Questions tagged [mathematics]

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23 views

How to determine how often a planet's center will be collinear with its moon's?

Expanding on the question: Let's say I have a planet orbiting some star (earth-like, sun-like, for the sake of example). If this planet has two moons, M1 with orbital period of 30 earth-days and M2 ...
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2answers
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What if Earth gained 1 km/s orbital velocity?

How would Earth's orbit be affected if we (hypothetically) added $1 {\rm km/s}$ to its orbital velocity? Would Earth reach close to Mars' orbit? Could Earth get gravitational assist from Mars and go ...
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1answer
119 views

Confusion when calculating the length of the day

I'm trying to solve this task: Tula and Moscow are located on the same meridian. In which city length of the day is bigger on 22 of June? 22 of December? I was thinking like that: we need to ...
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2answers
83 views

What is the rate of change by day for a given right ascension?

I am writing a small Julia app to get my feet wet in that language. And I want to calculate "what's up tonight" based on a table of right ascension (RA)/Dec(lination) (table of stars), a ...
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3answers
209 views

Role of power laws in astronomy?

I often see astronomers fitting data to power laws. What about power laws makes them so useful in astronomy? Why are so many astronomical observations well-fit by power laws? I know it's a relation ...
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45 views

How did pressure evolve in the (early) universe?

I am trying to derive how the cosmological pressure $p(t)$ evolved over time in the universe, especially in the radiation and matter dominated epochs. There are some very nice explanations how $H(t)$ ...
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2answers
73 views

Basic, learning examples of applications of CFD and MHD in astrophysics, and current research directions using these techniques?

I am an undergraduate in Physics, and I have an opportunity to work with a some of my seniors to learn Computational Fluid Dynamics (CFD) and Magnetohydrodynamics (MHD). I would like to choose my ...
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1answer
60 views

Orbital resonances - expansion of disturbing function

I want to study the orbital resonance type 3:1 between an asteroid and Jupiter. For this purpose, I found the expansion of the disturbing function, $R$, in Celletti A., Stability and Chaos in ...
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2answers
2k views

At what distance from the Sun can planetary moons exist?

Mercury and Venus are theorized to have no moons because they are so close to the sun. Is there a theoretical distance in which moons tend to exist based on simulations?
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1answer
32 views

Flux vs. Velocity representation of spectra?

I'm looking for a basic explanation of the flux vs. velocity representation of a spectrum and how it's obtained from the regular flux vs. wavelength representation. A good example of this is in Arav ...
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1answer
91 views

How galactic density falls using Oort constants

I am given the observations that Oort constants $A$ and $B$ are, respectively: $14.5 \text{km s}^{-1} \text{kpc}^{-1}$ and $-12 \text{km s}^{-1} \text{kpc}^{-1}$. From these, I am supposed to conclude ...
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1answer
32 views

Poisson's equation-like formula in axis-symmetric Galactic potential in terms of Oort constants

I am tackling this problem, from a 2016 Cambridge Astrophysics Tripos past paper: Let $\Phi(R, z)$ be the axi-symmetric Galactic potential. At the Solar location, $(R, z) = (R_0, 0)$, prove that $$\...
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What is the difference between the two terms named “Eccentricity” and “Ellipticity”?

I don't get the difference between the two terms named "Eccentricity" and "Ellipticity", especially, in astronomy. I understand eccentricity as a measure of the curvature of a ...
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Stellar temperature ~ frequency relationship?

According to Wikipedia, 76% of all stars are of spectral type M, 12% are of K, 7.5% are of G, etc. (see this section on Stellar Classification). This is very helpful, but is too vague, as the ...
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Why can't we use the semi-minor axis in Kepler's third law?

Why can't we use the semi-minor axis in Kepler's third law? The formula for the third law is: $$\dfrac{a^3}{T^2} = \text{const.} $$ Instead of semi-major axis (a) why can't we use the semi-minor axis (...
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1answer
45 views

How to estimate the inclination of a galaxy between edge on and face on?

I have the images of a galaxy and the field of view and I would like to determinte the inclination of a galaxy between edge-on and face-on. Would that information be enough to do the calculation? Or ...
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2answers
138 views

Accuracy of calculating the vernal equinox?

Calculating the exact time of the vernal equinox is essential for many ephemeris calculations. NASA Goddard Institute for Space Studies uses (at least for some purposes) the following, rather short ...
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1answer
47 views

How do you carry errors for brightness magnitudes [duplicate]

I have a value for the relative flux $F_2/F_1$. With some uncertainty value $a$. If I use the equation to get relative magnitude: $m_1 - m_2 = 2.5 \log_{10}(F_2/F_1)$ How do you now calculate the ...
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2answers
176 views

Open source code for the maths behind a heliostat?

Theoretically, using a Raspberry Pi, (at least) one mirror, and two motors, one should be able to build a heliostat, i.e. a device which redirects sunlight to a fixed spot, like a scrub in the shadow ...
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1answer
44 views

Cosmology calculator where curvature density $\Omega_k$ can be independently set?

I am looking for a cosmology calculator that does not have the default that $$\Omega_k = 1 - (\Omega_r + \Omega_m + \Omega_{\Lambda}).$$ I particularly want to run $$\Omega_r = \Omega_m = \Omega_{\...
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2answers
127 views

Converting parsecs to light years in the dumbest way possible

I have to convert 132 parsecs to light years and I'm struggling to get the expected result. Here is my method: $132 \text{ pc} = 132'' = 2,2' = 0,03(6)°$ I have an equation for stellar parallax which ...
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1answer
54 views

Open source library to calculate image from signals of a distributed set of radio dishes?

The National Radio Astronomy Observatory's Q&A "How To Make Images With a Radio Telescope" says The most straightforward way to make a radio image with your satellite antenna system, ...
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How to calculate apparent brightness in relation to the sun

I know that we can determine the apparent brightness of an object in our solar system using the following formula: $$B=\frac{A\cdot L_S\cdot R^2}{D^2\cdot d^2}$$ $B$ = Brightness of observed object in ...
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Secular parallax calculation in Binney and Merrifield

I am now reading Galactic Astronomy (1998) by Binney and Merrifield. In this book at p. 44 there is this formula for calculating proper motion vector: $$\boldsymbol\mu_i = \frac{(\mathbf u_i \times\...
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Astronomy 101 Algebra Question [closed]

I’m taking Astronomy 101 this semester and this question on my homework is confusing me, You may assume these conversions: 3.3 feet in 1 meter, 5280 feet in 1 mile, 60 seconds in 1 minute, 60 minutes ...
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Heat map of portion of the sky visible for a given observatory on Earth?

Reading Calculating area of visible sky I started wondering which portion of the sky one could observe how long given the 3D coordinates of an observatory, and two points in time. In other words, I ...
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32 views

Classical Mechanics : Interaction Sun Radiation Pressure - Gravitation

I have a theoretical problem that merges the effects of a gravitational field and the Sun radiation pressure. The problem goes as follows: A spacecraft orbits the Sun in absence of any other body ...
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0answers
61 views

Math for the “universe in a black hole” hypothesis?

There are various pop-science article entitled Are we living in a Black Hole? or Did A Black Hole Give Birth To Our Universe? which say things like There’s a lot to like about the idea that there’s a ...
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1answer
138 views

In astronomical interferometry, what values do the points in the uv-plane have?

As I understand it, the image of an interferometer is the inverse fourier transform of the information in the uv plane. For each baseline (vector between any two telescopes in the array), representing ...
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1answer
139 views

Modeling egg shaped stars

I am well aware of one-dimensional stellar models: The simplest commonly used model of stellar structure is the spherically symmetric quasi-static model, which assumes that a star is in a steady ...
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Vector analysis of Kepler's Third Law

I want to prove Kepler's Third Law via Vector Analysis of motion. I know of other derivations, but want to know this as I think it will be interesting. I have been unable to prove it. But I know of ...
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25 views

Relation between core mass and red giant mass?

Yes, the title might be confusing (I'd appreciate some more clarification on it :D ). I have an estimated mass of hydrogen in the core of a star, and how much hydrogen will be in the core when the ...
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1answer
38 views

The role of 'the interference of waves' in VLBIs'

I've been trying to find out how VLBIs work. It says in this book I've read that many radio telescopes around the world work in tandem to use the interference of waves to get a clearer picture of ...
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1answer
140 views

What units are used for the Stefan-Boltzmann law?

I have a star with given temperature in Kelvin and radius in solar radii. I tried to calculate the luminosity of the star using Stefan Boltzmann's law, and got an absurd number (over 1 million). What ...
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0answers
50 views

Angles in Ptolemaic Model

I am about to work with Ptolemy's Model for the motion of an upper Planet (Mars). I use a epicycle rolling on the deferent. As a first step, I am just interested in the shape of the trajectory, which ...
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1answer
156 views

What is the RGB curve for blackbodies?

I created a program to convert the temperature (in Kelvin) of a blackbody to RGB color. However, it is slightly inaccurate, and the deviations increase for values greater than 10000K and less than ...
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1answer
49 views

How do you go from transit times to Earth-Sun distance?

In the early 18th century, Halley described a method to determine the value of the astronomical unit by observing a transit of Venus from multiple locations on Earth. How do you go from the transit ...
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80 views

Gravity on Mercury's highest elevation?

This post answers what is Mars' gravity at its highest point (Olympus Mons) compared to the Earth's and Mars' standard, it's 0.3736 g (Mars standard is 0.3794 g). This also seems to be the lowest ...
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1answer
139 views

Calculate the absolute magnitude for a multi-star system

We know that the absolute magnitude of a single star can be calculated with the formulae: $$M_{\rm bol} = 4.75 -2.5 \log_{10} \left(\frac{L_*}{L_{\odot}}\right)\ ,$$ $$M = -2.5 \log_{10}(L_* / L_0),$$...
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2answers
116 views

How to calculate the frequency of a gas giant eclipsing the sun from a moon?

Say you have a moon around a gas giant which goes around a star. If the moon has an inclination of around 0° relative to the gas giant's orbit, the gas giant will eclipse the star every orbit of the ...
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0answers
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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 ...
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2answers
308 views

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 ...
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2answers
330 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 ...
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3answers
154 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 (...
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3answers
475 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 ...
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1answer
45 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 ...
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0answers
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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 ...
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1answer
72 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 ...
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1answer
183 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
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1answer
196 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 ...