Questions tagged [celestial-mechanics]

Questions regarding the motions of celestial objects.

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Planetary Declination and Axial Tilt

Is it a coincidence that Earth's axial tilt and maximum declination are both approximately 23 degrees? Mechanically speaking, do planets physically cross the Solar equator, or is declination due to ...
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Eccentricity from Analemma

Can the eccentricity of a planet's orbit be found just from the analemma of its star? We can draw an analemma given the axial tilt and eccentricity, but how do we find the reverse? Note: I already ...
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Undisturbed planetary alignment after galactic collision

How do planets still orbit around the empty space where a black hole was after a black hole absorbs the milky way's black hole and keeps moving through space without disturbing surrounding planets ...
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93 views

Determine Julian Date from Gregorian without formula

As an exercise, I am trying to calculate the JD from a given date in the Gregorian Calendar at a time given in UT. Furthermore, I want to do so from first principles without relying on any formula. ...
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70 views

How was Cruithne's orbital time calculated?

How was it determined that Cruithne takes 770 years to complete its cycle with Earth? Janus and Epimetheus were disovered long enough ago, and have short enough cycle times, that we've had time to ...
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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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If Earth suddenly stops rotating, will be thrown at 465 m/s? [duplicate]

If Earth suddenly stops rotating, will be thrown at 465 m/s ?
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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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Expansion of Jupiter's perturbing effects on Kepler's third law treatment of orbits?

Does anyone know any good reference for how this was done? I remember reading once about how Jupiter's gravitation can be treated as a perturbation, but I cannot find it again now. I think they ...
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What does “all stop” mean in reality?

In science fiction, when a starship captain commands "all stop," the audience simply assumes that, like a terrestrial naval ship anchored to the ocean floor, the ship literally comes to a complete ...
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282 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 ...
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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-...
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Is the Milankovitch calendar provably better than the Gregorian one considering a non-constant tropical year?

It's somewhat of a no-brainer the revised Julian calendar (attibuted to Milankovitch) is more accurate than the Gregorian one just because it started with a more accurate estimate of the duration of ...
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Why planets and stars are always round/oval in size? [duplicate]

What kind of stability it provides to each and every celestial body that each one them are round in shape?
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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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187 views

How to compute the perihelion precession of Earth's orbit?

I want to simulate the perihelion precession of Earth. I tried searching other posts in stack exchange as well relating this question but may be it's my fault that I couldn't understand their answers....
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174 views

Can Two Stars of One Same Type Orbit Each Other?

This is a simple, textbook definition of a binary star orbit. One low-mass star orbits a higher-mass star in a narrow but definitive center. For example, the high-mass star would be our own sun--a G-...
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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 ...
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Calculate NEO object position with nasa Near Earth Object data

I wish to create a 3D visualisation of NEO's by date in relation to earth, but calculating their position at that time has got me stuck. From this question I was able to fine Nasa's NEO object data: ...
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412 views

Equations of motion for Earth and Moon

One of the simplest versions of Newton's equations of motion for the Sun, Earth and Moon can be obtained by making the approximation that the three bodies are perfect spheres. In this approximation, ...
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168 views

Is it true that open clusters have $E > 0$ and globular clusters have $E < 0$?

I just need to confirm or refute something I'm believing since a very long time, maybe without real evidence. Can we distinguish stellar clusters by their total mechanical energy ? Is it true that ...
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175 views

Celestial navigation from scratch

Is it possible to establish one's longitude and latitude by observing the stars? Can you use observations of the stars to find the relative distance between two locations, which would be useful in map-...
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Angles in Moon, Earth and Sun system

Consider the vector positions of the center of mass of Moon, Sun and Earth, $\vec{r}_{\rm M}$, $\vec{r}_{\rm S}$, $\vec{r}_{\rm E}$, respectively, in a given reference frame. Consider: the angle ...
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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....
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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 ...
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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 ...
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How can the next supermoon be analytically predicted?

The lunar motion can be predicted with basic celestial mechanics, but the perigee and apogee are not always the same, basically because the attraction of the Sun makes some oscilations in the semi-...
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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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620 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)^{...
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On orbital mechanics of evaporating planets

A planet orbits around its sun on an elliptic orbit, and loses mass slowly due to evaporation. How will the parameters of the orbital ellipse change as a function of time? Could we do a generalisation ...
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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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The path of the planets on the celestial sphere

I know that planets have a "wandering" movement on the celestial sphere. I also know that their period around the Sun vary largely as compared with the period of the Earth (one sidereal year), ...
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584 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 ...
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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, ...
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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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383 views

Two body orbit of equal masses

Given two bodies of equal mass in an elliptical orbit: I know they will be orbiting about a common center of mass, i.e. the barycenter. But, do the velocities have to be equal in magnitude and ...
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146 views

Is the motion of the Sun around the Galaxy a result of gravitational pull?

Does the orbit of the sun (and other stars within the Milky way) around the galaxy result directly from radial gravitational force toward the objects in the center of the galaxy, or is there ...
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Has celestial navigation been materially impacted by the imperfect nature of celestial reference frames over time?

In this video on inertial reference frames, it is mentioned that the stars are humanity's best inertial reference frame: the earth experiences a subtle acceleration relative to the sun due to the ...
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Why is it so difficult to discover the earth Trojan?

It is discovered only in 2011. Why is it so late? We know where to find it.
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In a binary star system, what relation determines the eccentricity of the three orbits (for $m_1$, $m_2$, and the reduced mass)?

In a binary star system, why does $$e_1 = e_2 = e$$ where $e_1$,$e_2$, and $e$ are the eccentricities of the three orbits of $m_1$,$m_2$, and the reduced mass, respectively.
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Why don't the stars in a binary star system of equal masses always orbit their center of mass in a circular orbit?

If I have a binary object system of equal masses, why don't they always have the same circular orbit around their center of mass, like in the photo?
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Do orbital resonances always form naturally?

For example, if I throw two planets to orbit a star at random direction, would they form an orbital resonance?
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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, ...
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How do rogue planets orbit around stars in other planetary systems?

I got some interesting answers for What would happen if a rogue planet hit one of the planets in our Solar System? But I have seen some documentaries that state that rogue planets from other ...
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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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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 ...
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Roll, Pitch and Yaw of Orbital Planes

I have been reading about celestial mechanics and particularly about planetary orbits. I understand that a planet's orbit can be tilted (pitched) with respect to the Earth's ecliptic and that it might ...
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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 ...