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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5
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104 views

Same area, different shape. pro's & cons

Pure speculation about a future replacement for the JWST that I almost certainly won't live to see. The JWST's mirror (and then some) would fit unfolded and flat into the Starship's 8m diameter ...
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2answers
2k views

14,000 square degrees

The DESI Legacy Imaging Surveys says it produces a model of “the 14,000 square degrees of extragalactic sky visible from the northern hemisphere”. But I thought the whole celestial sphere (like any ...
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Probability of transit of an exoplanet in front of its star

I'm trying to calculate the probability of transit of an exoplanet in orbit around a star of diameter $d$, at a distance of $4d$ from its centre. Here's what I did: In this figure, we are only ...
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1answer
55 views

What's the Right Ascension & Declination of Galactic Left & Galactic Right?

For the purpose of being able to align my model to the galactic plane, I want to know the directions of the galactic center, anti-center, north, south, left & right. This gives me the answer for ...
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1answer
114 views

Is it still called an orbital resonance if the ratio is irrational?

Previously, I asked At what point are orbital resonances no longer "ordered" but "chaotic?", and received an answer from @CarlWitthoft: Perhaps if the calculated fraction had an ...
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708 views

At what point are orbital resonances no longer "ordered" but "chaotic?"

Orbital resonances are typically in small valued integer ratios, like 2:1, 3:2, or 4:7. However, there are some resonances whose ratios have large reduced values, including the 73:69 Naiad:Thalassa ...
2
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1answer
96 views

Sun Moon earth Angle

I want to do a theoretical prediction before trying out an experiment. I just noticed that the arc separating the illuminated side of moon and the shadowed side is an ellipse arc. So Is it possible to ...
4
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1answer
110 views

Scaling Relations

In this picture , Keplers third law is written in a scaling relationship with solar mass. $$a^3=\frac{G(m_1+m_2)}{4\pi^2}P^2 \rightarrow m_1+m_2 = \frac{4\pi^2a^3}{GP^2}$$ $$m_1+m_2=(1 M_{\odot})\, \...
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37 views

Converting a Satellite's position in Lat/Lon/Alt/Time to RA/Dec

I'm trying to convert a satellite's position given in latitude/longitude decimal degrees, altitude in meters, and time in milliseconds since epoch to right ascension and the declination. I have found ...
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1answer
95 views

Is it true that the 3 body problem can't be solved using the four basic functions, radicals, and integrals?

The two-body problem can be completely solved via two one-body problems, which only uses the four basic binary functions. However, the three-body problem cannot be solved with these functions and ...
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23 views

Relative orientation in a 1:1 resonance of a planet and a satellite

To my understanding, in a two-body problem of a planet and a satellite, a 1:1 resonance means that the orbital period of the satellite is the same as its angular frequency (maybe not, so please ...
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38 views

Physical Meaning of the Principal Tidal Fourier Modes and Their Integers

I'm trying to understand tides evolution of planets, and I often come across the Prinicipal Tidal Fourier Modes expressed as: $$ \omega_{lmpq}$$ For example, see the discussion after Eq. A15 in ...
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1answer
74 views

Why is there a deviation between the ratio of $a^3$ and $T^2$ for the outer planets?

The Wikipedia article about Kepler's third law includes a nice table about the ratio between $a^3$ and $T^2$. However, for Mars, Jupiter, Saturn, Uranus, and Neptune, the ratio $\frac{a^3}{T^2}$ in $...
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2answers
229 views

Pendulum clock correction

I'm trying to solve this task: The pendulum clock was transported from the Earth's equator to Antarctica (in the vicinity of the southern geopole) for scientific experiments. Estimate the pendulum ...
5
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1answer
147 views

Calculate lines of equal solar altitude

I'm attempting to calculate lines of equal solar altitude, essentially a generalized case of the Earth terminator for solar altitude $ h $. For a given sun position with declination $ \delta $ and ...
2
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1answer
156 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
35 views

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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0answers
46 views

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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0answers
72 views

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
5k views

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 ...
4
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1answer
132 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
148 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
280 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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0answers
50 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
84 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
68 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
40 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
103 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
36 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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2answers
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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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0answers
39 views

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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4answers
1k views

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
233 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 ...
2
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2answers
328 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
60 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 ...
2
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2answers
358 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 ...
2
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1answer
96 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_{\...
2
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2answers
130 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 ...
3
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1answer
67 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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0answers
39 views

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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0answers
47 views

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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0answers
58 views

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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0answers
28 views

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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0answers
35 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
169 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 ...
7
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1answer
143 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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0answers
91 views

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 ...