21 votes

What is the time dilation between Mars and Earth resulting from the mass difference?

From my answer to Parker Solar Probe passing extremely close to the Sun; what relativistic effects will it experience and how large will they be?: From here (or here if you are ambitious) the lowest ...
uhoh's user avatar
  • 149k
17 votes
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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)...
David Hammen's user avatar
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11 votes
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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?

Sorry it took so long to post an answer. I've spent the past day researching this question, reading over two dozen PDFs (at least 1000 pages of material) and reading the Apollo 13 flight journal (...
DrSheldon's user avatar
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11 votes
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What is the correct thrust curve for a solid rocket with a simple circular hole, and why?

Hill and Peterson "Mechanics and Thermodynamics of Propulsion", third printing, November 1970, page 385, has a diagram that agrees with your intuition. (sorry for poor scan quality) You are ...
Organic Marble's user avatar
10 votes

What is the correct thrust curve for a solid rocket with a simple circular hole, and why?

Underneath the diagrams in the Wikipedia article you link, there's a mention of the BATES grain geometry: Circular bore: if in BATES configuration, produces progressive-regressive thrust curve ...
Russell Borogove's user avatar
10 votes
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Inconsistencies in calculating exhaust velocity

You are simply calculating the wrong parameter. You are calculating exhaust velocity. You can't calculate this without knowledge of the nozzle geometry because exit plane pressure is used in the ...
Organic Marble's user avatar
10 votes
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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)

How do you find the propellant mass needed to reach an inputted altitude?(altitude at end of burn plus altitude during coast) The first thing you should be considering for any rocket mission is the ...
A McKelvy's user avatar
  • 2,482
10 votes
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Why is the value of the Isp of the Rocketdyne J-2 Saturn V engine in my calculation so off?

You're just mixing up data from different sources. The fact sheet you got the flowrates from also gives a different Isp value, 424. Notice that the thrust given on that same fact sheet is lower than ...
Organic Marble's user avatar
9 votes

Calculating mass expelled from cold gas thrusters

The concept and formula are correct for a coherent system of units. You have chosen to use US customary units and these are not a coherent system, i.e. in the situation in the OP one is bound to run ...
Puffin's user avatar
  • 9,504
8 votes
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How can I calculate the orbital elements from two position vectors and a time difference?

If you have no other infomration about the orbit of your satellite (e.g. the orbit is circular), I believe you have to solve this problem with the Lambert's theorem assuming an elliptic transfer orbit ...
Xavi's user avatar
  • 196
8 votes
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How were Frenet frames and Gram–Schmidt orthonormalization used in spacecraft orbit calculations?

From my experience, the fundamental theorem of space curves isn't all that fundamental with regard to spaceflight. This is just a movie, and even the most historically accurate of movies get ...
David Hammen's user avatar
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8 votes
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different ways to calculate satellite height

The first formula gives you the altitude at a particular point in the orbit, assuming that the position vector is the satellite's current position relative to the center of the Earth. The second ...
Russell Borogove's user avatar
8 votes
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Orbit Elliptical Fitting

What you are looking for is called orbit determination, and in particular batch least squares orbit determination. To learn about it I can recommend Statistical Orbit Determination by Bob Schutz, ...
yzokras's user avatar
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8 votes
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How to find the hyperbolic angle given the mean anomaly?

Like the corresponding eccentric anomaly for elliptical orbits, there is no closed-form formula for going from mean anomaly to hyperbolic anomaly. You're going to have to use some sort of numerical ...
notovny's user avatar
  • 5,429
7 votes

What are the energy-to-mass ratios of some fuels/oxidizers, when including the oxidizer?

First we have to go back to the chemical equations, and this time, include the standard enthalpy of combustion. Hydrogen: 2 H$_2$ + O$_2$ → 2 H$_2$O + 572 kJ/mol Methane: CH$_4$ + 2 O$_2$ → CO$_2$ + ...
DrZ214's user avatar
  • 4,556
7 votes

Calculating the planets and moons based on Newtons's gravitational force

Aside from numerical issues, "With Sun as centre" may be part of your problem. Get all the data from Horizons relative to the Solar System Barycenter, not the Sun, which moves relative to the ...
Mark Adler's user avatar
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7 votes
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How to calculate the time to reach a given true anomaly?

Assumptions: The value you are requesting is the time-of-flight from, or to the periapsis of your specified orbit to the specified True Anomaly. We will designate this value as $t$. We have the ...
notovny's user avatar
  • 5,429
7 votes
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Which programs are used to calculate delta V and launch dates to get to other objects?

Both linked examples use the same "program" (mine), they just show different representations & interpretations of the output data. My "program" is a messy collection of MATLAB ...
BrendanLuke15's user avatar
6 votes

What formulas do I use to calculate the gravity and drag forces on an object ascending from Earth's surface?

One thing that may be tripping you up is that the d term in the gravitational formula is the distance between the centers of mass of the objects, not the altitude ...
Russell Borogove's user avatar
6 votes
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Are hyperbolic trigonometric functions used to calculate hyperbolic orbits?

The equations for the position in a hyperbolic trajectory contain the hyperbolic sine, cosine and tangent. A hyperbola is defined by the equation: $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$ It can ...
Uwe's user avatar
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6 votes
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How I can find the angular orbital velocity of satellite in circle orbit?

per Kepler's third law The ratio of the square of an object's orbital period with the cube of the semi-major axis of its orbit is the same for all objects orbiting the same primary. You've specified ...
Erin Anne's user avatar
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5 votes

How to get true anomaly from time?

edit: @DavidHammen has just posted a much more thorough and insightful answer, which also points out some problems applying Newton's method to the current form. I'm pretty sure there are has never ...
uhoh's user avatar
  • 149k
5 votes
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"Pythagorean Three Body Problem" - need some points from an accurate solution for comparison

I just ran it, and mine look pretty much like those in the paper. See some coordinates at the bottom. Here are some {x,y} coordinates at the times in the left column: ...
Mark Adler's user avatar
  • 58.1k
5 votes
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A more accurate way of solar sail calculation?

In his text Solar sailing: Technology, Dynamics and Mission Applications (see here for some of his open access titles), Colin R. McInnes derives the pressure on a perfect sail face on to Sol as $$P(r)...
MBM's user avatar
  • 181
5 votes
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What is this perturbation effect called, and what would be an analytical expression for the resulting eccentricity oscillations?

As the comments on the original question have stated, this is due to the spherical harmonics of the Earth. This answer is adding more context. In the two-body problem, one assumes that the central ...
Alfonso Gonzalez's user avatar
5 votes
Accepted

How to calculate position of GPS Satellite with transmitted ephemeris data?

You can find a C++ method contained in the source code of Andrew Holme homemade GPS receiver project. The method is called GetXYZ and is the EPHEM (ephemeris) namespace and looks as the following: <...
cy8berpunk's user avatar
5 votes

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

In the case where the spacecraft can achieve relativistic speeds and no gravity is involved, $\Delta v$ is actually $c$ times the maximal change of rapidity which can be achieved. So the maximal speed ...
Litho's user avatar
  • 2,040
5 votes

Accuracy of converting from TLE/Orbital Elements to Cartesian if used for other propagator?

If a two line element represented the exact state of a satellite at the epoch time of the element set, there would be zero penalty in applying the SGP4 algorithm to cartesian coordinates, which are in ...
David Hammen's user avatar
  • 73.8k
5 votes

Calculating mass expelled from cold gas thrusters

Puffin's answer is correct; this is just a supplemental that was a bit too involved for a comment. A physical interpretation of specific impulse measured in seconds is "the length of time for ...
Russell Borogove's user avatar
5 votes
Accepted

GMAT: Finite burn targeting, solving for burn duration and quaternion

First off: Chris you may already know some/all of my response due to your background. I will attempt to both answer your GMAT question and provide insight to others who may not be as familiar with ...
Ravi Mathur's user avatar

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