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I discovered these is an addon by FastFourierTransform that puts that star in the position that is predicted to be in the future, and it's awesome! But I was wondering... did they take gravitational pull of other stars into account to calculate the distance of approach? Also the research says the star is moving very slowly, so I think their attraction must be considered! Or is it negligible?
It is negligible. In the paper
, they calculate the closest approach by numerically integrating the motion (derived from Gaia data) of the stars within an axisymmetric model of the gravitational field of the Milky Way. But they do not model the attraction of individual stars. By how much would their answer change if they did account for the attraction by the Sun?
Let's say that, without the attraction, the star approaches at a minimum distance (called the "impact parameter"), b
, with a speed v
. A quick approximation for how much the minimum distance would be changed by attraction is to calculate the acceleration a
of the star due to the Sun at the former minimum distance, then apply that through a time Δt
equal to the impact parameter divided by the speed, and then double the result. This gives a reasonably close approximation to the true amount of deflection.
Putting it all together, the correction to the minimum miss distance is Δx = 2*0.5aΔt2 = (GM/b2)(b/v)2 = GM/v2
The star is projected to miss the Sun by about 13365AU with a speed of about 13.8km/s. Plugging those values in with the mass of the Sun, I find the correction to the minimum miss distance is about 4.7AU, which is only about 0.03%. Pretty negligible. You would not be able to see the difference in an orbital overview (it will be smaller than a pixel in a 2048x2048 image).
As a sanity check, I also calculated the actual deflection directly by integrating the path using the Sun's gravitational field, which gave me a change of 3.46AU (0.026%). So the approximation was close but a slight over-estimate.