Questions tagged [mathematics]

Questions explicitly involving numerical analysis.

Filter by
Sorted by
Tagged with
3
votes
1answer
76 views

How do you calculate the percentage of light-speed a ship with a certain delta-v can achieve, accounting for relativistic effects?

I was doing some back-of-a-postage-stamp calculations on high-isp interstellar spacecraft earlier and realised something. If I design a spaceship which according to the rocket equation has a very high ...
3
votes
2answers
300 views

Why is the bend angle of a hyperbolic trajectory giving different results?

The bend angle ($\delta$) is the reflex angle between the two asymptotes of a hyperbolic trajectory. From this Stack Exchange answer, the formula to calculate the bend angle is: $$ \delta = 2 \sin^{-...
3
votes
1answer
94 views

Different results for Orbital Period?

I am making a hypothetical solar system with random masses and distances (but still physically and mathematically accurate). I want to calculate the trajectory of a spacecraft, and to do that, I need ...
4
votes
0answers
42 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
2answers
106 views

Is a polar geosynchronous orbit described by Viviani's curve?

This answer to Is there a name for the great circle where latitude and longitude are equal? says (in part): More generally, a clélie is the name given to any spherical curve where the longitude $\...
0
votes
1answer
166 views

How did NASA calculate 22 million “rocket horsepower” for the SLS Booster?

This answer to Does NASA really report the power of rockets in horsepower? cites NASA news item Space Launch System Booster Aimed and Ready to Fire which says "What's impressive about this test is ...
1
vote
1answer
127 views

Are hyperbolic trigonometric functions used to calculate hyperbolic orbits?

The following comment is really intriguing! I would say, "Yes, The equations for going from Mean Anomaly to Eccentric Anomaly to True Anomaly are indeed different for hyperbolic orbits than for ...
0
votes
0answers
47 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 ...
0
votes
3answers
317 views

How to solve this exercise in orbital mechanics; the moon stops in its orbit, what happens next?

As an exercise in orbital mechanics, suppose the moon were to suddenly stop orbiting Earth, and instead at time $t=0$ begin moving in the same direction as Earth so that their relative velocity were ...
3
votes
2answers
205 views

What does Earth's J₂₂ moment look like?

Wikipedia's Geopotential model give's the form of the potential component linked to $J_2$ as $$u = J_2\frac{P^0_2(\sin \theta)}{r^3} = J_2\frac{1}{r^3}\frac{1}{2} \left(3 \sin^2\theta-1 \right) = ...
4
votes
1answer
87 views

Do Lagrange points still exist if there is significant radiation pressure on the third body from the first?

From this answer: To obtain the distance to L1, find the smallest value of $r$ such that $$\frac{M_2}{r_1^2} + \frac{M_1}{R^2} - \frac{r_1(M_1+M_2)}{R^3} - \frac{M_1}{(R-r_1)^2} = 0.$$ To ...
1
vote
1answer
52 views

How to find instantaneous mass of a central body that results in a given osculating orbit?

This question was underspecified, so I'm going to try again. Osculating orbital elements are Keplerian elements of a hypothetical orbit around a specified center which would be tangent to a specified ...
4
votes
1answer
86 views

Analytical treatment of relative positions between satellites?

I have been searching the internet for estimation of relative position between two satellites. However, all sources seem to be pointing to methods used for proximity operations, where the math ...
2
votes
0answers
95 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 ...
1
vote
2answers
83 views

Given r/a, what are the limits on the direction that an orbiting body could be moving (e.g. solid angle vs r/a)?

An orbiting object at distance $r$ and semimajor axis $a$ will move at $\sqrt{2 - \displaystyle \frac{r}{a}}$ times the speed of a circular orbit at $r$, no matter what the eccentricity or which ...
1
vote
1answer
96 views

When is it okay or at least helpful to use energy arguments in orbital mechanics?

When faced with energy-based questions about spaceflight we often comment something like orbits are about momentum, not energy and use delta-v math in answers. But in this answer to How big a nuke ...
3
votes
1answer
138 views

How can Earth-Centered Inertial (ECI) coordinates be properly called “inertial” if the Earth's orbit is always accelerating towards the Sun?

I've just realized (again) that I don't understand anything, something that often happens to me after reading a @DavidHammen answer. How can Earth-Centered Inertial (ECI) coordinates be inertial if ...
2
votes
2answers
186 views

At a height of 100 km, what speed do you need to be going to escape Earth's gravity?

I understand that the escape velocity of Earth is 11 km/s. However, Earth's gravitational sphere of influence is not infinite, so it is possible to go slower than that and still escape the sphere of ...
4
votes
2answers
303 views

What information can I get if an elliptical orbit intersecting a circular orbit of radius 𝑟 and velocity of ellipse is equal to velocity of circular?

How can I approach solving the question below? Consider an elliptical orbit intersecting a circular orbit of radius $r$ as shown below. If $v_{ellipse} = v_{circular} = v $, find: True ...
3
votes
1answer
144 views

How much less delta-v would it take to reach the Sun using Venus and Earth flyby's compared to direct?

@TomSpilker showed that the minimum delta-v to go from Earth orbit into the Sun is about 20.89 km/s. That's going from 200 km LEO to "perihelion at the sun's photosphere (guaranteed complete entry!)" ...
8
votes
2answers
708 views

What's the eccentricity of an orbit (trajectory) falling straight down towards the center?

Discussion below this answer has got me thinking. A circular orbit has eccentricity of $\epsilon = 0$, ellipses $ 0 < \epsilon < 1$ (between but not including 0 and 1), and parabolic and ...
1
vote
1answer
97 views

Understanding line of sight between two satellite with oblate Earth using “scaling k-component”

I have been doing some reading on accuracy of determining line-of-sight between two satellites give a WGS84 oblate earth. The paper Rapid Determination of Satellite Visibility Periods (Alfano, Negron ...
4
votes
1answer
73 views

How does one impulsively null spacecraft nutation?

The Scott Manley video The Only Pilot to Shoot Down A Spacecraft - A Space Ace talks about the ASM-135 ASAT and its successful test launched from an F-15. He shows images from the page The F-15 ASAT ...
16
votes
1answer
278 views

What is the optimal inclination change strategy?

Consider a transfer between two circular orbits of similar radius, the only difference being the inclination difference, $\alpha$. What's the minimal $\Delta v$ required to perform this transfer? ...
1
vote
1answer
117 views

How do you calculate the ∆v required to increase apoapsis to a certain height?

To calculate the ∆v needed to increase our apoapsis from a low orbit of 100km to 400km, we find the velocity at 100km using the semi major axis (which is 250km, in this case), and then find the ...
2
votes
1answer
201 views

How do you calculate gravity loss (simplified)?

Assume a rocket with constant mass and thrust. To simplify things, we can ignore aerodynamic drag, and we'll also not perform a gravity turn, hence our flight plan is as follows: -Burn radially from ...
2
votes
0answers
45 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 ...
4
votes
1answer
991 views

Why does the eccentricity vector equation always equal -1?

This is the eccentricity vector equation, $$e=\frac{1}{\mu}[(v^2-{\mu \over r})r-(r \cdot v)v]$$ $$e=|e|$$ Now this equation is written differently from many different sources but they essentially ...
3
votes
0answers
49 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 ...
28
votes
3answers
8k views

Time at 1 g acceleration to travel 100 000 light years

How long would it take to go 100,000 light years at a constant 1 g acceleration?
3
votes
0answers
79 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/...
2
votes
2answers
136 views

What is the formula for Legendre Polynomials from EGM96 calculated in F447.f program?

The F447.f program is designed to calculate the geoid undulation for EGM96. I'm trying to understand how it accomplish this calculation. I stuck in ...
1
vote
1answer
152 views

How were the geodetic and geocentric latitudes of the Space Shuttle defined and calculated?

The image below is cropped from https://i.stack.imgur.com/4XFaJ.jpg as described in this answer. It shows a geographic state of a space shuttle at a given instant in time. There is only one value for ...
1
vote
1answer
53 views

What do the axis labels mean in this plot (apparently from Sutton 8th edition)?

In the Analytical Graphics Inc. video Low-Thrust Space Trajectory Design and Optimization the speaker Pradipto Ghosh of AGI shows a slide at around 07:00 shown ...
2
votes
1answer
63 views

What Methods are Used for Satellite to Site Visibility Calculation?

In the paper, Rapid Satellite-to-Site Visibility Determination Based on Self-Adaptive Interpolation Technique it is claimed that "Satellite-to-site visibility periods are typically determined by the ...
0
votes
2answers
92 views

How to find instantaneous positions of a central body of specified mass that results in an osculating orbit?

If I understand correctly, osculating orbital elements such as those posted in JPL's Horizons represent the mathematical osculating (tangential or "kissing") Keplerian orbit about a specified location ...
4
votes
1answer
75 views

Mechanics of Sun-Synchronous Orbit & North Korea's KMS-4

QUICK QUESTION: Is North Korea's KMS-4 in a proper Sun-synchronous orbit? https://www.n2yo.com/?s=41332 2016-009A FOLLOW-UP QUESTION: How do I tell? I want to understand the mechanics. RESEARCH:...
9
votes
1answer
201 views

Launching east from a mountain on the equator at midnight during a new moon; ranking of each contribution?

This answer is intriguing and I'm curious if it's correct, and especially which effects are most important. If you want to avoid gravity assists, the most fuel-efficient way out of the Solar System ...
1
vote
1answer
147 views

Help with my tensor tension; how to derive and calculate this rigid body gravity gradient torque?

Tensors make me tense. Imagine a long thin rod in a circular orbit. The gravity gradient will produce a net torque on the rod whenever it is not oriented parallel, or perpendicular to the radius ...
3
votes
1answer
126 views

Help with Scott Manley's rigid body dynamics narration

I've just watched Scott Manley's video SpaceX's Water Landing Reveals Rocket "Secrets" (or, What We Learned from CRS-16) (again) and there's some rigid body dynamics in there where I'm not sure I am ...
1
vote
0answers
89 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? ...
3
votes
1answer
68 views

How can I convert HGI coordinates to J2000 coordinates?

I am looking at old mission data such at this one from Vega 1. The coordinate system provided is HGI. Most of the data I have is in ICRF/J2000.0, as JPL Horizons provides. How can I convert between ...
9
votes
2answers
353 views

Explanation of weird values in New Horizons data?

In this answer I computed (methods given later in post) the estimated time, distance, range, and resolution for the science capture for New Horizon's closest approach to Ultima Thule (2014 MU69). ...
2
votes
2answers
166 views

Ideal shape for a long, skinny reaction mass for LEO to cis-lunar and beyond? (a “space rail gun”)

@Ingolifs' answer got me procrastinating thinking further. What you're asking about is a mass driver space station in low earth orbit that a payload or ship launched from earth can dock with, and ...
1
vote
0answers
240 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 ...
6
votes
2answers
755 views

From the General Thrust Equation towards Tsiolkovsky, how to explain dropping these terms along the way?

The NASA Glen Research Center tutorial page Rocket Thrust Equation links to the General Thrust Equation page which starts with: Which transcribes into MathJax as: $ \ \ \ F = \dot{m}_\mathrm e ...
0
votes
1answer
304 views

Analytical approximations for the shapes of these plots of ISP vs nozzle diameter? (Raptor engine)

A comment on the currently unanswered question Is there an authoritative catalog for rocket launch identifiers? led me to this Github page which links to r/spacexlounge on which currently appears a ...
3
votes
0answers
109 views

What is this perturbation effect called, and what would be an analytical expression for the resulting eccentricity oscillations?

In this answer I've generated some oscillations of eccentricity by being somewhat naughty and propagating a TLE for +/-250 days from epoch. I believe it's okay for the purposes of demonstrating gross ...
4
votes
2answers
350 views

What exactly means universal variable x and z?

I have been studying by myself Orbital Mechanics, and when solving the Lambert Problem, it's common to use the universal variable approach. I understand the algorithm, but I haven't found any book ...