Trust Kepler, and devote your energy to more immediate and productive thoughts.

It's a LOT more complicated than a simple ellipse. Recently PBS Space Time did an explainer video on how the earth (and solar system) moves through the galaxy... It's bloody fascinating and quite complex. There wasn't as much info on how we know it, but there's some explanations that make sense to me, especaially with the diagrams they use.

This PBS SpaceTime video may interest you

I think it’s always a good idea to start with the basic principle that our planet, or sun, our solar system is nothing special. That is, our solar system won’t be doing anything different than the others, and given the configuration of the Milky Way arms, these stars (and their planets) are not getting “flung out”. So we wouldn’t either. Our solar system is too gravitationally bound to not just SagA, but all the mass, including dark matter, holding us together.

By that same logic, we have to assume the Milky Way, which has very old stars itself, isn’t special than most spiral galaxies we see. It’s bigger than average, yes, but within normal. And those distant galaxies we see are not ejecting their stars either. The galactic escape velocity is very high.

In fact, I bet astronomers have already calculated the mass of the Milky Way, it’s escape velocity, and the speed at which our star and solar system move through it. I think we’re safe.

Sag A* is a flea-speck in the context of the mass of the Milky Way galaxy, or even the mass of its core region. The solar system does not explicitly orbit SagA*. It orbits the barycenter of the entire galaxy.

Thank you but that does not answer how we know that it orbits the barycenter.

The Sun is 99.98% of the mass of the Solar System. Sun's overwhelming mass compared to the other planets controls their orbits.

Sag A" is only 0.003% of the mass of the Milky Way Galaxy.

• Sag A* has a puny 4 million solar masses.

• Milky Way Galaxy has 200 billion stars plus a much greater mass of Dark Matter, together totalling 1.2 to 1.9 trillion solar masses.

• 4 million vs over 1.2 trillion solar masses. The stars and the Dark Matter should have a much greater control of the Sun's orbit. And prevents the Sun from flying away.

Not a astrophysist at all but Given that we know the velocity of the solar system roughly* and the have a good estement for the mass of the milky way we can do fancy orbital mechanics math to plot the orbit.

Simmilar to pluto since it has not completed an orbit since its discovery in the 1930s, yet we still know it orbits the sun

We look at things and infer from that our movement to it

The source for that information I believe is the answer to my question then. I will watch these videos also as well to see if that provides any more clarity.

Theoretically, you are right. We haven't proven that we aren't currently flying off into space right now, but based off of what we can observe and know, it's very likely that we are orbiting our galaxy (not necessarily SagA, but, rather, a sort of galactic barycenter). It's not a fact in the scientific/mathematical sense of the word, but the probability of any other explanation is so low that we can treat it as such and form our assumptions around it. That's how most high-level science and mathematics work though. Many things that we treat as facts or proofs are actually just theories and very educated guesses, but they work very well for us and help us innovate and learn about the world around us; sometimes we don't have to prove something for it to be useful to us.

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