# Questions tagged [celestial-mechanics]

Questions regarding the motions of celestial objects.

23 questions with no upvoted or accepted answers
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### 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-...
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### 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 ...
• 771
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### 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:...
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 ...
• 365
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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 ...
48 views

### Tools and algorithms for angles-only orbit estimation

I've seen discussion threads where amateur astronomers estimate a satellite's orbital parameters from angles-only telescope observation. Are there any community tools or algorithms to help with this ...
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### Code for Gauss's method orbit determination

I'm trying to calculate the state vectors of the ISS using Gauss's method with three sets of values (right ascension, declination and sidereal time). I'm following the method described in "...
152 views

### Virial theorem for a binary system

I am trying to derive the virial theorem but for two stars orbiting each other. I know the derivation for the general virial theorem with i particles but I am wondering if there is a quicker or more ...
• 103
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### Orbital resonance 2:1

I considered the motion of an asteroid around the sun, in a $2:1$ orbital resonance with Jupiter. Following the study of this resonance, it was observed that the angle between the major axis of the ...
• 153
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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), ...
1 vote
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### What causes the short term variation in the length of a march-equinox year

By a "march-equinox year" I mean the time between successive march/vernal equinoxes. I understand that this is different from the mean tropical year, and I also understand why this would be ...
• 101
1 vote
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### How is the amount and direction of the Sun's axial tilt as observed from other planets calculated?

Not long ago I asked this question; turns out that was fairly simple to figure out given the equatorial coordinates of the Sun's north pole (just convert to ecliptic coordinates, and see when the Sun ...
• 225
1 vote
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### Looking for data and models for events of Sun and Moon apparent motion in distant past?

For the current Julian Era (from 1, 1, 4713 BCE to modern day), I am looking for a raw data tables or a model that allows to predict the following events related to apparent motion of Sun and Moon: ...
1 vote
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### Why is Earth at centre of Celestial Sphere?

Why do we consider Earth to be at the centre for Celestial Sphere ? If so, then how will Sun revolve around Earth ? Doesn't it mean its like the geocentric model ?
1 vote
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### Constants of three body problem(2 fixed centers)

I was solving two fixed centers problem and got answer in quadratures. After that i want to find constants of motion. First one is full energy - E. Second is $p_{\varphi}$. And third one comes from ...
1 vote
52 views

### Variation in g acceleration due to gravity

I want to find a routine which will enable me to calculate the variations in g as a result of the motion of sun and moon. I need to have the date as a variable. I realise that Dennis Milbert's earth ...
1 vote
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### Will the United States Presidential Election (day asteroid) be back soon?

My google news feed is awash with mono-themed articles, including a near Earth asteroid that passed by around election day 2020 in the US. We can all hope that neither will lead to an extinction level ...
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1 vote
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### When and why was zero right ascension defined to be at the vernal equinox?

When (and why) was zero right ascension defined to be at the vernal equinox? Who established or defined this standard?
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1 vote
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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 ...
1 vote
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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 ...
• 161
1 vote
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### 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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### Accretion disk formation

Why a mass transfer in a binary star system, from the less dense star to the denser star forms an accretion disk? Why the material does not fall directly to the denserstar?
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