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.
171
questions
1
vote
0
answers
32
views
Equation for calculating boolean answer to "is this Earth satellite in eclipse"
I have found plenty of math for determining duration of satellite eclipse, but I am having trouble finding an equation that produces a simple boolean answer to the question "Is this Earth ...
- 245
1
vote
0
answers
22
views
What would be the new Equation of motion if the magnetic field's origin is shifted from the origin of a co-rotating spherical polar coordinates?
The equation of motions due to the dipole magnetic force of a planet in a frame corotating with the planet and origin at the centre of planet assumed to be sphere components wise are given as below:
\...
- 145
2
votes
0
answers
44
views
How is an index of n=0 possible for the Lane-Emden equation?
I was recently showing that an index of $n=0$ for the Lane-Emden equation results in constant density throughout the star. However, in my calculations I had to use the constant $\alpha$ which can be ...
- 21
2
votes
0
answers
116
views
Understanding the Julian Date equation in detail
I am trying to figure out the Julian date equation by myself. Unfortunately, there are not many resources I could find which explains in depth. Moreover, there are several variations of the same ...
- 173
-4
votes
1
answer
103
views
Estimate the mass of Saturn based on the given data below
In September 2017, the Cassini 1 mission was nearing its end after 20 years due to fuel shortages. The NASA space probe reached its apoapsis on 12 September at 1:27 AM EDT (time on Saturn) with a ...
- 45
1
vote
1
answer
67
views
Meaning of "variables of date" in VSOP87 files
When I read the description of VSOP87, I find out that there is a file with "variables of date" and a file with "variables J2000". In Astronomical Algorithms of J. Meeus I can find ...
- 113
2
votes
2
answers
1k
views
Confusion over habitable zone
I am confused over the habitable zone, as I calculated the expected temperature of Earth (minus greenhouse effects), and it would be -17 C. Which is below the freezing point of water.
I also made a ...
- 227
6
votes
1
answer
161
views
On the Radiation Field of large Gas Giants
I am woring on creating a fictional star system, and I need to find an answer to a question to find an accurate way to depict this.
I am aware that Gas Giants create a dangerous field of radiation ...
- 227
1
vote
0
answers
51
views
Question regarding potential moon sizes
I am planning out ideas for a science-fiction world, and I want to make sure that what I include is reasonable and mathematically sound (outside of things like FTL as that is neccessary for the story ...
- 227
1
vote
1
answer
149
views
Celestial Navigation - How to calculate Longitude?
I'm trying to learn celestial navigation using the Sun to determine longitude. I'm starting to understand some of these concepts, but I can't figure out how to calculate longitude accurately. Hoping ...
1
vote
0
answers
49
views
How do nuJ(nu) units work?
I'm working with (Nublado) Cloudy, which is essentially a spectral modelling tool for stellar matter. Using the software, I model my own stellar object and obtain its continuum.
According to Hazy, ...
- 53
2
votes
1
answer
108
views
What is the mathematics needed for understanding DE440 and translating it into xyz coordinates?
I would like to write my own code to process NASA's DE440/DE441 ephemerides, but I do not know the mathematics needed to do this.
I understand packages such as pyephem have implemented variations of ...
- 181
1
vote
0
answers
20
views
How can Aggregation of Gravitational Fields of subplanetary solar objects improve our understanding of the motion of the planets?
If we imagine magnets on a table as a simplified analogy in regards to gravitational attraction between objects, then it may be demonstrated that when three objects are placed in a row labeled in ...
- 11
-1
votes
1
answer
121
views
Whis my planetary volume formula wrong? (volume = mass/density)
I'm having trouble with this and am unsure what I'm doing wrong. Let's use Earth as an example.
Earth has a mass of 5,972,168,000,000,000,000,000,000 (5.97E+27) kg and a density of 5513.4 kg/m3 or 5....
- 19
2
votes
1
answer
108
views
By analytical geometry, how to calculate the fraction of the visible area of the Sun at a point during an eclipse?
Assume a perfectly spherical Sun and Moon, and ignore atmospheric effects for simplicity. I'm an observer in the origin of my coordinate system, and I know the positions of the centers of the Sun and ...
- 31
2
votes
4
answers
1k
views
How does each degree equal to 60 minutes?
I was searching in the internet to find the reason each degree equals to 60 minutes and I found this:
60 seconds make up a minute. One day is equal to 24 hours, and the hour hand completes two 360-...
- 985
2
votes
0
answers
37
views
References to learn about algorithms/mathematics related to building planetarium / astronomy software?
I'm a beginner in astronomy with a background in engineering and mathematics. I'm interested in learning how to build astronomy software to model the position and movement of planets and stars, ...
- 181
0
votes
0
answers
41
views
Trying to understand how to properly implement this equation to a healpix map
So i am working on reproducing a paper (Secrest, N. J., von Hausegger, S., Rameez, M., Mohayaee, R., Sarkar, S., & Colin, J. (2021). A test of the cosmological principle with quasars. The ...
0
votes
1
answer
77
views
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 ...
- 635
2
votes
1
answer
121
views
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 ...
- 73
2
votes
0
answers
26
views
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}= -\...
- 779
2
votes
0
answers
61
views
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 ...
- 1,648
2
votes
0
answers
73
views
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 ...
- 1,648
2
votes
1
answer
127
views
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 ...
- 31
0
votes
0
answers
39
views
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 ...
- 61
2
votes
0
answers
171
views
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 ...
- 1,366
6
votes
0
answers
122
views
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 ...
- 1,648
5
votes
1
answer
278
views
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 ...
- 151
2
votes
0
answers
224
views
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 ...
- 31.4k
2
votes
2
answers
248
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 ...
- 1,366
3
votes
1
answer
231
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 ...
- 31
-1
votes
1
answer
93
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 ...
- 547
2
votes
1
answer
79
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
0
answers
236
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 ...
- 141
4
votes
0
answers
36
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 (...
- 41
3
votes
1
answer
58
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 ...
- 415
4
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 ...
- 75
5
votes
0
answers
35
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 ...
- 151
4
votes
1
answer
231
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 ...
user45319
6
votes
3
answers
2k
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 ...
- 6,613
2
votes
1
answer
64
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 ...
- 31.4k
1
vote
1
answer
137
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 ...
- 335
6
votes
2
answers
189
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 ...
- 69
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 ...
- 383
5
votes
2
answers
816
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 ...
- 779
3
votes
1
answer
317
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 ...
- 131
3
votes
1
answer
160
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 ...
- 6,613
8
votes
2
answers
773
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 ...
- 6,613
2
votes
1
answer
209
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 ...
- 547
4
votes
1
answer
219
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})\, \...
- 547