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triffid_hunter t1_iwtye4y wrote

If you only use the central force theorem with a single body then yeah, gravitational capture looks impossible because there's nothing to remove energy from the original hyperbolic orbit.

If you consider perturbations from eg n-body stuff or aerobraking however, it becomes quite possible ;)

Also, celestial objects don't have a hard boundary on their hill sphere, the border is very fuzzy and shifts around depending on what other bodies are doing.

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BlueWhoSucks t1_iwu1mgi wrote

Love that you're using Spaceflight simulator to demonstrate your point. One very important factor which you're missing out on is the existence of other gravitational influences from other moons. and the parent star.

Another thing which you missed is the rotation of the planet. If an object approaches slowly enough and it's trajectory is approximately within the plane of rotation which is perpendicular to the axis of rotation of the planet, it's possible that the satellite might be captured, in return for an increase in the speed of rotation of the planet such that angular momentum is conserved, as well as a change in momentum of the satellite+planet system according to conservation of linear momentum.

Games like Spaceflight Simulator have inspired me to take engineering, but they are vastly oversimplified. They are just enough to get a cursory glance at the topic of orbital mechanics, which is a deep rabbit hole.

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smoke-frog t1_iwtxyhb wrote

I was under the impression that a 2 body system would be needed to capture a 3rd. That is if an object of the correct mass passed by the moon from a certain trajectory, its heliocentric orbit could be changed enough to be captured by the earth. Not sure what that says about Phobos and Deimos though!

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House13Games t1_iwu7guc wrote

Those are just clearly artificially placed as a signpost.

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PoppersOfCorn t1_iwtyaeg wrote

Post on /r/astrophysics and receive an in-depth response

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lawblawg t1_iwvuizv wrote

There are a number of ways that a primary can capture a passing secondary. For a large secondary, one way that's fairly straightforward and easy to understand is ejection capture. Triton's orbit around Neptune is retrograde, making it unique among all the large moons in our solar system.

The most likely origin for Triton is that it started as a binary Kuiper belt object, like the Pluto-Charon system, but passed too close to Neptune. During the pass, the momentum of the orbit between Triton and its partner was added to the partner and subtracted from Triton, allowing Triton to be captured while its partner was ejected.

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PhyneasPhysicsPhrog t1_iwurph2 wrote

What you’re wanting to learn about is Hohmann Transfer Orbits. This is the process by which an object departs the Hill Sphere/Orbit of one object and enters that of another. In the case of interplanetary motion it accounts for the planets and host star’s gravity.

This is a good explanation with calculations: http://jwilson.coe.uga.edu/EMAT6680Fa05/Bacon/hohmanntransfers.html

I can also give you a Matlab and STK file with this built in.

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lawblawg t1_iwvgd9l wrote

Hohmann Transfers are an important (and very interesting) topic but they're not relevant to ballistic capture, which is what the OP is asking about.

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PhyneasPhysicsPhrog t1_iwvgp0s wrote

I’ve generally seen ballistic capture done in terms of the final steps of a transfer orbit. It’s generally easier to explain gravity assist and ballistic capture (rendezvous) using the Hohmann framework.

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diogenes_shadow t1_iwxigyz wrote

In a two body universe, objects starting far apart will either collide or fall into an oval orbit retaining the original distance as the major axis.

For a planet to capture a wandering moon, as your question might mean, it takes help. If the original vectors are helpful, and the time sequence imposes the right acceleration, the moon wandering past can be permanently captured. Orbit might not be circular at first, but yes, it is possible.

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Ivanka_Gorgonzola t1_iwu0b69 wrote

The planet, (proto)moon and sun are a 3 body system.

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Mono_Clear t1_iwtzmvk wrote

It's not just about whether or not an object enters into the sphere of influence of another object in space.

Orbit is a balancing act between the mass of two objects their angular momentum and their shared center of mass.

The Moon is slowly moving away from the earth because it's angular momentum is pushing it to a stable orbit between the shared center of mass with the Moon and the Earth.

If you drop an object from the surface of the Earth toward the center is already parts of the mass of the Earth it's just moving toward the center of mass like every part of the earth is moving toward the center of mass.

Depending on how an object approaches the Earth it'll cross the gravitational field in different places depending on the angle it might be on a trajectory to become part of the mass of the Earth because of a degrading orbit but if it comes in at the right angle it'll simply transfer its momentum into maintaining a stable orbit around the shared center of mass of the two body system

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