# 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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### How can I identify which planet I'm in ? Using only sensors

I'm working on a personal project where I want to identify on which planet I'm in using the following sensors: Accelerometer, Gyroscope, Pedometer, Magnetometer and an Altitude Sensor. My first idea ...
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### Kepler's Equation of Elliptical Motion in Terms of Cosine

Virtually all material discussing Kepler's Equation of Elliptical Motion resolves its solution to solving the following equation numerically: $$E - \textit{e}\;\sin(E) = M$$ where E is the Eccentric ...
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### Which function resembles this graph?

I am plotting the apparent magnitude of all visible stars sorted from brightest (-1.46) to dimmest (8ish) and this graph is the result. I feel like I've seen this graph's shape before, but I can't ...
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### What does it mean for the dots in the concentric circles when their wave functions intersect in a Fourier representation?

I saw a piece of code on github which transforms the planetary movement into the Fourier wave function. These circles are given by the $x$ and $y$ ordinates: $x=\cos (\omega t)$, $y=\sin (\omega t)$, ...
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### Mathematical formulation of a gravitational law for galaxies beyond newtonian

The author is not familiared with the current theories and the specific model for dark matter, nor the PDE aspect of mathematical theories related to the dark matter problem, so I apologize in advance ...
1 vote
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### What is the equation describing earth's orbit around the sun in 3 dimensional space?

I'm trying to draw a 2d ellipse in 3d space, which describes earth's orbit around the sun. such as image of a 2d ellipse in 3d space or the same image but different perspective. I'd like to be able to ...
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1 vote
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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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### 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
132 views

### 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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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 ...
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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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### Can there be an energetically unbounded three-body orbit where escape is impossible due to conservation of angular momentum?

This question evolved from a discussion below this answer which explains (among other things) that the total energy of a system offers insight as to the possibility of one (or all) members "escaping". ...
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1 vote