# Questions tagged [calculation]

How to calculate things directly related to Space Exploration as defined in the help center, or how the calculations have been done in the past or will be done in the future.

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### How accurately (maximum possible accuracy) can future satellite positions be predicted?

Agencies/organizations who own/operate satellites want to know their future positions after a certain amount of time. We know that models of satellite dynamics are imperfect and also perturbations ...
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### What is the accuracy / uncertainty of Two Line Elements (TLEs)?

I use TLE sets supplied on this website to find the future position of satellites (well usually just the ISS) using the SGP4 propagation method implemented in C++. My question is: What is the ...
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### What is the EXACT time that the sun will rise, at the Apollo 11 landing site, in Feb 2173

So this was only supposed to be a fun little easter egg in my sci-fi novel for any eagle-eyed reader who decided to run the numbers, but I've driven myself quite literally - to distraction for the ...
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### How accurate are modern ephemerides, and how does their accuracy degrade over time?

I was reading about what is involved in making an ephemeris and wondered about this. Feeling I'd read pieces that extrapolated orbits over many thousands of years, I looked for an example and found ...
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### Doing an experiment to point a laser to the moon and back

After reading this question: I got an itch to to test out the mirrors myself (and maybe record whole process to irritate conspiracy nuts). What equipment would I need? I assume a high powered laser ...
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### How can I calculate the orbital elements from two position vectors and a time difference?

I have two position vectors for my satellite, and I know that the satellite reaches these two positions 15 minutes apart. I know I can find the inclination using linear algebra and my position ...
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### Usage of the coordinate systems in orbit propagation

For the orbit propagation in ECI coordinate system, considering the effects of zonal harmonics and Sun/Moon perturbations the following procedure was formed: Convert the state vector to ECEF ...
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### What is the correct thrust curve for a solid rocket with a simple circular hole, and why?

Going to wikipedia's article on solid-fuel rockets, I come across some graphs of thrust curves for certain bore-hole geometry. Right now I'm interested in the simplest bore-hole: a circular hole right ...
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### Calculations Apollo astronauts were trained to do by hand if loss of guidance computer and/or data & coms link to Earth?

This answer to the question is it possible to navigate space travel with no computer? currently contains the line Yes, as long as you don't care where you end up but I am not so sure this is true. ...
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### 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 ...
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### How do you find the propellant mass needed to reach an specified altitude? (altitude at end of burn plus altitude during coast)

This question is basically entirely explained in the title, but I'll explain it more so this question doesn't get shut down. Basically, does anyone have an equation to find the propellant mass(solid) ...
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### Could an astronaut with a jump and a "jet pack" "jump" off of the Moon?

The initial naïve question was: "Could an astronaut with a jump and a "jet pack" "jump" off of the Moon?" :) For fun, let's assume the optimal circumstances: Gemini era ...
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### Accuracy of converting from TLE/Orbital Elements to Cartesian if used for other propagator?

Say that I wanted to propagate a real-life satellite based on an initial position in space. However, the only source of data I can get is from a tracking website like CelesTrak or Space-Track, where ...
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### What are the energy-to-mass ratios of some fuels/oxidizers, when including the oxidizer?

Energy-to-weight ratio is an important parameter. We would like it to be high so we don't have to carry around much fuel. Maybe you've heard some of the numbers for common fuels. Hydrogen is about ...
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### Calculation of V1 (orbital speed) during ascent

I am studying instrumentation of NASA's Orion spacecraft, and there is a readout for V1 (I am assuming this is the "first orbital velocity", for circular orbit), and it seems to be in small decimals. ...
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### How to get true anomaly from time?

An exercise that was left unsolved from last year's class gives me this equation : $$t-t_{p} = \sqrt{\frac{a^3}{\mu}}*(\arcsin(X) - e*X)$$ where : $$X = \frac{\sqrt{1-e^2}*\sin(v)}{1+e*\cos(v)}.$$...
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### Calculating the planets and moons based on Newtons's gravitational force

I am trying to understand how to calculate the orbits of solar system bodies in an n-body framework, based on the pair-wise gravitational interaction between the objects. At present, I am considering ...
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### How were Frenet frames and Gram–Schmidt orthonormalization used in spacecraft orbit calculations?

I haven't seen the film Hidden Figures yet, but I have read and listened to some dialogue clips in this NPR Review. In it they mention a Frenet frame and the Gram–Schmidt process for ...
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### How to calculate the time to reach a given true anomaly? [closed]

I'm looking for a general formula or procedure calculate time to reach any given true anomaly.
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### "Pythagorean Three Body Problem" - need some points from an accurate solution for comparison

note: if you up-vote (or even if you don't), don't forget to scroll down and see the excellent answer as well - it's beautiful! The Pythagorean Three Body Problem also know as Burrau's problem is a ...
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### Calculate Date of Spring Equinox, possibly using JPL's Horizons website?

I'm familiar with orbit ephemerides and the ways to use those to plot orbits and positions. However, in all the charts I find, I can't seem to find a way to determine when an equinox on another planet ...
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### What is the time dilation between Mars and Earth resulting from the mass difference?

I am not sure I understand the time dilation correctly, but if mass has direct impact on time, then let's consider cosmological event - one orbit of planet Earth around the Sun. This event will person ...
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### Perifocal coordinates and the orbit equation

Given the position $(p,q)$ and velocity $(v_p,v_q)$ of a satellite in perifocal coordinates $(\hat{p},\hat{q})$ where $\hat{p}$ is pointing toward periapsis, I can easily calculate the specific ...
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### How to find the hyperbolic angle given the mean anomaly?

I'm modelling a hyperbolic gravity assist trajectory around Jupiter and trying to calculate the coordinates for each hour interval before/after passing periapsis. I've calculated $M_h = 0.0176$ is the ...
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### 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 $T(t)$ ...
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### Where can I learn to calculate the physics of an ion thruster?

I am trying to build an ion thruster, but I don’t know where to start learning the actual numbers behind one. I know how they work on a basic level, but not much more. Basically I want to be able to ...
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### How to calculate the optimal mass ratio for a multistage water rocket?

I do know about the Tsiolkovsky rocket equation for optimising multistage rockets, however the equation requires a fixed exhaust velocity which is something that water rockets don't have, however I ...
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### When was Lucy's mission first scripted in Excel and why is that what Lockheed Martin chose to do it with?

CNBC's NASA spacecraft launches toward Jupiter asteroids on an intricate path charted by Excel Years before Lucy took off, Lockheed Martin mission architect Brian Sutter used Excel to chart the ...
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### Calculating mass expelled from cold gas thrusters

Consider a cold gas thruster rated at 1 lbf per firing. The thruster is on-off: there is no throttling, so when it fires it's at a constant full thrust. Assume the gas is nitrogen, and that it has a ...
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### Inconsistencies in calculating exhaust velocity

I'm quite sure this is either a small or just plain stupid mistake but my anxiety is getting the better of me. when calculating exhaust velocity this is the equation used: however I keep getting ...
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### How to calculate position of GPS Satellite with transmitted ephemeris data?

How can I calculate the position of a satellite using the ephemeris data transmitted by each satellite? I will then use positions generated from each GPS satellite's self-reported ephemeris to ...
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### Orbit Elliptical Fitting

Question: Given a set of XYZ (3D) coordinates in the Earth-fixed frame, after converting them to the inertial frame, how do I perform orbit fitting in the least-squares sense (meaning minimising all ...
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### Which programs are used to calculate delta V and launch dates to get to other objects?

I have noticed that many people here have used different programs to calculate the launch dates and delta V to get to other planets. For example: https://space.stackexchange.com/a/59585/44505 https://...
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### A constant parameter in a three body system?

In a two body system, there are a lot of orbital parameters not changing over time, like eccentricity or the orbital plane. A constant parameter can be a combination of two or more, like even though ...
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### 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 ...
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### Do monopropellants have a characteristic length?

I was reading about calculating thrust chamber geometry, and a key tool seems to be the characteristic length, L*. The engine I'm modelling (hypothetically! please don't take down the question) uses ...
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### Why doesn't the Merlin 1-D use higher LOX to RP-1 mixture ratios?

So I've been screwing around with CEARUN, which is the chemical equilibrium with applications program created by NASA. I've been using it to calculate theoretical Isps for rocket engines using RP-1 ...
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### Moment of Inertia of rocket

I am trying to model a rocket launch, and am trying to calculate its moment of inertia at each instant. I am assuming a two-stage rocket with a liquid fuel tank, plus a payload (nosecone-shaped for ...
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### I'm trying to create a trajectory to Mars for a low thrust ion thruster engine using astrogator

I'm trying to create an optimize a trajectory to Mars for a number of low thrust high specific impulse engines. I am having trouble with the initial set up. I created a LEO exit spiral using a ...
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### Why is the value of the Isp of the Rocketdyne J-2 Saturn V engine in my calculation so off?

While calculating the delta V the Saturn V has on its second stage, I wanted to also calculate the Isp of the J2 rockets engines. However, the value difference between my results and the values given ...
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### How fast would one have to move to achieve permanent lunar day by perpetually moving along with the solar terminator?

This comment got posted and I did not understand it. for those interested, one rod per moonhour is about a quarter furlong per fortnight. If I googled correctly and jumped to the right conclusions.....
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### Distinction between spacecraft data and telemetry - difference in spacecraft resource use?

What is the distinction (if any) between spacecraft data and spacecraft telemetry? Do these terms tend to represent different kinds of information? While each case is different, in what ways do they ...
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### 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 ...
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### What am I missing about rocket nozzle isentropic flow?

Playing a bit with Cpropep-Web, something looked wrong to me about how it models isentropic flow through a CD nozzle. I'm taking the RS-25 characteristics as an example. I ask for a frozen equilibrium ...
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### GMAT: Finite burn targeting, solving for burn duration and quaternion

I'm trying to using GMAT to design a finite burn with a fixed attitude throughout the burn. I do not know the attitude needed at the start, nor do I know the burn duration needed. I set up six ...
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### Finding the mass flow rate of a blowdown system?

This is a rather amateur question I will admit but how does one find the mass flow rate of an engine with a given tank pressure? Is it really as simple as calculating the cross-section of all plumbing,...
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### Are there any equations out there that can calculate the burnup of an asteroid depending on angle?

Are there any equations that can calculate the burnup of an asteroid depending on the angle? I want to be able to calculate the magnitude of an asteroid impact with the angle being the changeable ...
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### What was NASA's “LUROVA” Operational Thermal Computer Model analog or digital? How were capacitors used?

@GremlinWrangler's answer links to Apollo Rover Lessons Learned Applying Experiences on the Apollo Lunar Rover Project to Rovers for Future Space Exploration by Ronald A. Creel, Space and Thermal ...
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### How to calculate the Lagrangian points positions?

I have two bodies, one rotates around another on orbit. For i.e. Earth and Sun or Moon and Earth. If we know masses, velocity, distance and keplerian elements of orbit, how can we find the positions ...
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