Questions tagged [mathematics]

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19
votes
2answers
5k views

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, ...
18
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2answers
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 ...
11
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1answer
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 ...
9
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2answers
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 ...
7
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3answers
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 (...
7
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2answers
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 ...
6
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3answers
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 ...
5
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2answers
197 views
+100

Data to “check” Kepler’s first law

I want to "check" Kepler’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 ...
5
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3answers
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 ...
5
votes
1answer
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 (...
4
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2answers
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 ...
4
votes
1answer
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 ...
4
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2answers
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 ...
4
votes
1answer
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., ...
3
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1answer
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 ...
3
votes
1answer
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 ...
3
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3answers
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....
3
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1answer
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 ...
3
votes
1answer
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 ...
3
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1answer
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 ...
3
votes
1answer
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, ...
3
votes
1answer
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 ...
3
votes
1answer
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 ...
3
votes
1answer
580 views

Simple mathematical models of solar systems

I’m a hobbyist programmer with a profound love for procedural content generation. I’m working on a 2D space exploration game and while it’s not meant to simulate anything real, I’d like to give it a ...
3
votes
1answer
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?
3
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0answers
85 views

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 ...
3
votes
0answers
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 ...
2
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2answers
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 ...
2
votes
1answer
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 ...
2
votes
1answer
99 views

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

In this answer to Who called the Lagrangian points as “Libration” points and and why was the terminology “Libration” used? I described my feeling that Lagrangian points were also sometimes called &...
2
votes
1answer
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 ...
2
votes
1answer
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 ...
2
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2answers
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 ...
2
votes
1answer
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 ...
2
votes
1answer
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. ...
2
votes
2answers
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 ...
2
votes
2answers
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 ...
2
votes
2answers
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 ...
2
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2answers
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?
2
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0answers
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 ...
2
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0answers
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 ...
2
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0answers
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 ...
1
vote
1answer
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 = ...
1
vote
3answers
642 views

Calculating the sun’s position in ECI

I’m trying to calculate visible ISS passes and I need to calculate if the ISS is behind the earth by “drawing” a line between the ISS and the sun and seeing if it crosses earth. I have the ECI ...
1
vote
1answer
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 ...
1
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1answer
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. ...
1
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1answer
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 ...
1
vote
1answer
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 ...
1
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1answer
98 views

What is meant by the bifurcation of hydrostatic equilibrium shapes in planetary formation?

An intriguing comment below this question links to this Quora question and points to the answer by Robert Walker. The sentence that particularly intrigued me is: It turns out that there are two ...
1
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1answer
65 views

How can I correct for transit time?

I know the exact time a radio telescope detected a transient event. I also know the exact location of the telescope, and the galactic coordinates (galactic longitude, latitude) and right ascension and ...