# Questions tagged [mathematics]

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### Generate an uniform distribution on the sky

How to generate an 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 ...
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 celstial dome), by brightness? I want to know if they are uniformly distributed. For example, ...
1k views

### Calculating the apparent magnitude of a satellite

I'm writing a program that involves calculating the apparent magnitude of satellites from a ground location. I currently have the intrinsic magnitude of the satellites and the solar phase angle in ...
1k views

### Why does the Earth's orbital eccentricity oscillate with a period of about 100,000 years?

This answer says: Earth's orbital eccentricity varies over time from being nearly circular (low eccentricity of 0.0034) and mildly elliptical (high eccentricity of 0.058). It takes roughly 100,000 ...
130 views

### What natural mechanisms could lead to the unlikely case of the same rogue asteroid or planet passing through our solar system twice?

I find he following answer to the question What's the soonest Oumuamua could return? unsatisfying and oversimplifying and the last five words "Therefore it will never return." unsupported at a minimum....
98 views

### What is the RGB curve for blackbodies?

I created a program to convert the temperature (in Kelvin) of a blackbody to RGB color. However, it is slightly inaccurate, and the deviations increase for values greater than 10000K and less than ...
503 views

### What is the 2D elliptical projection of the Celestial Sphere called, and how can I make one?

I see this kind of projection of the celestial sphere into 2D frequently, usually with an image of the milky way galaxy or cosmic microwave background. This particular image shows the path of visible ...
64 views

### Gravity on Mercury's highest elevation?

This post answers what is Mars' gravity at its highest point (Olympus Mons) compared to the Earth's and Mars' standard, it's 0.3736 g (Mars standard is 0.3794 g). This also seems to be the lowest ...
64 views

### What kind of triangle is formed by three unequal masses in a circular restricted three body orbit?

This answer to Are the orbits of all triple star systems at least technically unstable? mentions: There are known solutions to the gravitational three body problem that can be shown to be stable. ...
34 views

### Help understanding why these two sub-Hill sphere moon stability limits are so different?

Comments under this answer to What orbital period would produce one New Moon (and one Full Moon) each year? What other effects would this produce? link to Stable satellites around extrasolar giant ...
67 views

### How can I correct for transit time?

I know the exact time a radio telescope detected a transient event. I also know the exact location of the telescope, and the galactic coordinates (galactic longitude, latitude) and right ascension and ...
I have two ephemerides for orbital elementsāthat is, each contains $a$ (semi-major axis), $e$ (ecc.), $i$ (incl.), $\Omega$ (long. asc. node), $\omega$ (arg. of peri.), $\tau$ (time of peri.), $T$ (...