# 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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### 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 ...
1 vote
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: \...
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 ...
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 ...
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 ...
1 vote
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 ...
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 ...
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 ...
1 vote
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 ...
1 vote
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
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, ...
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 ...
1 vote
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 ...
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....
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 ...
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-...
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, ...
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 ...
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 ...