Questions tagged [celestial-mechanics]

Questions regarding the motions of celestial objects.

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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://...
puzzlet's user avatar
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36 votes
1 answer
12k 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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27 votes
2 answers
9k views

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 ...
Ioannes's user avatar
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25 votes
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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 ...
peterh's user avatar
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20 votes
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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 ...
mr_tuna's user avatar
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14 votes
5 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?
Soba's user avatar
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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 ...
Youngsub Yoon's user avatar
11 votes
3 answers
2k views

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 ...
Jim421616's user avatar
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11 votes
2 answers
4k 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)^{...
Carlos Vázquez Monzón's user avatar
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 ...
B--rian's user avatar
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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, ...
questionhang's user avatar
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9 votes
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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 ...
user177107's user avatar
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9 votes
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780 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 ...
LocalFluff's user avatar
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8 votes
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Would be possible to detect Planet Nine as a microlensing event along the line of its projected orbit?

Theoretically proposed by Konstantin Batygin and Mike Brown (@Caltech), Planet Nine could have a mass of $\sim 6.3 \pm 2 M_{\oplus}$. Even though I don't know if the hypothesis is still feasible at ...
nuwe's user avatar
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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 ...
Cqoicebordel's user avatar
8 votes
1 answer
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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 ...
Andres Huster's user avatar
8 votes
3 answers
2k views

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 ...
Danny F's user avatar
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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 ...
user avatar
7 votes
4 answers
341 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 ...
Pierre Paquette's user avatar
7 votes
4 answers
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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, ...
W. Christopher Moses's user avatar
7 votes
1 answer
504 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 ...
Augustin's user avatar
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7 votes
2 answers
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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 ...
Tazz250's user avatar
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799 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 ...
LocalFluff's user avatar
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6 votes
3 answers
1k 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 ...
B--rian's user avatar
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6 votes
2 answers
866 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 (&...
Nilay Ghosh's user avatar
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6 votes
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 ...
altitudeFinder's user avatar
6 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, ...
Ninjanoel's user avatar
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5 votes
1 answer
766 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,...
Questioner's user avatar
5 votes
2 answers
595 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 ...
Harthag's user avatar
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5 votes
3 answers
615 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. ...
User's user avatar
  • 51
5 votes
2 answers
393 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 ...
Lucas Tan's user avatar
  • 147
5 votes
1 answer
257 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 ...
Adrien Chimay's user avatar
5 votes
0 answers
202 views

Different techniques for calculation of celestial bodies dynamics with different time-scales

Differential equations describing the dynamics of celestial bodies (rotation, nutation, precession and other effects) can be solved numerically, which makes it possible to study their general non-...
dtn's user avatar
  • 706
5 votes
0 answers
133 views

Positional astronomy - Speed of the sun in sky

Let $\vec{r}$ be the position of the Sun in the sky, from Earth. How could I estimate the magnitude of $d\vec{r}/dt$, to measure the rate of change in time of the arc it traces? I suppose it would be ...
nuwe's user avatar
  • 769
5 votes
0 answers
53 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:...
Carlos Vázquez Monzón's user avatar
4 votes
3 answers
2k 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 ...
Carlos Vázquez Monzón's user avatar
4 votes
1 answer
1k views

Do all the planets travel along the same constellations?

If humans ever moved to another planet in this solar-system, what constellations would the sun meet from that perspective? What constellations would the sun look like it is meeting from the ...
Atlas's user avatar
  • 67
4 votes
2 answers
1k views

Accuracy of calculating the vernal equinox?

Calculating the exact time of the vernal equinox is essential for many ephemeris calculations. NASA Goddard Institute for Space Studies uses (at least for some purposes) the following, rather short ...
B--rian's user avatar
  • 5,616
4 votes
2 answers
286 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 ...
chasly - supports Monica's user avatar
4 votes
1 answer
301 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, ...
Majoris's user avatar
  • 535
4 votes
1 answer
162 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-...
Tyler Durden's user avatar
4 votes
3 answers
154 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 ...
the-baby-is-you's user avatar
4 votes
1 answer
3k views

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 ...
RUNN's user avatar
  • 165
4 votes
1 answer
443 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 ...
user8110's user avatar
4 votes
2 answers
213 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 ...
Gary Ilijevich's user avatar
4 votes
2 answers
547 views

How is Earth's Rotation Angle (ERA) defined and measured

UTC typically ticks with TAI. But to keep UTC from drifting far from the rotation angle of the Earth we occasionally add leap seconds to ensure that UTC does not drift too far from the UT1 timescale. ...
Jagerber48's user avatar
4 votes
0 answers
65 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 ...
Helena Wells's user avatar
3 votes
2 answers
603 views

How to find zero velocity contours for circular restricted 3-body problem in x-y plane?

(I am having physics background; I am not an astronomer/astrophysicist.) How to solve a single nonlinear algebraic equation in two variables, $x$ and $y$? (I know that - if there are two variables, ...
atom's user avatar
  • 169
3 votes
3 answers
2k 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://johnlucey.webspace.durham.ac.uk/users/solar-year/ Is the sinusoidal path due to Earth’s ...
keynes's user avatar
  • 31
3 votes
1 answer
137 views

Is the Moon really oscillating around its orbit as seen from Earth?

While simulating today's eclipse, I see something I have never noticed or learnt: Stellarium shows an oscillation of the Moon's trajectory around its orbit as seen from Earth. Is it real or a ...
Cingonius Varro's user avatar