### When will Sirius be closest to the solar system?

• Sirius is currently approaching the solar system, at a rate of 5.5 km/s, consequently in the future it will be closer and therefore brighter. When will Sirius pass closest to the solar system? How far will it then be from the sun, and what magnitude will it reach?

https://en.wikipedia.org/wiki/Sirius "Sirius is gradually moving closer to the Solar System, so it will slightly increase in brightness over the next 60,000 years. After that time its distance will begin to increase"

Appears to be answered in http://astronomy.stackexchange.com/questions/3601/how-often-do-stars-pass-close-1ly-to-the-sun/3605#3605 though it is not a duplicate. I cannot vouch for the answer, but the radial velocity and proper motion of Sirius is readily available for the interested.

7 years ago

Sirius is moving towards the sun at 5.5 km/s, and according to Sky and Telescope, will reach its closest distance in 60000 years, at which time it will be 7.8 light years distant, and be at magnitude -1.64, only slightly brighter than it's current magnitude -1.46.

Calculations using the latest Hippacos results give a slightly different value: a closest approach of 8.18 ly in 46000 years, and consequently a slightly dimmer peak. However Sirius is not moving rapidly relative to the sun, and will not change its brightness greatly in the next 100000 years or so

It will be the brightest star in the sky for another 90000 years, and no star will match its current brightness for another million years (when delta Scuti will reach magnitude -1.84.

This disagrees with the SE answer I referred to. So which, if either, is correct?

The Wikipedia page is based on an edition of Sky and Telescope. Its an older issue, but it checks out, the radial velocity given is -5.5km/s This agrees with Simbad http://simbad.u-strasbg.fr/simbad/sim-basic?Ident=sirius&submit=SIMBAD+search . The SE answer has a velocity of Sirius of 17.66km/s, though that may be a speed, not a radial velocity. Its not clear. However either way, it is clear that Sirius is moving slowly wrt the sun, and given the uncertainty in the values, the two values may be within experimental accuracy.

There is very little uncertainty in the motion of Sirius I think. The answer of course depends on the total velocity, not just the radial velocity.

Well instead of relying on wikipedia, or SE, I did the calculations myself... The results are in a google sheet: https://docs.google.com/spreadsheets/d/1p8y7LeipylmtacHEMXLq28b7wPJZIBwve-ZT_etVWD8/edit?usp=sharing . And my calculations agree well with the table in SE, using data from Simbad. A closest approach of 8.18 ly in 46000 years +- 2500 years

Of course my calculation doesn't model the acceleration of stars around the galaxy, which may be significatn'

Only *differential* acceleration between Sirius and the sun would be an issue. In practice they are both sitting in an almost identical potential.

I am *assuming* though that you have correctly used the centre of mass velocity for the Sirius system right?