Questions tagged [mathematics]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
4
votes
2answers
47 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 ...
7
votes
3answers
137 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 (...
5
votes
3answers
124 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 ...
0
votes
0answers
28 views

How are all the intermediate images between the “lensed” and “unlensed” endpoints of this video generated?

Phys.org's ALMA sees most distant Milky Way look-alike describes the numerical image reconstruction of a strongly and very nicely lensed z = 4.2 galaxy by a by a foreground galaxy at z = 0.263 and ...
1
vote
0answers
21 views

how to calculate the star formation rate (simplified) for a galactic model

we are (programming summer project Y10-11) making a very simplified model of a disk galaxy. would love to know if there's a simplified equation for the average star formation rate of the stellar disk ...
1
vote
1answer
55 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 ...
3
votes
1answer
57 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
60 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 ...
1
vote
0answers
12 views

Using altitude, azimuth to determine a baseline vector?

I know the equatorial coordinates of a “beam” pointing from an Earth-based observer toward some distant star. I have converted those coordinates to altazimuth coordinates for that observer and a ...
18
votes
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 ...
1
vote
1answer
58 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
1answer
64 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 ...
2
votes
2answers
82 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 ...
1
vote
0answers
16 views

Total luminosity of total population of galaxies!

I'm trying to get the total luminosity of a total population of galaxies. I have the Schechter Function like $$\Phi(L) = \frac{\Phi^{*}}{L^{*}} \left(\frac{L}{L^{*}}\right)^{\alpha} \exp \left(\frac{...
1
vote
1answer
59 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. ...
2
votes
1answer
93 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
98 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 &...
4
votes
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 ...
3
votes
1answer
69 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 ...
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 (...
2
votes
1answer
100 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. ...
1
vote
0answers
36 views

What are good resources to study Gravitational Waves?

I am undergraduate student having basic knowledge of Physics. I'm looking for resources (books, video lectures, research papers, etc) to study Gravitational Waves from scratch, I think initially I ...
2
votes
1answer
62 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
0answers
103 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 ...
3
votes
1answer
84 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 ...
0
votes
0answers
33 views

Stellar interior structures

im really confused on how i relate mass to radius of a star with a non constant density. more specifically i cannot seem to find an equation that states how density varies throughout a main sequence ...
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, ...
1
vote
1answer
285 views

How to calculate parallactic angle from a fixed alt-az position?

Say we have an observer at a specified latitude and longitude on Earth who would like to observer a specific fixed alt-az sky position (rather than RA and dec), for example to look at geosynchronous ...
2
votes
2answers
353 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
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
0answers
241 views

evaluate solar eclipse Besselian elements? [closed]

I found this NASA website which says that to predict eclipse, we should solve the Besselian elements ..what does this mean, how can I solve for Besselian elements? Is there a numerical method? I need ...
0
votes
1answer
34 views

Generate East and North unit vectors tangent to a point on the celestial sphere, using vectors?

I am stuck and a little embarrassed. I'm trying to implement this answer. I have a unit vector $w$ pointing in the direction of a radio source on the celestial sphere. $u$ and $v$ are the two other,...
1
vote
2answers
128 views

What natural mechanisms could lead to the unlikely case of the same rogue asteroid or planet passing through our solar system twice?

I find he following answer to the question What's the soonest Oumuamua could return? unsatisfying and oversimplifying and the last five words "Therefore it will never return." unsupported at a minimum....
1
vote
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 ...
2
votes
1answer
843 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 ...
1
vote
3answers
628 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 ...
9
votes
2answers
959 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
votes
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 ...
0
votes
2answers
390 views

Explanation of Longitude of Periapsis [duplicate]

I'm looking for a mathematical justification of the longitude of periapsis as it makes no mathematical sense to me as a notion. By definition, it is the sum of the argument of periapsis and the ...
0
votes
1answer
107 views

angles on the celestial sphere

This is a somewhat simplified, and drawn / formulated in a manner more targeted to astronomy, version of a diagram and a question that I've also posted in math.stackexchange.com. In the diagram below ...
1
vote
0answers
93 views

Rotating azimuth/altitude to a focal point?

This is really a math question, but it's for use in astronomy, so: Because reasons, I'm writing my own sky-viewing code. I've found a few references for converting right ascension and declination to ...
4
votes
1answer
258 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
votes
1answer
236 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 ...
1
vote
0answers
49 views

Generate an uniform distribution on the sky between limits

I have an analog question of this one : Generate an uniform distribution on the sky I generate an uniform distribution on the sky, but just a patch of it, with $$\alpha_{min} \leq \alpha \leq \alpha_{...
3
votes
1answer
544 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 ...
2
votes
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 ...
3
votes
1answer
185 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, ...
2
votes
2answers
254 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 ...
11
votes
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 ...
1
vote
0answers
46 views

Study astrophysics [closed]

I don't know where to ask this question and I have found this site. If this is not the right place to ask it, please tell me and I will delete it. I'm a computer engineer for 20 years but my true ...