# Questions tagged [mathematics]

Questions explicitly involving numerical analysis.

220 questions
Filter by
Sorted by
Tagged with
146 views

### How is the equation for non-spherical gravitational accelerations derived?

I am referencing Vallado (4th edition) to understand the acceleration contributions on a spacecraft due to non-spherical gravitational effects. Generally, I understand this derivation, except for how ...
• 215
1 vote
116 views

### Objects move clockwise instead of counter-clockwise

I'm trying to write an orbital simulation with patched conics. For my sources I'm using https://orbital-mechanics.space/ and Fundamentals of Astrodynamics (Second Edition). Both sources suggest to use ...
• 63
982 views

### Object slowest at periapsis - despite correct position calculation

I'm coding up a simulation of celestial bodies using patched conics. At the moment I'm stuck with calculating the velocity of the object in the perifocal frame. For the position I'm simply using the ...
• 63
6k views

### Person falling from space

A person at rest 500 km above the Earth falls straight downwards. She has a snug magical force field around her that is totally rigid and completely protects her from outside heat. The force field ...
• 199
476 views

### Euler Angle Notation

Fundamental Question Correct me if I am wrong here. For Euler Rotations, we use the right hand rule. So a positive rotation in X-Axis will represent a clockwise rotation; whereas a positive rotation ...
• 101
138 views

### Which notes and/or books on mathematics, physics, 3D geometry preparatory to the study of orbital dynamics?

I have a master's degree in aerospace engineering and I'm preparing for job interviews for orbital mechanics/space flight dynamics engineer positions and I need material about maths, physics, 3D ...
• 433
3k views

### What is the velocity of the ISS relative to the Earth's surface?

This was asked once before, but I believe there was no clear answer given and accepted. The ISS has an orbital period of 92.9 minutes, or 5574 seconds. If it were in a completely equatorial orbit, ...
586 views

### Rewriting the equation of motion as a system of first order differential equation

I am required to rewrite the equation $$\ddot{\mathbf{r}} = - \frac{\mu}{r^3} \mathbf{r}$$ as a first order differential equation. How do I go about doing this? I understand how this equation was ...
1 vote
230 views

### How can I determine a rotation matrix from unit vectors?

I want to determine the rotation matrix from which compute the Euler Angles to rotate my spacecraft in order to point in a specific direction. For example, i want the z body axis of the spacecraft to ...
• 315
96 views

### Optimal numerical method to solve BVP for optimal low thrust control

I need to solve a boundary value problem (BVP) for an optimal control in case of low thrust trajectories optimization. I want to include the J2 perturbations to the Edelbaum solution (multiple ...
51 views

### Calculating period/SMA delta and other parameters from Clohessy-Wiltshire

I'm working on the camera system for a game about relative motion. The orbital motion is completely described by Clohessy-Wiltshire. I would like to be able to calculate some things like eccentricity ...
84 views

### How can I show the ideal path from Earth to Mars in a vacuum using calculus?

I would like to use calculus to try and model the optimal path to mars in space, assuming the rocket starts with an initial velocity in the vacuum of space, and only accelerates due to the Sun's ...
• 31
172 views

### Is it possible to determine the classical orbital elements for an Elliptic Repeating SSO?

As in the title, it is possible to have a repeatable Sun-synchronous orbit but with an elliptic eccentricity? If yes, which equations I have to consider to determine its classical orbital elements?
• 315
189 views

### Relationship between osculating eccentricity and Brouwer-Lyddane short eccentricity

I was under the impression that the mean elements are given by taking the average over an orbital period of the satellite, i.e.: $e_{mean}(t) = \int_{t}^{t+T(t)}e_{osc}(t')dt'[0.367in]$ where $T(t)$ ...
• 169
113 views

### GMAT: What causes the error "ArrayTemplate error : dimension error"?

I have made various scripts that work with GMAT, but once in a while I get an "ArrayTemplate error : dimension error" error. I do not know what causes it, as in this case my script appears ...
• 339
1k views

### How does one calculate the look angle for non-geo satellites (i.e. LEO, HEO, etc.)

I'm trying to find a way to calculate look angles to not just GEO satellites, but LEO, MEO, and HEO sats. The only calculator I've found myself is here, which was referenced for a similar problem on ...
• 71
4k views

### What is the maximum distance between two satellites orbiting at 400 km that would still allow them to communicate with each other using radio waves?

All satellites have the same inclination. At an altitude of 400 km, the circumference of their orbit is $2\pi \cdot (6371+400) = 42\ 543$ km. If, for example, you have only 2 satellites separated by ...
77 views

### How does one generate a formula(s) for an artificial satellite's location at time t given a set of known locations at discrete times?

Given a set of spatio-temporal points in space {(Lat_1, Lon_1, Alt_1, Time_1), ... (Lat_n, Lon_n, Alt_n, Time_n)}, I need a function (i.e. a formula) that takes these points (or subset of points) as ...
• 71
515 views

### Optimizing trajectories with GMAT: how to understand the "Vary" parameters, and how to know what values to use for them?

I've been using GMAT in my free time to optimize trajectories, and have varied burn component values and spacecraft states, usually with success. The vary command in GMAT, with the Yukon optimizer ...
357 views

### GMAT: How do I prevent infinite propagation into the future, which causes the "requested epoch 95008.513478505 is not on the DE file" error?

I have a spacecraft I am trying to get from Earth to Mars. I use an Earth propagator until the SC is out of the Earth's sphere of influence, then a deep space propagator until Mars' sphere of ...
1 vote
1k views

### Formula for Determining Time to Perform Delta-V Burn Given Propulsion System Parameters

Question is as stated. Determining how much delta-V one needs to change orbits is pretty straight forward with the rocket equation. However, I’d like to see if there’s a way to calculate delta-V from ...
• 371
91 views

### How to calculate laser link spot size

In the reseach paper " A laser link from lunar surface..." , chapter 2.1.3.: When employing, for example, 20 cm diameter apertures at the transmitter telescopes and considering a carrier ...
• 121
1 vote
148 views

### What is the equation to find how much fuel you need to reach a velocity? [closed]

Theoretically, I need to launch a rocket, and I need to find how much fuel I need to reach a velocity however I do not know the equation.
864 views

### What is the equation for fuel equals distance for a rocket? [closed]

Theoretically, I am trying to launch a rocket from space and trying to figure out how much fuel I would need to get to a certain distance.
1 vote
178 views

• 51
865 views

### What is the numerical procedure to find the next closest approach between two bodies on keplerian orbits?

Given two bodies on Keplerian orbits, what is the procedure to find the next closest approach of the two bodies? The bodies would be effectively massless objects like two spaceships orbiting around a ...
• 993
645 views

### How to calculate the height above the horizon of a geostationary satellite on a given latitude?

Wikipedia's Geostationary orbit; Communications says: Geostationary communication satellites are useful because they are visible from a large area of the earth's surface, extending 81° away in both ...
• 123
939 views

### Is there a neat formula for hyperbolic Kentucky windage?

When doing some back of a napkin calculations for a recent question Where would the Pascal B manhole cover be now?, I realised a quick way of solving these class of orbital mechanics question is to ...
338 views

### Can mascons have Lagrange-like points? In principle? At the Moon?

Background Lagrange points are a mathematical consequence of the The Circular Restricted Three Body Problem (CR3BP or CRTBP); two massive bodies orbiting around their center of mass and a third ...
• 149k
717 views

### Modeling a rocket using Tsiolkovsky's equation and ordinary differential equations

So I have this uni assignment to make a model out of ODEs, and my idea was to use rockets. After some research I found about Tsiolkovsky's equation and tried using it on a Falcon 9 (disconsidering ...
617 views

### Estimating thrust and kg fuel for a generation ship's journey to Alpha Centauri

Premise: A generation spaceship leaves Earth around the year 2060 on a journey to colonize Alpha Centauri A (ACA). In this fiction, fusion power is achieved in 2040, improved over 20 years, and used ...
• 263
352 views

### Could this three-thruster spherical spacecraft de-tumble itself with zero final velocity?

@Joshua's answer to What is the minimum number of RCS thrusters capable of stabilizing a satellite against an arbitrary rotation? begins: I know this question is old, but I randomly discovered a ...
• 149k
166 views

### Do geodesics close on an ellipsoid?

I want to calculate the shortest distance between two points (Point A and Point B) on the ellipsoid surface. For this I need to use geodetic passing through these two points. Well, if I continue this ...
• 73
1k views

### Is there an intuitive reason for why the shape of the orbit at perigee is the mirror image of that at the apogee?

Is there an intuitive reason for why the shape of the orbit at perigee is the mirror image of that at the apogee? It seems strange to me, because the situation is so different at the perigee compared ...
366 views

### Difference between rotated frame and rotating frame

Suppose we have a spacecraft orbiting around Earth and we neglect all effects of Earth's $z$-axis motion, i.e., no wobble, precession, or nutation. For simplicity, we only assume a rotation rate \$\...