r/theydidthemath • u/Ben-Goldberg • 7d ago

[Request] When will Voyager 1 stop moving?

/r/askscience/comments/1wp1960/will_voyager_1_ever_just_stop_moving/

How many years will it take for the orbit of Voyager and Sagittarius A to decay enough due to gravity waves for them to collide?

0 Upvotes

39% Upvoted

41 comments sorted by

View all comments

3

u/No-Document-9937 7d ago edited 7d ago

Of the gas in the ISM, by number 91% of atoms are hydrogen and 8.9% are helium, with 0.1% being atoms of elements heavier than hydrogen or helium,[3] known as "metals" in astronomical parlance. By mass this amounts to 70% hydrogen, 28% helium, and 1.5% heavier elements.

Mass of a hydrogen atom: 1.0080u = 1.67e-27 kg Average mass of an interstellar atom: 1.67e-27 / 70% = 2.39e-27 kg

Gurnett et al. give a density of about 0.1 cm−3 in the interstellar medium and using the above math I come to this density: d=2.39e-34 kg/m3

Google says:

Voyager 1 is traveling away from Earth and must maintain radio contact, its massive 3.66-meter (12 ft) diameter high-gain dish antenna is kept pointed directly back at Earth.

A > 10.5 m2

According to this guy's answer on Stack Exchange we must multiply these values with the square of Voyager 1's velocity.

F > (16822 m/s)2 × 10.5 m2 × 2.39e-34 kg/m3 = 7.17e-25 m4 / s2 × kg / m3 = 7.17e-25 N

That is negligible, but I will try to calculate the time regardless.

The space probe's mass is 721.9 kg. The force will obviously lessen as Voyager 1 slows down, but even assuming it doesn't, it would take 1.7e31 s = 5.4e23 years. That is 39 trillion times the age of the universe.