Questions tagged [mathematics]

Questions explicitly involving numerical analysis.

29 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
7
votes
0answers
1k views

For the mathematical relationship between J2 (km^5/s^2) and dimensionless J2 - which one is derived from the other?

The term $J_2$ seen in discussions of nodal precession of orbits (e.g. sun-synchronous) appears to come in two flavors. For example, in the Wikipedia article Geopotential model it has a value of $1....
7
votes
0answers
431 views

Understanding formula for geocentric position of Moon

I am trying to understand a basic formula in a Celestial Mechanics reference. The formula is for the position of the Moon in a geocentric frame. The reference claims in line (981) that this should be ...
6
votes
0answers
165 views

What are the contributions of ancient Indian astronomers in mapping of the solar system and galaxies?

In the history of astronomy we usually come up with the name of European astronomers like Kepler and Galileo. Earlier Indian astronomers, for example Aryabhata and Bhaskaracharya, are not usually ...
4
votes
0answers
105 views

How to get lunar L, B, C parameters from the Moon's 3x3 rotation matrix from the Python package Skyfield?

Answers to What are the “Moon L, B, C” angles shown in this solar eclipse simulation? explain that L and B (or "l" and "b") are the "selenographic coordinates of the Moon's apparent center" (latitude ...
4
votes
0answers
217 views

Mathematical reasoning behind pe=pa leading to maximum thrust

I've been looking at both the thrust and thrust coefficient equations (below) and I understand that they will be optimum in a vacuum when $P_a=0$. But, I see in textbooks that $p_e=p_a$ corresponds to ...
3
votes
0answers
81 views

Mean to Osculating conversion for non-J2 averaged elements

What is the appropriate technique to convert mean elements (true anomaly averaged) into osculating elements when the model has J2, SRP, drag and additional forces modeled. Brouwer's transformation is ...
3
votes
0answers
53 views

How accurate can a point in space be determined by the likes of the ICRF?

How accurately could a 3D point in open space (i.e. not on an object), say at an elevation of 30,000m above sea level, be located or modelled using the likes of the International Celestial Reference ...
3
votes
0answers
95 views

Can we calculate elliptical properties in a spherical coordinate system?

Can we calculate the elliptical properties like the semi-major axis and eccentricity using the state vectors (position and velocity) in the spherical coordinate system? http://www.braeunig.us/space/...
3
votes
0answers
54 views

variables affect the trajectory in a stochastic way

What are the different variables affecting the trajectory of a rocket in a stochastic way for getting potential three-sigma trajectory?
2
votes
0answers
45 views

What are the limitations to using this “trick” to quantitatively relate altitude changes (via their speed) with applied forces that cause them?

In this comment I used a "trick" to double check a calculation in the post above it. Using the vis-viva equation I first determined that if the ISS lost 10 meters of altitude in 86400 ...
2
votes
0answers
44 views

Understanding the paper “Determination of Satellite Orbital Elements by Means of On-Board GPS Receiver and Its Verification” by Yoshiwo Okamoto et. al

I have been assigned with implementing the algorithm proposed in the paper "Determination of Satellite Orbital Elements by Means of On-Board GPS Receiver and Its Verification" by Yoshiwo ...
2
votes
0answers
45 views

Why does Gravity Simulator's rendering of TESS' orbit look like a pretzel? How can I unpretzefy it?

Below is a screen shot from the amazing Gravity Simulator driven by our own @HappyKoala. If you haven't seen it recently go check it out now, then come back in 30 minutes and read the rest of my ...
2
votes
0answers
104 views

Why does SpaceIL's Beresheet landing graphics show m\s instead of m/s?

I just noticed that the software displayed in the video of the landing had the velocity and acceleration units with a backslash (m\s) instead of the usual convention of a forward slash (m/s). Out of ...
2
votes
0answers
48 views

How can I “debounce” these TDRS satellite inclinations? (reconstruct the zero-crossings)

The plot below is from the question Why do the geosynchronous TDRS satellites have this distribution of inclinations?, and the explanation says Inclination and mean motion (rev/day) for TDRS ...
2
votes
0answers
132 views

Is there a calculator or set of formulas for estimating aerobraking on Mars?

I am looking for a calculator or formulas that can be used to calculate the aerobraking on Mars mission. I have found some data on previous Mars flights where aerobraking was used and all my current ...
2
votes
0answers
141 views

Do Lissajous orbits have stable/unstable manifolds?

The question Did DSCOVR travel “along the stable manifold of it's future SE L1 Halo orbit” to get there? is specific to DSCOVR's trajectory from Earth to its primarily heliocentric orbit near Sun-...
2
votes
0answers
187 views

Software (besides Ltool) to simulate CR3BP (three body) problems?

Are there any other softwares for CR3BP besides Ltool? As I've learnt here Ltool is not generally available to the public. I would like to simulate three body orbits within the standard circular ...
2
votes
0answers
139 views

Roughly how many kinds of closed or periodic orbits are there in the circular restricted three-body problem?

Question: Roughly how many kinds of closed or periodic orbits are there in the circular restricted three-body problem? Has anyone made an attempt to enumerate and classify/categorize them? Notes: If ...
2
votes
0answers
880 views

What is a “synodic frame”? Can one be defined for an elliptical orbit?

A description of a "synodic frame" was one of the main ingredients in this excellent answer to a question about an animation of a funky-looking orbit that several different and distinctly interesting ...
1
vote
0answers
45 views

How to find/extract the semi-major axis from a TLE with Skyfield?

I have a TLE: 1 33591U 09005A 21024.46740879 .00000049 00000-0 52095-4 0 9997 2 33591 99.1927 41.5349 0014084 172.6670 187.4709 14.12449679616592 And I would like ...
1
vote
0answers
138 views

Kepler prediction problem, fundamentals of astrodynamics

I needed help with problem 4.3 of Fundamentals of Astrodynamics by Roger R. Bate, Donald D. Mueller, Jerry E. White (dover, archive.org) Given that $r_0 = (I+j)$ and $v_0 = 2k$ find $r$ and $v$ for ...
1
vote
0answers
96 views

What is wrong with my orbit sim equations? How can I fix them?

Edit: Partial question: The object now moves in an ellipse like it's supposed to, but it orbits around a different point than I intend. How can I make it orbit around a particular object at a point? ...
1
vote
0answers
327 views

How to make satellite ground track on map?

I want to make satellite ground track using matlab. I already had a position of satellite(ECI) by solving Kepler equation. And I know convert ECI to ECEF using rotation determinant. Then I convert ...
1
vote
0answers
170 views

How to get from the perturbative acceleration formula to the acceleration on the 3 axis in the case of the oblate Earth, considering j2?

If we start from the pertrubative acceleration formula, how do we get the expression for the acceleration for the 3 axis written under that form. I've used the partial derivative for the gradient ...
1
vote
0answers
143 views

Will these equations give me the approximate apparent RA and Dec using positions from Horizons?

In this answer @DavidHammen showed me how to get coordinates from JPL's Horizons using the Earth's equatorial plane as a reference plane by selecting ...
1
vote
0answers
941 views

Need help calculating delta-v required for Earth to Mars low orbit Hohmann transfer

I'm trying to calculate the required delta-v to travel from a 200 km Earth orbit to a 200 km Mars orbit using the last equation from this answer: $\Delta V=\sqrt{{\mu_S\over r_1}\left(\sqrt{\frac{...
0
votes
0answers
96 views

How should mass specific impulse calculated for relativistic exhaust?

This answer says: Optimising for Isp only is problematic, as it's simply: $$I_{sp} = \frac{v_e}{g}$$ Which is the same as optimising for exhaust velocity. With no constraints on thrust, particle ...
0
votes
0answers
74 views

Is a 2:1 “figure-eight” Lissajous orbit possible in the Circular Restricted Three Body Problem?

Was Queqiao in a halo or Lissajous orbit? Why do sources disagree? says Proper halo orbits have the same period for their in-plane oscillations and out of plane oscillations, so they are closed ...
0
votes
0answers
65 views

Help on Rocket Injector Equation

Hello can someone explain me how can I get the value of (6340) because when I try to solve the given values on the book I get (6423.980075) when I round it off it is still not the right answer can ...