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 Theory | Orbital ...
Link to N-body perturbations software video: • N-body Perturbations Software | Orbit...
Link to Voyagers SPICE kernels: https://naif.jpl.nasa.gov/pub/naif/VO...
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 (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
#sphereofinfluence #gravityassists #flybytrajectories
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