For questions related to the mathematical operations and analysis of astronomical and astrophysical observations, processes and dynamics.
Questions tagged [mathematical-astronomy]
128 questions
9
votes
2 answers
How to calculate sunrise and sunset times?
I need to create a function (in C++) to calculate the sunrise and sunset times, but I am not a mathematician and I cannot find a correct (and easy) way to do that.
I need to get the same results as can be found…
KelvinS
- 255
3
votes
1 answer
Right ascension / Declination of a satellite
I work whit Heavensat program to understand the behavior of satellites around the Earth, lately something surprised me.
The question is that "Are Right ascension / Declination values of a satellite invariant for different observer on the earth at a…
Saeed Naseri
- 31
2
votes
1 answer
Deriving the first moment of Collisionless Boltzmann Equation in Spherical Polar Coordinates
I am following these notes: Dynamics and Astrophysics of Galaxies.
After equation 6.37, we have:
\begin{equation*}
p_r\,\frac{\partial f}{\partial r} + \frac{p_\theta}{r^2}\,\frac{\partial f}{\partial \theta} +
…
zabop
- 1,011
1
vote
1 answer
How to get velocity dispersion from density profile of a stellar system
I know that one of the Jeans equations can be written in this way [source]:
$$\frac{\partial}{\partial t}\left(\nu \overline{v_{j}}\right)+\frac{\partial\left(\nu \overline{v_{i} v_{j}}\right)}{\partial x_{i}}+\nu \frac{\partial \Phi}{\partial…
zabop
- 1,011
1
vote
0 answers
Do all spherically symmetric stellar systems have zero anisotropy?
My notes are telling me that anisotropy of a stellar system is given by:
$$\beta \equiv 1-\frac{\sigma_{\theta}^{2}+\sigma_{\phi}^{2}}{2 \sigma_{r}^{2}}=1-\frac{\overline{v_{\theta}^{2}}+\overline{v_{\phi}^{2}}}{2 \overline{v_{r}^{2}}}$$
For a…
zabop
- 1,011
0
votes
0 answers
Calculating specific degrees when the sun is below the horizon given 3 other known values
Reference: Types of Twilight
Hi all, I have a question that I'm unsure how to approach and I was hoping someone could help me.
**
I'm trying to calculate the time when the Sun is 16.1 degrees below the Horizon.
**
What We Know
On October 5th, 2021,…
0
votes
0 answers
Number of full moons between two given dates
How does one calculate the number of full moons between two given dates d1 and d2 > d1. The date d3 of a full moon is also given.
Say, what is the number of full moons between:
15-Nov-1936 and 23-Oct-2017
or
21-Sep-1940 and 24-Jul-2021?
Given that…
0
votes
0 answers
Two Body Problem Differential Equation help
I was watching the video linked below. I am confused around part 32:50. The differential is being rewritten as the derivatives of two other quantities. This is where I get confused. What is the point of rewriting terms in a differential equation as…
Dylan
- 1
- 1
0
votes
1 answer
Does the angle between Venus and the Sun max out when the former is half lit?
Christiaan Huygens accurately calculated the distance from Earth to the Sun in 1659 to be 1.023 times our modern figure of 1AU=1.495978707e11 metres. They say he noticed, like Galileo before him, that Venus underwent phases just like the moon does.…
Michael Lee
- 872
0
votes
1 answer
Taking the ratio of the Inverse Square Law for 2 values
I've been given the inverse square law
$$F= L / (4 π d^2)$$
and told to compare the brightness of two stars by taking the ratio of the inverse square law for Star 1 (with quantities $F_1, L_1$, and $d_1$) and Star 2 (with quantities $F_2, L_2$, and…
