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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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 ...
Astrovis's user avatar
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calculating Sun's J band mag via integrating the Planck’s law

...
questionhang's user avatar
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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 ...
Papa Solen'ya's user avatar
1 vote
0 answers
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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 ...
Hunter's user avatar
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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 ...
w94n9's user avatar
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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 ...
Curious Cat's user avatar
2 votes
2 answers
347 views

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 ...
Pierre Paquette's user avatar
4 votes
1 answer
164 views

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 ...
Michael Bonnet's user avatar
2 votes
1 answer
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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 ...
Michael Bonnet's user avatar
1 vote
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23 views

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: \...
Lunthang Peter's user avatar
2 votes
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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 ...
Kian31's user avatar
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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 ...
Thinker-101's user avatar
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1 answer
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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 ...
mathgirl752's user avatar
1 vote
1 answer
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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 ...
lazyboy's user avatar
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2 answers
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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 ...
DanceroftheStars's user avatar
6 votes
1 answer
172 views

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 ...
DanceroftheStars's user avatar
1 vote
0 answers
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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 ...
DanceroftheStars's user avatar
1 vote
1 answer
229 views

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 ...
Joseph Samela's user avatar
1 vote
0 answers
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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, ...
Berkin's user avatar
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2 votes
1 answer
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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 ...
Ana's user avatar
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1 vote
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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 ...
Darren's user avatar
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1 answer
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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....
Harry Korone's user avatar
2 votes
1 answer
164 views

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 ...
arda güler's user avatar
2 votes
4 answers
3k views

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-...
Snack Exchange's user avatar
2 votes
0 answers
42 views

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, ...
Ana's user avatar
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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 ...
qasidaleem's user avatar
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1 answer
78 views

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 ...
VansFannel's user avatar
2 votes
1 answer
149 views

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 ...
isdi0's user avatar
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2 votes
0 answers
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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}= -\...
Ambica Govind's user avatar
2 votes
0 answers
64 views

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 ...
2080's user avatar
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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 ...
2080's user avatar
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2 votes
1 answer
146 views

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 ...
xone-a's user avatar
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0 answers
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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 ...
Ankit Biswas's user avatar
2 votes
0 answers
236 views

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 ...
lucas's user avatar
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6 votes
0 answers
124 views

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 ...
2080's user avatar
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5 votes
1 answer
300 views

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 ...
Pa_'s user avatar
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2 votes
0 answers
265 views

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 ...
uhoh's user avatar
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2 votes
2 answers
309 views

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 ...
lucas's user avatar
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3 votes
1 answer
270 views

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 ...
Itsme's user avatar
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-1 votes
1 answer
95 views

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 ...
Particle king's user avatar
2 votes
1 answer
98 views

Using Saha's equation knowing the overall pressure

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, $...
Pedro Nogueira's user avatar
2 votes
0 answers
256 views

What is the relationship between true anomaly and solar longitude?

So, my ultimate objective is to map solar longitude values onto a pseudo-Gregorian calendar. I thought this would be simple, but it has turned out to be anything but. I have asked several questions on ...
Grant Hartlage's user avatar
4 votes
0 answers
39 views

Total scattered flux and polarization for a ring of dust particles close to a star

I have an important problem and maybe some of you can help me with the following question: I have a mathematical expression for the total scattered flux in Jansky and the total linear polarized flux (...
Lyapunov's user avatar
3 votes
1 answer
63 views

How does this Toomre GI criteria have the period in the denominator?

I saw this equation in a literature review recently talking about the Toomre criterion for gravitational instability: Given here in section 2.1.1: https://arxiv.org/pdf/1801.06117.pdf, viz. But I am ...
WDUK's user avatar
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4 votes
2 answers
1k views

What kind of perspective projection is shown in this image?

I’m trying to develop software that overlays sky coordinates over 2d images of the sky taken by an iphone. I’ve done the sky coordinates part, but I’m trying to figure out what kind of perspective ...
amr gameel's user avatar
5 votes
0 answers
36 views

How to model the kinematics of gases expelled from comets and planetary atmospheres?

Once the ices of comets sublimate, where do they move to, and with which equations do you describe their motion in the interplanetary medium? Similarly, where do the gases that are stripped from the ...
Astrolien's user avatar
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4 votes
1 answer
325 views

Accurate formula for calculating the mass of an exoplanet using the transit method

A friend and I did some work on exoplanets with the help of a research institute (IEEC in Spain) for a major high school project. What we did was to "redetect" the exoplanet XO-6b through ...
user avatar
6 votes
3 answers
2k views

N-body simulation still losing precision despite using arbitrary-precision arithmetic and symplectic integrator

A while ago I asked 2-body orbits expanding in nbody simulation?. One thing that I noticed was that JavaScript does not have arbitrary precision, and that I used RK4 as my integrator, while it is ...
WarpPrime's user avatar
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2 votes
1 answer
66 views

What does "RV model including a GP with a quasi-periodic covariance structure" mean?

A candidate short-period sub-Earth orbiting Proxima Centauri says: 4.1 Simple periodogram analysis ]We first consider a very simple pre-whitening procedure applied to the CCF RVs in order to ...
uhoh's user avatar
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1 vote
1 answer
144 views

Finding the Laplacian of the deflection potential: I obtain 4𝜅(𝜃⃗ ), not 2𝜅(𝜃⃗ ). Why am I wrong?

From the review paper Bartelmann and schneider, 1999) Weak Gravitational Lensing, page 48. Like above, the Laplacian of the deflection function is convergence, $\kappa(\vec{\theta})$. I tried to ...
BAO's user avatar
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