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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3answers
1k views

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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0answers
365 views

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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1answer
1k views

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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2answers
617 views

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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1answer
445 views

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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1answer
950 views

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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2answers
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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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0answers
941 views

Need help calculating delta-v required for Earth to Mars low orbit Hohmann transfer

I'm trying to calculate the required delta-v to travel from a 200 km Earth orbit to a 200 km Mars orbit using the last equation from this answer: $\Delta V=\sqrt{{\mu_S\over r_1}\left(\sqrt{\frac{...
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1answer
627 views

Taper ratio for partial space elevator

The calculations for the taper ratio of a space elevator don't seem to be all that difficult and it is easy to find some equations to use. You can even find an expression written out for the total ...
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2answers
189 views

Terminal velocity on Europa

What would be someone's terminal velocity based on the gravity of Europa (.1335G) but given the drag coefficient and air density of Earth? I have a protagonist who is currently plummeting about four ...
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1answer
505 views

Laplace Method for Orbit Estimation

I have a question about Laplace angle-only method for orbit determination where the line of sight vectors are being interpolated. I read somewhere that the method fails (due to a matrix being singular)...
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1answer
371 views

Does the opening angle of the cone matter?

When discussing orbital mechanics, you learn that all orbits roughly follow an ellipse which is obtained as the intersection of a cone with an inclined plane, creating conic sections. Below is a plot ...
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2answers
6k views

Solar sail thrust calculation

In Space Mission Engineering: The new SMAD, page 555, section 18.7.2, the following thrust formula is given for a solar sail: $$F=\frac{2RSA}{c}\sin^2\theta=9.113\times10^{-6}\frac{RA}{D^2}\sin^2\...
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2answers
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How can I predict what an object's orbital state vectors will be in the future?

I have a position and velocity vector for an orbiting object and can calculate the orbital elements. From a simple two-body situation, how can I predict where in the orbit the object will be at some ...
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1answer
334 views

Specifying a position and velocity of body in a Kepler simulation

I've built a model of the Solar System by calculating Keplerian orbital elements. The model takes a time $t$ which is incremented with each frame of the simulation. I then calculate the new positions ...
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1answer
5k views

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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2answers
2k views

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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3answers
21k views

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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3answers
45k views

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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1answer
1k views

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 ...
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3answers
1k views

Physics and math behind flight through solar system [closed]

I wrote a program that simulates a solar system. I was able to calculate the locations for every planet on its elliptical route for any given time. In a second project, I managed to simulate newtonian ...
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1answer
3k views

What branches of mathematics are widely used in astrodynamics?

We knew that Voyager 1 and 2 exploited the gravitational slingshot from Saturn and Jupiter back in 70s, and the trajectories were predicted by Newton's laws of motion, and this law we used a lot in ...

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