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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112 views

Where can I build my house on Mercury so that I can see double sunsets (and sunrises)? Can I do it near the poles where it's cooler?

CNN'S Mercury mission flies by closest planet to the sun for the first time says at the end: Mercury's unusual rotation and oval-shaped orbit around the sun (sic) means our star seems to quickly rise,...
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1answer
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How long does the "eclipse" last on a space station at the L1 point between a moon and a planet last when the moon blocks the sun in front?

The situation I am asking about is as depicted in the picture. Supposing I have a space station staying perpetually at the L1 point, the moon will completely block the space station from all sunlight ...
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What's the formula for change in argument of periapsis over time due to J2 perturbations for a geocentric satellite?

I'm trying to propagate the orbit of the ISS, but it became very clear to me very quickly that the J2 perturbations were nothing to scoff at. A quick google search gave me the equation for the change ...
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Is there a formula for a planet's orbit in a 3D space?

I'm trying to model the orbits of Earth and Mars and their positions at a given point in time. But I can only find 2D equations of elliptic orbits, which only contain the x and y variables. I have to ...
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25 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
131 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
93 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
239 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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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
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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
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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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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
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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
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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
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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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2answers
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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
273 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
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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
250 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
60 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
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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
59 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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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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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
155 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 ...
2
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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
163 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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52 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 ...
4
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1answer
226 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
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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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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
306 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
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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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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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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
402 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
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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
570 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
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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 ...