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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Get (X, Y, Z) coordinates from Horizontal Coordinates
I'm developing a planetarium software using the Hipparcos Catalogue. I have also implemented all the formulas of the book: "Practical astronomy with your Calculator and Spreadsheet".
With ...
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How can I Mathematically Calculate the Luminosity of a Post-Main-Sequence Star from Mass and Age?
So, I saw this question (which is quite old) and that's all well and good, but what if I need to (very) roughly calculate the luminosity of a star from the end of the main sequence? Let's assume that ...
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Equation describing Energy Transport due to Radiation in the interiors of stars
I am considering a very elementary stellar structure and I'm required to derive an equation to describe the energy transport due to radiation. The answer I am supposed to obtain is:
$$\frac{dT}{dr}= -\...
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It is possible to estimate an exoplanets' orbital period from just one transit?
Is one lightcurve containing a dip in brightness obtained from the transit method sufficient to obtain or estimate the orbital period of an exoplanet - such that one (first) observation could be used ...
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Probability of exoplanet transit
An exoplanet is in a circular orbit around its star.
The radius of the star is $r_{star}$
The radius of the exoplanet is $r_{planet}$
The radius of the orbit is $r_{orbit}$.
The orbital period of the ...
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What is the diameter of a telescope lens that will capture the surface of Proxima Centauri b?
I been trying to find the way I can calculate the telescope lens diameter needed to see a star by the distance of the star or the planet from the earth. Is there any mathematical relation we usually ...
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How do I code the formula for the minimum mass of a stellar fragment from Whitworth & Stamatellos, 2006?
I was researching the formation of brown dwarfs, and I stumbled into the paper "The minimum mass for star formation, and the origin of binary brown dwarfs", and I am attempting to code a ...
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Calculate the uncertainty in measured flux density from an integrated intensity map
I have some ALMA data, in the form of a spectral cube, which I have integrated along the velocity axis to create an integrated intensity ('moment 0') map.
The integrated intensity map shows emission ...
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Would it be possible to create a telescope from a hanging reflective cloth?
A chain suspended on two points hanging under gravity forms a curve called a Catenary, which can look pretty similar to a parabola. I'm not sure if this generalizes to the two dimensional case where ...
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How do I calculate the closest point to the sun on Earth's surface?
Couldn't find an answer so here I come:
On 21st of June and 21st of December these points would lie on the tropics.
But what about the other days of the year?
Is there a simple formula to calculate ...
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How the heck does JPL actually do the numerical integration for their development ephemerides? (general questions)
After writing this answer to JPL Horizons - "highly accurate measurements of planetary positions" - how do they do it? which draws from Park, Folkner, Williams & Boggs 2021 The JPL ...
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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 ...
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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 ...
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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 ...
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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, $...
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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 ...
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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 (...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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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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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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 ...
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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 ...
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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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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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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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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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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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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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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 ...
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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 ...
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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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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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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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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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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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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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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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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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