Gravitational Sphere of Influence | Orbital Mechanics with Python 42

The gravitational sphere of influence of a planetary body can be used for approximating when one body’s gravity (like the Earth or Jupiter) dominates over the body that it itself is orbiting (the Sun). Note that this isn’t an exact value, and there are multiple accepted definitions of this value, like the planetary sphere of influence and hill sphere.
This can be used to switch the center of propagation when getting close to planetary bodies (like when a spacecraft is approaching Jupiter, when it gets close enough you want to switch the propagation from being modeled as a heliocentric elliptical orbit to a Jupiter hyperbolic orbit), and can also be used to switch from modeling a planetary system as a barycenter (like the Jupiter barycenter) or as each body separately (like modeling Jupiter separate from its moons, like Callisto, Europa, Io, etc.). This video will be using the Voyager 2 flyby of Jupiter as an example to illustrate how the gravitational sphere of influence is defined.
Link to N-body perturbations theory video: • N-body Perturbation Th...
Link to N-body perturbations software video: • N-body Perturbations S...
Link to Voyagers SPICE kernels: naif.jpl.nasa....
In the two body problem of orbital mechanics, we model one larger body to be the center of the gravitational force that a smaller body is influenced by. In this case, the larger body is the sun, and the Voyager 2 spacecraft is the smaller body who is orbiting the sun.
The two body problem gives us an equation of the acceleration of the small body due to the large body’s gravitational pull, which is a function of the mass of the large body and the vector pointing from the large body to the small body. We can then model the gravitational force of other bodies as a perturbing force onto the spacecraft.
Links to the Space Engineering Podcast (TH-cam, Spotify, Google Podcasts, SimpleCast):
• Space Engineering Podc...
open.spotify.c...
space-engineer...
podcasts.googl...
Link to Orbital Mechanics with Python video series:
• Orbital Mechanics with...
Link to Spacecraft Attitude Control with Python video series:
• Spacecraft Attitude Co...
Link a Mecánica Orbital con Python (videos en Español):
• Mecánica Orbital con P...
Link to Numerical Methods with Python video series:
• Numerical Methods with...
#sphereofinfluence #gravityassists #flybytrajectories

[@kshitijpatil4793]

hey, i found a book that defines soi as the point where the force on the satellite is the same as the sun as the planet as in no perturbations. Is that also a valid method

[@alfonsogonzalez-astrodynam2207]

There is no strict definition of sphere of influence. Especially since its application usually is center switching between which body you are modeling as the central body and which one is the perturbing body. There is also the hill sphere definition: en.wikipedia.org/wiki/Hill_sphere

[@johnstanfield7406]

How do you make these visuals?

[@alfonsogonzalez-astrodynam2207]

I go over the Python scripts I used to make the plots in this video (including what I added to the 3D plotting function for the sphere of influence wireframes). I've also posted a bunch of this software on the GitHub repository for this page here: github.com/alfonsogonzalez/AWP
And then a long video explaining the Spacecraft class thats in that repo line by line: th-cam.com/video/yMJ_VU3jt7c/w-d-xo.html

[@_KerinR_]

Great!! Thanks for your work.

[@alfonsogonzalez-astrodynam2207]

My pleasure!

[@EBgCampos]

Awesome videos. Only issue is that I feel they are too straightforward and I wanted to enjoy them longer haha

[@alfonsogonzalez-astrodynam2207]

There are some long videos too! Like this one where I explain the Spacecraft class in the GitHub repository for this channel: th-cam.com/video/yMJ_VU3jt7c/w-d-xo.html
And the podcast! th-cam.com/play/PLOIRBaljOV8gYALpxUJywrHZuvZ9NFpz0.html