Earth-Venus-Mars-Earth Trajectory Calculated via V-Infinity Matching (Lambert & Newton Root Solvers)

Опубликовано: 01 Январь 1970
на канале: Alfonso Gonzalez - Astrodynamics & SE Podcast

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This interplanetary trajectory with 2 flybys was calculated via a v-infinity matching scheme that calculates each leg of the trajectory by using a universal variables Lambert's problem solver and a Newton root solver (estimating a derivative via finite differences). This example is used to validate against Richard H. Battin's book called: An Introduction to the Mathematics and Methods of Astrodynamics.

The general algorithm is as follows:
1. For the first planet, pick a time of departure (Earth in this case)
2. For the second planet, pick a time of arrival (Venus in this case)
3. Use an ephemeris model (SPICE's de432s.bsp in this case) to get the ephemeris of planets 1 and 2.
4. Use the position vectors and time in between them to solve Lambert's problem for the spacecraft
5. Calculate the v infinity value of the Spacecraft arriving at planet 2
6. Use a Newton root solver to calculate the time of flight to the next planet (Mars in this case) that will result in an equal magnitude v infinity at planet 2 (Venus) arrival and departure. This is calculated via Lambert's problem and estimating the derivative via finite differences (time of flight is the independent variable, and deviation from the desired v infinity is the dependent variable)
7. Repeat steps 5 and 6 for all subsequent planets

Its difficult to explain in text without visuals, so don't worry. The next ~5 videos in the Orbital Mechanics with Python series will be covering this topic in depth and I'll be posting software in the GitHub repository for this channel ( https://github.com/alfonsogonzalez/AWP )

Links to the Space Engineering Podcast (YouTube, Spotify, Google Podcasts, SimpleCast):
   • Space Engineering Podcast Full Episodes
https://open.spotify.com/show/01Gcgly...
https://space-engineering-podcast.sim...
https://podcasts.google.com/feed/aHR0...

Link to Orbital Mechanics with Python video series:
   • Orbital Mechanics with Python

Link to Spacecraft Attitude Control with Python video series:
   • Spacecraft Attitude Control with Python

Link a Mecánica Orbital con Python (videos en Español):
   • Mecánica Orbital con Python

Link to Numerical Methods with Python video series:
   • Numerical Methods with Python

#interplanetarytrajectories #flybys #vinfinity