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.

Filter by
Sorted by
Tagged with
2 votes
2 answers
76 views

Measure the deprojected distance between two points?

I have an image of a protoplanetary disk, from which I would like to measure the distance of various points from the centre. See below image for an example, where I would like to measure the distance ...
3 votes
1 answer
75 views

Azimuth angle and elevation angle of a heliostat mirror

for the control of a heliostat I have a program for the calculation of azimuth and elevation. Now I am still missing the calculation of azimuth angle and elevation angle for setting the mirror. While ...
-2 votes
1 answer
82 views

Projection from Earth [closed]

If a Particle is projected from Equator due north with a velocity $v$ and Earth is rotating with a uniform angular velocity $\omega$. How can it be shown that the highest latitude reached will be ...
9 votes
1 answer
192 views

Error propagation methods for orbit parameters

Recently I've encountered an article in our local astronomical popularization magazine. It is about a well known task of Sgr A*-black hole's mass estimation. The article is written as a step by step ...
8 votes
4 answers
2k views

Generate a uniform distribution on the sky

How to generate a 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 ...
1 vote
1 answer
34 views

Using Saha's equation knowing the overall pressure

Knowing the pressure, $P_g$, how can I calculate $\frac{N_{I+1}}{N_I}$ using Saha's equation? If I assume that $P_g=(n_e+n_{H^+}+n_H)K_B T$ and that $n_e=n_{H^+}$, I can find the electronic pressure, $...
2 votes
1 answer
95 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_{...
1 vote
0 answers
69 views

What is the relationship between true anomaly and solar longitude?

So, my ultimate objective is to map solar longitude values onto a pseudo-Gregorian calendar. I thought this would be simple, but it has turned out to be anything but. I have asked several questions on ...
3 votes
0 answers
32 views

Total scattered flux and polarization for a ring of dust particles close to a star

I have an important problem and maybe some of you can help me with the following question: I have a mathematical expression for the total scattered flux in Jansky and the total linear polarized flux (...
2 votes
1 answer
46 views

How does this Toomre GI criteria have the period in the denominator?

I saw this equation in a literature review recently talking about the Toomre criterion for gravitational instability: Given here in section 2.1.1: https://arxiv.org/pdf/1801.06117.pdf, viz. But I am ...
3 votes
2 answers
1k views

What kind of perspective projection is shown in this image?

I’m trying to develop software that overlays sky coordinates over 2d images of the sky taken by an iphone. I’ve done the sky coordinates part, but I’m trying to figure out what kind of perspective ...
4 votes
0 answers
30 views

How to model the kinematics of gases expelled from comets and planetary atmospheres?

Once the ices of comets sublimate, where do they move to, and with which equations do you describe their motion in the interplanetary medium? Similarly, where do the gases that are stripped from the ...
5 votes
2 answers
147 views

Does a star shaped mirror present problems either optically, or in signal processing over a more nearly circular mirror?

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 ...
1 vote
1 answer
96 views

Triangular Asterism Trigonometry between Alnitak, Saiph, and Sirius?

I am using the SIMBAD database for Alnitak, Saiph, and Sirius: ...
3 votes
1 answer
70 views

Accurate formula for calculating the mass of an exoplanet using the transit method

A friend and I did some work on exoplanets with the help of a research institute (IEEC in Spain) for a major high school project. What we did was to "redetect" the exoplanet XO-6b through ...
6 votes
3 answers
1k views

N-body simulation still losing precision despite using arbitrary-precision arithmetic and symplectic integrator

A while ago I asked 2-body orbits expanding in nbody simulation?. One thing that I noticed was that JavaScript does not have arbitrary precision, and that I used RK4 as my integrator, while it is ...
2 votes
1 answer
32 views

What does "RV model including a GP with a quasi-periodic covariance structure" mean?

A candidate short-period sub-Earth orbiting Proxima Centauri says: 4.1 Simple periodogram analysis ]We first consider a very simple pre-whitening procedure applied to the CCF RVs in order to ...
2 votes
1 answer
54 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
1 answer
98 views

Finding the Laplacian of the deflection potential: I obtain 4𝜅(𝜃⃗ ), not 2𝜅(𝜃⃗ ). Why am I wrong?

From the review paper Bartelmann and schneider, 1999) Weak Gravitational Lensing, page 48. Like above, the Laplacian of the deflection function is convergence, $\kappa(\vec{\theta})$. I tried to ...
1 vote
1 answer
69 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 ...
4 votes
2 answers
276 views

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 ...
11 votes
2 answers
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 ...
2 votes
1 answer
84 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 ...
2 votes
0 answers
62 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 ...
3 votes
1 answer
126 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 ...
8 votes
2 answers
726 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 votes
1 answer
113 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 votes
1 answer
122 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})\, \...
1 vote
0 answers
68 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 ...
1 vote
1 answer
133 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 ...
1 vote
0 answers
25 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 ...
4 votes
0 answers
45 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 ...
1 vote
1 answer
84 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 $...
3 votes
2 answers
230 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 votes
1 answer
156 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 votes
2 answers
461 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 votes
1 answer
161 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,...
3 votes
2 answers
499 views

Is there 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 votes
1 answer
41 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 ...
2 votes
0 answers
83 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 ...
1 vote
0 answers
106 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 ...
1 vote
0 answers
29 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 ...
4 votes
1 answer
135 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 ...
8 votes
2 answers
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 ...
19 votes
2 answers
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 celestial dome), by brightness? I want to know if they are uniformly distributed. For example, ...
3 votes
2 answers
135 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
2 answers
234 views

How to calculate the distance to galaxies with standard candles?

I was wondering how the distance in Mpc could be calculated between Earth and a galaxy using the luminosity provided? Do not be shy to use all math necessary :) Clarification: Luminosity is inversely ...
3 votes
1 answer
72 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 ...
10 votes
3 answers
433 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 ...
4 votes
1 answer
94 views

Reference for equation of state?

I am a post graduate studying mathematics and currently working on the mathematical theory of stars though not an expert. When I am making some assumption about the equation of state (for a star or ...