# Questions tagged [mathematics]

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### Are the stars distributed in uniform distribution, on the celestial dome, with respect to brightness?

Has there ever been a statistical analysis of the distribution of stars in the sky (on the surface of the celstial dome), by brightness? I want to know if they are uniformly distributed. For example, ...
3k views

### Why does the Fourier transform of this CMB image have a hole in it?

The BBC's Desert telescope takes aim at ageing our Universe contains the image below of the Cosmic Microwave Background from the Atacama Cosmology Telescope or ACT. It looks like this is plotted with ...
1k views

### Why does the Earth's orbital eccentricity oscillate with a period of about 100,000 years?

This answer says: Earth's orbital eccentricity varies over time from being nearly circular (low eccentricity of 0.0034) and mildly elliptical (high eccentricity of 0.058). It takes roughly 100,000 ...
985 views

### Calculating the apparent magnitude of a satellite

I'm writing a program that involves calculating the apparent magnitude of satellites from a ground location. I currently have the intrinsic magnitude of the satellites and the solar phase angle in ...
139 views

### What is meant by the notation $A^{\times{B}}_{\div{C}}$; where A,B,C are real numbers?

I have come across a few papers using the notation $A^{\times{B}}_{\div{C}}$; where A,B,C are real number. For example, $3000^{\times{3}}_{\div{4}}$. An example can be Eqn (4) in Stern & Laor (...
106 views

### What are the present, and potentially the future roles of data scientists in Astronomy? [closed]

I am a data scientist and curious about their roles in modern Astronomy, both now, and in the near future. What are type of roles and projects where data scientist are most active in Astronomy? What ...
2k views

### Generate an uniform distribution on the sky

How to generate an uniform distribution of stars on the sky ? What I want is make a simulation of random points following uniform distribution on a part of the sky (making the assuption that we have ...
197 views
+100

### Data to “check” Keplerās first law

I want to "check" Keplerās first law by using real data of Mars. From the equation of the ellipse, I derived $$\frac{1}{r}=\frac{a}{b^2}+\frac{a}{b^2}\cdot\epsilon\cdot\cos(\varphi),$$ where ...
127 views

### Moving from mathematics to astronomy/astrophysics

I'm currently studying for a PhD in pure mathematics (the topic is the cohomology of differential graded categories, just to give you an idea of how pure I mean), although the first year of my ...
57 views

### What is the physical interpretation of the derivative of the emitted and observed wavelength?

The flux F of an event at redshift $z$ is related to its luminosity L as $$F=\dfrac{L}{4\pi d_L^2}\,,$$ where $d_L\equiv d_L(z)$ is the luminosity distance between us (the observer) and the event (...
80 views

### Where is the sun relative to my lunar rover?

I'm a robotics researcher writing orienteering code for a solar-powered lunar rover. I have two similar problems: Given the position of a robot on the moon in lunar latitude/longitude, where is the ...
497 views

### What is the 2D elliptical projection of the Celestial Sphere called, and how can I make one?

I see this kind of projection of the celestial sphere into 2D frequently, usually with an image of the milky way galaxy or cosmic microwave background. This particular image shows the path of visible ...
50 views

### Calculating distance from center of mass of two stars in a binary system

I am confused on how to calculate the distances for each star in a binary system to their centre of mass. I am trying to solve it from a book I am reading which shows the solution but I do not ...
265 views

### How to calculate the time for the solar disk to pass the horizon and transit's lines

For a given date, longitude, and latitude: Popular apps and websites give the time when the sun's center or edge is on the horizon (i.e., the time of sunrise and sunset) or its transit (i.e., ...
101 views

### How to mathematically describe a planet's eccentric orbit?

Is there a formula for describing a planet's position along an eccentric orbit over time? I am particularly interested in the elliptical case (0 < e < 1). I understand that the planet has a ...
77 views

### Total apparent magnitude of eclipsing binary system

This is a question from the 2016 USAAAO national exam, for which no solutions are given: An eclipsing binary system has a magnitude $m_p$ = 14.2 during the primary transit and $m_s$ = 13.7 during ...
5k views

### How to calculate the position of the sun in long/lat?

I have a world map, and I want to know, given a timestamp, where is the sun located right now, in terms of long/lat. Here is a website that does that: https://www.timeanddate.com/worldclock/sunearth....
62 views

### Calculate object apparent diameter by distance and radius [duplicate]

I'm trying to create a dynamic starfield for game using the HYG database. Because there are no data about the apparent size of the stars from earth, I will need to get it myself. I found a formula ...
91 views

### What is a thermal distribution of eccentricities?

The abstract of the new (open access) paper in Nature A statistical solution to the chaotic, non-hierarchical three-body problem says: The three-body problem is arguably the oldest open question in ...
900 views

### How to Calculate Planetary Equilibrium Temperature in Binary systems

I'm working on a program that generates the basics stats of a terrestrial planets in binary star systems. I'm not the best at this kind of math, so I'm having trouble calculating the planetary ...
186 views

### Given sunrise, noon, sunset, longitude and latitude can I calculate the “hight” or “ascension” of the sun?

I'm trying to make a simple app for my own use to be able to check which of my favorit restaurants have outdoor seating sun and for how long etc. Given the data in the title (sunrise, noon, sunset, ...
67 views

### How to calculate how much of the Earth's (or another planet's) surface is visible? [duplicate]

My latter three questions remain unanswered but I won't wait with this one, I'd like to learn the formula and hope this question gets an answer. As you're going higher respectively farther away from ...
240 views

### Stellar Classification Table and Star RNG

I found a table that was based on data from 2003 for Stellar Classification, and I can't get to the given data source. I plan on using the table as a basis for a program that spits out random star ...
580 views

### Simple mathematical models of solar systems

Iām a hobbyist programmer with a profound love for procedural content generation. Iām working on a 2D space exploration game and while itās not meant to simulate anything real, Iād like to give it a ...
83 views

### What is the accuracy of an artificial satellite at a certain magnitude?

When we say that 'accuracy of gaia satellite is 10 $\mu$as at $V = 10$ magnitude in position and annual proper motion'. What does this mean? Does it change over time?
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### On the geodesics of the metric $ds^2=-\rho^2d\alpha^2+d\rho^2$ and the constant $l=\rho^2\frac{d\alpha}{d\tau}$

In my assignment I have to deal with the 2D spacetime metric $$ds^2=-\rho^2d\alpha^2+d\rho^2.$$ During this assignment we have shown that the constant $$l=\rho^2\frac{d\alpha}{d\tau}$$ is a constant ...
111 views

### Average effect of a planet on a comet

I'm considering a problem involving star S, planet A, and a comet B. The orbits of the planet and comet are eccentric, with eccentricities $e_A$ and $e_B$. I'm trying to calculate the average change ...
152 views

### How far away is this galaxy?

Arp 299 is in the news, with most sources reporting it as 140 or 150 million light-years away. But what kind of distance is this? The paper which is trhe source for the news item has Supplementary ...
308 views

### What is the probability that there is life on other planets?

From a mathematical point of view, what is the probability that 1) There is organic life on other planets 2) There are advanced species like us or even greater than us on other planets? Is there ...
99 views

### Do Astronomers really never call Lagrangian points “libration points”?

In this answer to Who called the Lagrangian points as āLibrationā points and and why was the terminology āLibrationā used? I described my feeling that Lagrangian points were also sometimes called &...
68 views

### How to calculate the true length of day on a celestial body?

When I only know the sidereal rotation period, how do I determine the true length of day on a body? We know the Earth's sidereal day doesn't have full 24 hrs unlike the true length of day. It's ...
233 views

### Does the given radius of a planet/moon include its atmosphere?

In NASA fact sheets, such as this one for Venus, a radius of the planet is given. Is that radius the radius of the surface of the planet, or of the envelope of atmosphere? Put another way, if ...
83 views

### Mathematical astrophysics subjects for math graduate students

I'm looking for a cool and interesting subject in mathematical astrophysics to study for my master's project. What I really aim for is certain processes in the cosmos (multiple body-problem, black ...
94 views

### How many stars are there max and average per galaxy?

What is the range of the number of stars possible in a galaxy? What is the rough average? Googling leads to vague answers, things like "billions upon billions". But what is a more pinpointed set of ...
103 views

### Convolve a SED with a filter. Is convoluting the mathematical operation?

I know that in order to get the Flux of a star (or something else) in a particular filter from its SED (luminosity per unit wavelength), I need to convolve the spectrum (SED) with the filter response. ...
450 views

### How to calculate the integrated source flux density of a continuous source?

I'm working with data from radio surveys. My images are .fits files with BUNIT Jy/beam. I want to calculate the net flux from a continuous source (not point source). When I simply added all the ...
367 views

### How to calculate phase angle of a satellite?

I'm making a program for predicting satellite passes. I'm trying to find out if the satellite is illuminated by the Sun and not in Earth's shadow. I need to know its phase angle: the angle between the ...
257 views

### A rough analytical expression for the Milky Way's radial mass distribution?

I found the image below in Space.com's article This 3D Color Map of 1.7 Billion Stars in the Milky Way Is the Best Ever Made, although it is not the map mentioned in the title. The caption for this ...
90 views

### What happens if one day aliens want to talk to us. How can we talk to them? [closed]

Always I wonder about that if some day alien wants to talk to us, then how can we talk to them? They didn't know any of the language on the Earth. What will be the basic building blocks for it?
32 views

### Help understanding why these two sub-Hill sphere moon stability limits are so different?

Comments under this answer to What orbital period would produce one New Moon (and one Full Moon) each year? What other effects would this produce? link to Stable satellites around extrasolar giant ...
104 views

### How are small objects automatically identified and their locations determined in digital images?

I have a large quantity of old digital images of low energy electron diffraction (LEED) patterns that I must process to identify and locate small, sometimes elongated gaussian-like blobs of a few ...
44 views

### Speed of Moonrise relative to fixed point on ground

Due to the curvature of the earth, and the way the moon interacts with the atmosphere (especially close to the horizon), is there a known function that describes the speed of the moon relative to its ...
61 views

### How did Kepler come to the potencies in his Third Law?

How did Kepler come to the conclusion, that exactly the square of the period and the third potency of the great semi-axis of the ellipse is proportional? Why is only square divided by cubic = ...
642 views

### Calculating the sunās position in ECI

Iām trying to calculate visible ISS passes and I need to calculate if the ISS is behind the earth by ādrawingā a line between the ISS and the sun and seeing if it crosses earth. I have the ECI ...
57 views

### how to find the approximate [stellar radius]? (distance from center to most distant star) of a circular flat disk galaxy based on its stellar mass?

I'm doing a high school programming project on drake's equation (simple galactic model) and wondered if there was a (simplified) way to find the radius (measured by the distance between the center and ...
60 views

### What kind of triangle is formed by three unequal masses in a circular restricted three body orbit?

This answer to Are the orbits of all triple star systems at least technically unstable? mentions: There are known solutions to the gravitational three body problem that can be shown to be stable. ...
62 views

### Is there any positive N on which it's agreed among astronomers that 10^-N is accepted as 0 (zero)? [closed]

Is there any positive N on which it's agreed among astronomers that 10^-N is accepted as, or treated as 0 (zero)? I think one of the sciences that most precision is required is astrophysics. I'm ...
191 views

### What do “star noise” and “sky noise” refer to for TESS (Transiting Exoplanet Survey Satellite)?

The eoPortal article for TESS (Transiting Exoplanet Survey Satellite) gives a fairly in-depth summary of the space telescope design and planned operation. Some further background information on its ...