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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Discovery of a Formula for Geostationary Orbit Distance: Seeking Expert Feedback
I’m an amateur enthusiast without a formal academic background in mathematics or science. Recently, I stumbled upon an idea and derived a formula that I believe calculates the distance traveled along ...
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Help with understanding combination of probability distributions
I have two probability mass functions (PMFs) across the surface of a sphere. They are localised Gaussians (a few degrees in expanse), whose centres have arbitrary positions though they are quite close ...
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Calculating absolute Astronomic Field Rotation over a known duration
This is sort of a cross post of my question over on the Astronomy Stack Exchange (https://astronomy.stackexchange.com/questions/57545/calculating-field-rotation-between-two-times).
Example: I'd like ...
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A weird integral
It needs to be noted that he whole motivation is to find an expression for $u(\tau)$ in the end, where u is the scale factor ($u = \frac{a}{a_0}$) and $\tau = H_0 t$.
I'm having issues with solving ...
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Relationship between lifetime of tech civilisations and time taken for a roundtrip between two such civilisations
Here is a statement of the question, which is taken from Chaisson and McMillan's Astronomy: A Beginner's Guide to the Universe.
Assume that the number of (technological) civilisations in the Milky Way ...
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Practical Math Problem: Ideal positioning for multiple 2-axis solar arrays
I live around 32°N latitude, and I am trying to figure out the optimal positioning for six 2-axis solar arrays so they don't interfere with each other when the sun is over 5° above the horizon. The ...
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κ̄₀ for Mercury—Formula (BIS—Different definition of the term/angle)
Following my other question about a specific “hidden” formula in Ptolemy’s model for Mercury, I am now looking for yet another “hidden” formula, this time the one used to find $\bar\kappa_0$ so that $...
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κ₀ for Mercury—Formula
I refer here to Ptolemy’s epicycle-and-deferent model of the Solar System, specifically that of Mercury (see drawing).
In this model, Mercury (not shown) revolves on an epicycle of center C, which ...
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Making a Geocentric Model of the Solar System Using Trigonometry
All.
I've made a post similar to this before, but I have since come up with a different way to tackle the problem of creating a Geocentric model of the Solar System, this time using trigonometry to ...
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Deriving small angle approximation $ \cos\delta_a\cos\delta_b\ \approx \cos^2\delta_a $
I'm trying to understand the derivation for the small angular distance approximation formula for the Angular Distance, as explained in Wikipedia
Almost to the end of the derivation, I'm presented with ...
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Prove Kepler's second law of planetary motion
An object moves in $\mathbb R^3$ it's position $r(t)$ satisfies $$r''(t) = s(t)r(t)$$ for some scalar function $s$ (a central force field, in which all acceleration is directly towards or opposite the ...
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Evaluating the integral of a double power law
So I have a double power law equation as a way to model the surface density $\Sigma$ of a debris disk as a function of radius $R$,
$$\Sigma(R)=\Sigma_c[(\frac{R}{r_c})^{-\alpha_\text{in} \gamma} + (\...
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Solar declination as a function of solar longitude [duplicate]
I'm trying to find the relationship between solar declination and solar longitude. Solar declination is the angle between the line Earth-Sun and the equatorial plane of the Earth. Solar longitude is ...
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Converting between two spherical coordinate systems with an application to astronomy
I am currently working on a sub-problem of a larger problem which involves being able to efficiently align an equatorial telescope mount with greater precision than the conventional amateur method, ...
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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 ...
