# Questions tagged [mathematics]

For astronomy questions with a heavy mathematical component, more than simple formulas. For regular mathematics question, visit our sister site Mathematics Stack Exchange.

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### How the heck does JPL actually do the numerical integration for their development ephemerides? (general questions)

After writing this answer to JPL Horizons - "highly accurate measurements of planetary positions" - how do they do it? which draws from Park, Folkner, Williams & Boggs 2021 The JPL ...
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### How do I actually apply the small-angle approximation in this problem?

I'm asked to use the small-angle approximation to calculate the angular diameter (in degrees) of Jupiter as seen from Earth, if Jupiter were at the average distance of the Moon of 384,000 km. I know ...
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### Measure the deprojected distance between two points?

I have an image of a protoplanetary disk, from which I would like to measure the distance of various points from the centre. See below image for an example, where I would like to measure the distance ...
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### Azimuth angle and elevation angle of a heliostat mirror

for the control of a heliostat I have a program for the calculation of azimuth and elevation. Now I am still missing the calculation of azimuth angle and elevation angle for setting the mirror. While ...
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### Projection from Earth [closed]

If a Particle is projected from Equator due north with a velocity $v$ and Earth is rotating with a uniform angular velocity $\omega$. How can it be shown that the highest latitude reached will be ...
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### What's the Right Ascension & Declination of Galactic Left & Galactic Right?

For the purpose of being able to align my model to the galactic plane, I want to know the directions of the galactic center, anti-center, north, south, left & right. This gives me the answer for ...
127 views

### Is it still called an orbital resonance if the ratio is irrational?

Previously, I asked At what point are orbital resonances no longer "ordered" but "chaotic?", and received an answer from @CarlWitthoft: Perhaps if the calculated fraction had an ...
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### At what point are orbital resonances no longer "ordered" but "chaotic?"

Orbital resonances are typically in small valued integer ratios, like 2:1, 3:2, or 4:7. However, there are some resonances whose ratios have large reduced values, including the 73:69 Naiad:Thalassa ...
116 views

### Sun Moon earth Angle

I want to do a theoretical prediction before trying out an experiment. I just noticed that the arc separating the illuminated side of moon and the shadowed side is an ellipse arc. So Is it possible to ...
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### What is the difference between the two terms named "Eccentricity" and "Ellipticity"?

I don't get the difference between the two terms named "Eccentricity" and "Ellipticity", especially, in astronomy. I understand eccentricity as a measure of the curvature of a ...
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### Stellar temperature ~ frequency relationship?

According to Wikipedia, 76% of all stars are of spectral type M, 12% are of K, 7.5% are of G, etc. (see this section on Stellar Classification). This is very helpful, but is too vague, as the ...
Why can't we use the semi-minor axis in Kepler's third law? The formula for the third law is: $$\dfrac{a^3}{T^2} = \text{const.}$$ Instead of semi-major axis (a) why can't we use the semi-minor axis (...