All Questions
Tagged with mathematics orbit
15 questions
3
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1
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99
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Orbit equation solver giving wrong orbits
Recently I've become interested in simulating orbital mechanics using Kepler's equations, and in Unity I created my own equation solver by following this paper I found. However, inputting Earth's ...
3
votes
0
answers
130
views
Kepler to Cartesian and Cartesian to Kepler inaccuracies
I am programming a computer simulation set in a star system. I've used Rene Schwarz's wonderfully concise memorandi explaining converting from Kepler orbital elements into cartesian coordinates and ...
- 51
2
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0
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299
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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
3
votes
1
answer
191
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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 ...
- 6,733
8
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2
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806
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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 ...
- 6,733
2
votes
1
answer
155
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Why is there a deviation between the ratio of $a^3$ and $T^2$ for the outer planets?
The Wikipedia article about Kepler's third law includes a nice table about the ratio between $a^3$ and $T^2$. However, for Mars, Jupiter, Saturn, Uranus, and Neptune, the ratio $\frac{a^3}{T^2}$ in $...
- 6,733
2
votes
0
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433
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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 ...
- 21
1
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0
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642
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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 ...
- 51
11
votes
2
answers
4k
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What is the difference between the two terms named "Eccentricity" and "Ellipticity"?
I don't get the difference between the two terms named "Eccentricity" and "Ellipticity", especially, in astronomy. I understand eccentricity as a measure of the curvature of a ...
- 121
3
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0
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54
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Classical Mechanics : Interaction Sun Radiation Pressure - Gravitation
I have a theoretical problem that merges the effects of a gravitational field and the Sun radiation pressure. The problem goes as follows:
A spacecraft orbits the Sun in absence of any other body ...
- 31
2
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1
answer
373
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How to calculate the true length of day on a celestial body?
When I only know the sidereal rotation period, how do I determine the true length of day on a body?
We know the Earth's sidereal day doesn't have full 24 hrs unlike the true length of day. It's ...
- 1,262
4
votes
1
answer
1k
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Simple mathematical models of solar systems
I’m a hobbyist programmer with a profound love for procedural content generation. I’m working on a 2D space exploration game and while it’s not meant to simulate anything real, I’d like to give it a ...
- 143
3
votes
1
answer
216
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How to mathematically describe a planet's eccentric orbit?
Is there a formula for describing a planet's position along an eccentric orbit over time? I am particularly interested in the elliptical case (0 < e < 1).
I understand that the planet has a ...
- 175
10
votes
1
answer
240
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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 ...
- 101
3
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0
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115
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Average effect of a planet on a comet
I'm considering a problem involving star S, planet A, and a comet B. The orbits of the planet and comet are eccentric, with eccentricities $e_A$ and $e_B$. I'm trying to calculate the average change ...
- 131