Voyager 1: order-of-magnitude cross-track drift and speed loss over 10

mumbletypeg
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TL;DR
How far will Voyager 1 deviate from straight-line motion over 100–1000 years due to interstellar gas/dust? Order-of-magnitude only. Has this been calculated?
I’m looking for order-of-magnitude bounds on how much Voyager 1’s trajectory would depart from a constant-velocity inertial extrapolation over long time scales (100, 500, 1000 years).

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Two separate quantities:
  1. Cross-track deviation
    Lateral displacement relative to a straight-line extrapolation.
  2. Along-track lag
    Distance difference due to cumulative slowing.
Assume (adjust if better values exist):
  • Mass ≈ 730 kg
  • Effective cross-section ≈ 10.75 m² (3.7 m antenna dish)
  • Speed ≈ 17 km/s
  • Neutral hydrogen density ≈ 0.1 cm⁻³
  • Dust-to-gas mass ratio ≈ 1%

I’m not looking for precise ephemerides - just whether the drift is on the order of meters, kilometers, 10³ km, etc., after ~10³ years.

Has this already been calculated in the literature, or is a back-of-envelope estimate the right approach here?
 

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