# 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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### 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 ...
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 ...
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 ...
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 ...
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
34 views

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 ...
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 ...
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 ...
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,...
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 ...
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 ...
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
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
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 ...
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 ...
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 ...
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, ...
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 ...
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 ...
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### 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 ...