# Questions tagged [mathematical-astronomy]

For questions related to the mathematical operations and analysis of astronomical and astrophysical observations, processes and dynamics.

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### Formula to calculate number of sunsets per year based on lattitude

How can I create a formula to turn latitude into number of sunsets per year? Let's keep it relatively simple. Assuming the Earth is a smooth ball, assuming the sun is a single point, not getting ...
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### Time and date from shadow

Given longitude, latitude and the height of a vertical stick at sea level, is it possible to determine date and time from the direction and length of its shadow? If yes, what are the formulas?
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### Deriving the equation of the centre

I'm failing to understand the derivation of the equation of the centre given on page 11 of Determining planetary positions in the sky for ±50 years to an accuracy of $\lesssim1$ degree with a ...
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### Graph theory interpretations of constellations

Bit of an informal question - but are there any notable connections between constellations and their respective graphs? i.e. do certain constellations have a hamiltonian cycle, are certain ...
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### Calculating specific degrees when the sun is below the horizon given 3 other known values

Reference: Types of Twilight Hi all, I have a question that I'm unsure how to approach and I was hoping someone could help me. ** I'm trying to calculate the time when the Sun is 16.1 degrees below ...
1 vote
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### How do I convert units from per radian seconds to arcseconds per year?

I am working on calculating axial precession of a planet orbiting a star, starting by attempting to follow along with Wikipedia's article on the topic. I have gotten through most of it without much ...
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### How do I account for the tilting of Earth's axis in right ascension and declination in a model solar system?

I am building a simplified model solar system in GeoGebra. Celestial objects are placed in a heliocentric coordinate system with the sun at the origin, the x-y-plane as the ecliptic, and the x-axis ...
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### Orbital resonances - expansion of disturbing function

I want to study the orbital resonance type $3:1$ between an asteroid and Jupiter. For this purpose, I found the expansion of the disturbing function in Celletti A., Stability and Chaos in Celestial ...
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### Algebric troubles while trying to get energy of orbit in isochrone (or plummer) potential

I am facing this problem, from a 2016 Astrophysics Tripos past paper: The gravitational potential $$\Phi=-\frac{G M}{b+\sqrt{b^{2}+r^{2}}}$$ where $G$, $M$ and $b$ are constants and $r$ is the ...
1 vote
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### Equation of Rotated Ellipse - Semi Major Axis is Changing

I am looking at astronomical observations of gas. The gas is orbiting a black hole with circular radius, $R$. However, from Earth it appears that the gas is an inclined ellipse. This is because ...
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### Is it special for a Lagrangian to equal its first integral?

Inspiration for this question: a this thread made me wonder if there is more to a story of a Lagrangian being equal to one of its first integral than "coincidence". Background I know that ...
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### Spherical Geometry Distance Between 2 Points

I try to calculate distance between 2 points on Earth. I have an a car and this car goes with speed 100 km/h and I know the start point latirude and longitude and car goes 5 hours. I want to calculate ...
1 vote
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### Fixing an orbit in space using r and v (Keplerian orbits)

I'm wondering what would be a good geometric method to compute orbital elements that fix the orbit in space, given that one is given the position vector $\vec{r}$ and the velocity vector $\vec{v}$ for ...
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