views

Need Simple equation for Rise, Transit, and Set time

I've been looking, unsuccessfully, for hours for a simple set of equations: Input: RA and Dec of an object Observers Lat and Lng Current Time Output: Rise Time Transit Time Set Time (and, ...
7 votes
1 answer
414 views

Degrees of freedom in restricted circular coplanar three body problem

How many degrees of freedom does a mechanical system consisting of three bodies, the Sun, Jupiter and an asteroid, have in the restricted circular coplanar problem of the three bodies? I know that if ...
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7 votes
1 answer
723 views

Could an ejected "extra ice-giant" still be lurking in distant solar orbit?

BACKGROUND Hot Jupiters are thought to have migrated inwards, implying that another giant planet has been ejected in order to conserve the orbital momentum of those planetary systems. The number of ...
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7 votes
3 answers
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Implementation of formulae for Meeus for the Moon

With Astronomical Algorithms by J. Meeus (1998) I have obtained the relevant illuminated fraction of the disk and position angle. But they're numbers (all Greek to me!) I know, Meeus explains that ...
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6 votes
2 answers
799 views

Has any moon achieved "retrograde equatorial orbit"?

There are many moons which have low (almost negligible) inclination and can be considered to rotate at the planet's equatorial plane. For instance, Galilean moons have almost negligible inclination (&...
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1 answer
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How to calculate the altitude of a star given the hour angle, declination, and latitude?

I'm trying to find the altitude of a star for observing, but all I have is the hour angle and declination of the star, along with latitude of the location I'm observing from. How can I find the ...
6 votes
2 answers
953 views

How can Earth-Sun Lagrange points L1 & L2 even be semi stable considering the moon?

I know that the Earth-Sun Lagrange L1, L2, and L3 points are not considered stable over longer periods, especially when compared to L4 and L5... But, with the moon orbiting the Earth in the general ...
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5 votes
1 answer
628 views

Coordinates in the Night Sky

I've learned about Orbits recently, and there are 6 orbital elements. Now, I've heard of three coordinate systems whereas, they can help you measure positions of stars in the night sky. The Altazimuth,...
5 votes
1 answer
5k views

What causes objects to become tidally locked?

I'm trying to write a gravity simulation (suns planets etc), and was hoping tidal locking could be one feature demonstrated. Using a simple equation for gravity has produced some interesting results, ...
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5 votes
2 answers
474 views

What variables are needed to calculate simple horseshoe orbit times?

EDIT This was NOT a duplicate of Horseshoe orbit cycle times. But that other question has been deleted, regardless. My original question asked for the answer to the equation(s), and provides many of ...
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5 votes
3 answers
568 views

Creating a basic "fixed" solar system to host a 3D space travel simulation

I'm trying to simulate a virtual/imaginary "solar system" in software--just a hobby project for now. Unfortunately this has made me realize exactly how much math I've forgotten since college. ...
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5 votes
2 answers
215 views

How to derive Kepler's 1st Law?

I was going through the derivation of Kepler's 1st Law in the textbook "An Introduction to Modern Astrophysics" by Carroll and Ostlie. From there, I got stuck in a few places in their ...
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5 votes
2 answers
954 views

How does the Sun orbit the Sun-Jupiter Barycenter?

I got the Orbital Elements of Jupiter around the Sun, which describe how it orbits relative to the "fix" Sun. Jupiter Semi Major Axis (AU): 5.20336301 Eccentricity: 0.04839266 Inclination to ...
5 votes
1 answer
86 views

Explanation about the resonance, mean motion resonance and libration

I am studying for a project the dynamics of multi-planetary system in resonance. I have two questions about this domain. In many articles they speak about 'mean motion resonance', what is the ...
4 votes
3 answers
1k views

Question about the Figure-eight periodic planar three-body motion

If this is a posible periodic solution for a three-body problem, can anybody tell me where is the center of mass of the system? As we know, in a n-body problem the bodies orbit around their center of ...
4 votes
2 answers
145 views

Why are solar systems stable and not chaotic?

I am not trained in applied mathematics and am asking as a layperson. It seems that the motions of the planets can be reliably predicted for thousands of years. Yet, if we consider a relatively simple ...
4 votes
1 answer
132 views

Why does the precession of the earth affect other planets?

In the Wikipedia article on numerical integration of planetary motion it states: ...the flattening of the Earth causes precession, which causes the axial tilt to change, which affects the long-...
4 votes
3 answers
117 views

Orbital terminology for satellites relative to one another

Basic question, but I'm trying to describe a planetary system and coming up short on vocabulary. Do either of the following exist?: A word for the closest pass between two satellites orbiting the ...
4 votes
1 answer
306 views

Determining North-South Line Via Watch Method: Theory & Reason

I recently read that if you're in the northern hemisphere and have an analog watch, then you can point the hour hand at the sun and know that a south line lies between (bisection) the hour hand and ...
4 votes
2 answers
195 views

Discrepancy between my results of Great Conjunction 2020 and Wikipedia

Using python-skyfield to calculate the upcoming conjunction of Jupiter and Saturn. I'm off a few minutes with the times on Wikipedia. Wikipedia Great conjunction times (1800 to 2100) Using Right ...
4 votes
0 answers
62 views

Charged black holes selective eaters

We have a charged black hole which is negatively charged. For this simple case the black hole is not rotating. If a negatively charged particle approaches the singularity the electromagnetic repulsion ...
4 votes
0 answers
48 views

Strange asymptotic behavior on the Kozai-Lidov cycles

So, in Naoz et al. (2013) is described the Kozai mechanism on three-body systems. I've tried to solve the equations (B1) - (B17) for the example described in the Figure 3 and I got something like this:...
3 votes
2 answers
639 views

Open source code for the maths behind a heliostat?

Theoretically, using a Raspberry Pi, (at least) one mirror, and two motors, one should be able to build a heliostat, i.e. a device which redirects sunlight to a fixed spot, like a scrub in the shadow ...
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3 votes
3 answers
769 views

Why does the Sun track out a seemingly sinusoidal path on the celestial sphere?

The question arose because I wanted to understand the path of the ecliptic after reading about it here: https://community.dur.ac.uk/john.lucey/users/solar_year.html Is the sinusoidal path due to ...
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3 votes
1 answer
157 views

Mars is getting closer to Earth through its elliptical orbit becoming more eccentric. Do Earth and Mars keep getting closer? [closed]

A NASA Mars article says: Mars' orbit is more elliptical than Earth's, so the difference between perihelion and aphelion is greater. Over the past centuries, Mars' orbit has been getting more and ...
3 votes
2 answers
124 views

Can we learn anything from the chaotic movement of Hydra and Nix?

The NASA Visualization Explorer Moons In Chaos says Hydra and Nix, two of the moons of Pluto, show chaotic movement due to the shifting gravitational field. How long a day lasts and where the sun ...
3 votes
3 answers
284 views

Why does the latitude of an observer affect the hour angle of a body in Stellarium?

I am using Stellarium for astronomical data to help in studying celestial navigation. While trying to track down a source of errors in my sextant reading or sight reductions I noticed that the local ...
3 votes
1 answer
135 views

Sky in the very far future / past

Motivated by this question about a stranded submarine in the Jurassic I would like to know: Is there anything remotely left of our current skyline if we go back or forward millions of years so that ...
3 votes
2 answers
106 views

constant semi-major axes of the planets

in Numerical Expressions for Precession Formulae And Mean Elements for the Moon And the Planets (Simon et al., 1994), the orbital elements of the planets are given for long time durations. The semi-...
3 votes
1 answer
657 views

Requirements for a satellite/planet to be tidally locked to a planet/star

The Moon is tidally locked to the Earth, the Four Galilean are tidally locked as well, and the recently found planetary sistem TRAPPIST-1 has seven tidally locked planets, but Venus or Mercury are not....
3 votes
1 answer
84 views

Can you compute the solar day?

For a given planet, if you know the sidereal rotation period and the sidereal revolution period, can you compute the length of one solar day? For instance, for Earth, if you know one rotation is ...
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3 votes
2 answers
118 views

Do moons experience periods of no sunlight when orbiting "behind" their planet?

I'm writing a story that takes place on the Saturn moon Iapetusand I was thinking that especially since Iapetus only has an inclination of about 17 degrees from the ecliptic, wouldn't there be a point ...
3 votes
1 answer
127 views

North Stars of each Solar system planet?

What are the North Stars of each individual body points too? E.g. Earth points to Polaris. Mars points to Deneb/Alpha Cygni. What about Sun, Mercury, Venus, Moon, Jupiter, Saturn, Uranus, Neptune, ...
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3 votes
1 answer
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Hohmann transfer orbit (Earth-Jupiter system)

Consider the Hohmann transfer orbit of a probe launched from Earth to Jupiter. Assume the orbits of Earth and Jupiter are circular. I want to calculate the following: The semi-major axis and ...
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