# 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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### Moon's ecliptic latitude and longitude [duplicate]

Is there a way to compute the Moon's ecliptic latitude and longitude without declination or right ascension? Note: I have a formula to compute the Moon's position that uses an ecliptic latitude and ...
96 views

### Orbit equation solver giving wrong orbits

Recently I've become interested in simulating orbital mechanics using Kepler's equations, and in Unity I created my own equation solver by following this paper I found. However, inputting Earth's ...
1 vote
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### calculate declination and right ascension with limited information

I'm trying to make a game with high accuracy moon position so I followed some equations on geoastro.de Basics of Positional Astronomy and Ephemerides and with some help from the questions answers, I ...
125 views

### visible solid angle of the moon

I'm reading an astronomy textbook for high schoolers, it contains an exercise to calculate the visible angle ratio of the moon in the sky (the textbook is not in english so my terminology is probably ...
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### How to calculate moon's distance and parallax in it's altitude

I'm trying to calculate moon's parallax in it's altitude depending on the day I need and I followed this formula by geoastro.de Basics of Positional Astronomy and Ephemerides but I need to calculate ...
334 views

### Wrong results of calculating moon's altitude and azimuth

I'm trying to calculate moon's altitude and azimuth and I followed this formula by geoastro.de Basics of Positional Astronomy and Ephemerides There is an example to test the formula at the end of the ...
1 vote
72 views

### Declinations from stars apparent motion w/o plate solving

I am trying to program the calculation of the declination of the stars, based on their apparent movement through a series of astrophotographs, purely algebraically, without using a solver based on the ...
249 views

### Plotting the path of an eclipse

NASA has published 5000 years of future solar eclipses at https://eclipse.gsfc.nasa.gov/SEpubs/5MCSE.html . They have included in them a number of low fidelity maps, and the parameters to calculated ...
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1 vote
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### Is there a specific constant name for the fifth root of 100?

I understand that each scale you go up on the absolute magnitude scale, the luminosity decreases by the fifth root of 100, or around 2.512. Is there a name for the constant 2.512, or not. Also, is the ...
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### What year will Gamma Cephei become the North Star?

I tried googling but I couldn't get any exact year, just any time between 3000 and 3100 CE. I want to know the exact year the north pole becomes closer to Gamma Cephei than Polaris. Apparently Polaris ...
1 vote
33 views

### Geocentric position of lunar ascending node relative to the true equator and equinox of date, using skyfield

The following is what I'm doing currently. Am I missing something here? I'm unsure if I am converting in and out of Skyfield objects correctly, and there is any unaccounted for behavior i'm not seeing ...
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### Kepler to Cartesian and Cartesian to Kepler inaccuracies

I am programming a computer simulation set in a star system. I've used Rene Schwarz's wonderfully concise memorandi explaining converting from Kepler orbital elements into cartesian coordinates and ...
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### Why is v lowercase and D uppercase in $v=H_0D$?

Why is v almost always written in lowercase and D in uppercase in $v=H_0D$? OK, v is in lowercase, as usual, but then why is D in uppercase? What's so different/special about it? In my physics school ...
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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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### Fixing satellite eclipse equations from textbooks that are seemingly failing

I have tried implementing equations from two different textbooks in Python to find if a satellite is in eclipse, but both fail a significant percentage of the time when tested against data from ...
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### Equation for calculating boolean answer to "is this Earth satellite in eclipse"

I have found plenty of math for determining duration of satellite eclipse, but I am having trouble finding an equation that produces a simple boolean answer to the question "Is this Earth ...
1 vote
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### What would be the new Equation of motion if the magnetic field's origin is shifted from the origin of a co-rotating spherical polar coordinates?

The equation of motions due to the dipole magnetic force of a planet in a frame corotating with the planet and origin at the centre of planet assumed to be sphere components wise are given as below: \...
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### How is an index of n=0 possible for the Lane-Emden equation?

I was recently showing that an index of $n=0$ for the Lane-Emden equation results in constant density throughout the star. However, in my calculations I had to use the constant $\alpha$ which can be ...
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### Understanding the Julian Date equation in detail

I am trying to figure out the Julian date equation by myself. Unfortunately, there are not many resources I could find which explains in depth. Moreover, there are several variations of the same ...
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### Estimate the mass of Saturn based on the given data below

In September 2017, the Cassini 1 mission was nearing its end after 20 years due to fuel shortages. The NASA space probe reached its apoapsis on 12 September at 1:27 AM EDT (time on Saturn) with a ...
1 vote
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### Meaning of "variables of date" in VSOP87 files

When I read the description of VSOP87, I find out that there is a file with "variables of date" and a file with "variables J2000". In Astronomical Algorithms of J. Meeus I can find ...
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### Confusion over habitable zone

I am confused over the habitable zone, as I calculated the expected temperature of Earth (minus greenhouse effects), and it would be -17 C. Which is below the freezing point of water. I also made a ...
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### On the Radiation Field of large Gas Giants

I am woring on creating a fictional star system, and I need to find an answer to a question to find an accurate way to depict this. I am aware that Gas Giants create a dangerous field of radiation ...
1 vote
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### Question regarding potential moon sizes

I am planning out ideas for a science-fiction world, and I want to make sure that what I include is reasonable and mathematically sound (outside of things like FTL as that is neccessary for the story ...
1 vote
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### Celestial Navigation - How to calculate Longitude?

I'm trying to learn celestial navigation using the Sun to determine longitude. I'm starting to understand some of these concepts, but I can't figure out how to calculate longitude accurately. Hoping ...
1 vote
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### How do nuJ(nu) units work?

I'm working with (Nublado) Cloudy, which is essentially a spectral modelling tool for stellar matter. Using the software, I model my own stellar object and obtain its continuum. According to Hazy, ...
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### What is the mathematics needed for understanding DE440 and translating it into xyz coordinates?

I would like to write my own code to process NASA's DE440/DE441 ephemerides, but I do not know the mathematics needed to do this. I understand packages such as pyephem have implemented variations of ...
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### How can Aggregation of Gravitational Fields of subplanetary solar objects improve our understanding of the motion of the planets?

If we imagine magnets on a table as a simplified analogy in regards to gravitational attraction between objects, then it may be demonstrated that when three objects are placed in a row labeled in ...
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### Whis my planetary volume formula wrong? (volume = mass/density)

I'm having trouble with this and am unsure what I'm doing wrong. Let's use Earth as an example. Earth has a mass of 5,972,168,000,000,000,000,000,000 (5.97E+27) kg and a density of 5513.4 kg/m3 or 5....
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### By analytical geometry, how to calculate the fraction of the visible area of the Sun at a point during an eclipse?

Assume a perfectly spherical Sun and Moon, and ignore atmospheric effects for simplicity. I'm an observer in the origin of my coordinate system, and I know the positions of the centers of the Sun and ...
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### How does each degree equal to 60 minutes?

I was searching in the internet to find the reason each degree equals to 60 minutes and I found this: 60 seconds make up a minute. One day is equal to 24 hours, and the hour hand completes two 360-...
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### References to learn about algorithms/mathematics related to building planetarium / astronomy software?

I'm a beginner in astronomy with a background in engineering and mathematics. I'm interested in learning how to build astronomy software to model the position and movement of planets and stars, ...
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### Trying to understand how to properly implement this equation to a healpix map

So i am working on reproducing a paper (Secrest, N. J., von Hausegger, S., Rameez, M., Mohayaee, R., Sarkar, S., & Colin, J. (2021). A test of the cosmological principle with quasars. The ...
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### Get (X, Y, Z) coordinates from Horizontal Coordinates

I'm developing a planetarium software using the Hipparcos Catalogue. I have also implemented all the formulas of the book: "Practical astronomy with your Calculator and Spreadsheet". With ...
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### How can I Mathematically Calculate the Luminosity of a Post-Main-Sequence Star from Mass and Age?

So, I saw this question (which is quite old) and that's all well and good, but what if I need to (very) roughly calculate the luminosity of a star from the end of the main sequence? Let's assume that ...
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### Equation describing Energy Transport due to Radiation in the interiors of stars

I am considering a very elementary stellar structure and I'm required to derive an equation to describe the energy transport due to radiation. The answer I am supposed to obtain is: \frac{dT}{dr}= -\...
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### It is possible to estimate an exoplanets' orbital period from just one transit?

Is one lightcurve containing a dip in brightness obtained from the transit method sufficient to obtain or estimate the orbital period of an exoplanet - such that one (first) observation could be used ...
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### Probability of exoplanet transit

An exoplanet is in a circular orbit around its star. The radius of the star is $r_{star}$ The radius of the exoplanet is $r_{planet}$ The radius of the orbit is $r_{orbit}$. The orbital period of the ...
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### What is the diameter of a telescope lens that will capture the surface of Proxima Centauri b?

I been trying to find the way I can calculate the telescope lens diameter needed to see a star by the distance of the star or the planet from the earth. Is there any mathematical relation we usually ...
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### How do I code the formula for the minimum mass of a stellar fragment from Whitworth & Stamatellos, 2006?

I was researching the formation of brown dwarfs, and I stumbled into the paper "The minimum mass for star formation, and the origin of binary brown dwarfs", and I am attempting to code a ...
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### Calculate the uncertainty in measured flux density from an integrated intensity map

I have some ALMA data, in the form of a spectral cube, which I have integrated along the velocity axis to create an integrated intensity ('moment 0') map. The integrated intensity map shows emission ...
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### Would it be possible to create a telescope from a hanging reflective cloth?

A chain suspended on two points hanging under gravity forms a curve called a Catenary, which can look pretty similar to a parabola. I'm not sure if this generalizes to the two dimensional case where ...
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### How do I calculate the closest point to the sun on Earth's surface?

Couldn't find an answer so here I come: On 21st of June and 21st of December these points would lie on the tropics. But what about the other days of the year? Is there a simple formula to calculate ...
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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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### 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 ...
Knowing the pressure, $P_g$, how can I calculate $\frac{N_{I+1}}{N_I}$ using Saha's equation? If I assume that $P_g=(n_e+n_{H^+}+n_H)K_B T$ and that $n_e=n_{H^+}$, I can find the electronic pressure, \$...