Jupiter and Saturn reach heliocentric conjunction in a cycle of 7253.45 days, on average. Multiply by nine, and you have 65281 days = 178.73 years. In that time period, Jupiter travels through 15 revolutions + 24.28 degrees, Saturn through 6 revolutions + 24.28 degrees, and Neptune through 1 revolution + 30.50 degrees. So after nine Jupiter-Saturn conjunctions (~179 years), Neptune returns to almost the same relative position - the error is 30.50-24.28 = ~6 degrees. Uranus hits tolerably close to the same period: 2 revolutions and 45.80 degrees during nine Jupiter-Saturn conjunctions, so it accumulates an error of ~21 degrees per 179-year cycle. The inner planets go around sufficiently quickly that they can be accommodated to the same rhythm with only a little tweaking.

Hence the famous 179-year cycle that is always mentioned in discussions of the Voyager 2 "Grand Tour" incorporating Earth, Jupiter, Saturn, Uranus and Neptune.

Grant Hutchison