# Questions tagged [mathematics]

Questions explicitly involving numerical analysis.

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### How to calculate Earth's velocity vector in ECEF?

I would like to write some AR mobile app that will show Earth velocity vector, but I have no any experience with astrodynamics. So how to calculate Earth's velocity vector in ECEF, having date and ...
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### Question about the Hohmann Transfer: why does delta-v go down when transferring to a higher orbit?

I'm trying to estimate the delta-v (and, by applying the Rocket Equation, the propellant) required to lift a payload from LEO to a higher orbit. As I understand it, the standard way to do this is with ...
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### Mathematics used for F9R flyback and landing [duplicate]

I was wondering if anyone may have useful links to the mathematics used by the F9R that allowed it to fly back to LZ-1 and land successfully. I'm hoping to find some papers that will give the broadest ...
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### How are the coefficients in the EGM96 model normalized?

For my own interest I'm trying to implement the EGM96 gravitational model. I found the coefficients here. The readme file says that they are "fully normalized", but I'm not 100% sure what this means. ...
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### Generating plot of LV's performance as a function of the C3 parameter

Following my previous question about Ariane 5 performance data for escape missions, I would like to know how the plot of launch vehicle capabilities like the next one are obtained: More specifically, ...
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### Calculate time to impact on elipisoid Earth

As a simple project to introduce myself to orbital mechanics I'm attempting to calculate impact times of an object close to Earth. Right now I am using only Keplerian mechanics (no air resistance or ...
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### Keplerian Orbital Elements ↔ Cartesian ECEI with WGS84 Corrections

I'm trying to write code to go back and forth between equatorial KOE (Keplerian Orbital Elements) and ECEI (Cartesian). ECEI→KOE I found here: How to programmatically calculate orbital elements ...
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### How are gravity assists conceived?

So there are some very complex gravity assists out there. The Cassini mission, for instance, used a VVEJ (Venus Venus Earth Jupiter) gravity assist to make it to Saturn. Similar flybys have been done ...
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### Can I derive a combined equation for velocity of solar sail?

In this article on The Planetary Society website, I read this about solar sails: At an acceleration rate of 1 millimeter per second per second (20 times greater than the expected acceleration for ...
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### Solar sail force calculation: Angle vector

In this Wikipedia article about solar sails, I read the following: The force on a sail and the actual acceleration of the craft vary by the inverse square of distance from the sun (unless close ...
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### Delta-V chart mathematics

Could someone explain me the mathematics behind the Delta-V charts one can find on internet such as:                 &...
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### How to programmatically calculate orbital elements using position/velocity vectors?

I would like to build some orbital mechanical software from scratch. I feel that this would be a great way to learn the steps required to calculate different Kepler orbital elements of an object, plot ...
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### Gravity drag Delta-v calculation for launches to orbit

It would appear that gravity drag has a exact formulation for an instantaneous moment in a rocket launch. I'm tempted to think that some calculus could get you an exact number for Delta-v of an ...