The imminent Great Jupiter/Saturn Conjunction, plus a recent comment on this blog, got me wondering about gravitational forces at conjunctions. When Mars and Jupiter are in conjuction (as happened in 1836-7 and 1979-80, and will recur in 2123, 2170, 2313, and 2456) which of them exerts the greater pull on planet Earth? Mars is 8 times closer but more than 3000 times lighter. Let's find out.
G = 6.674 x 10-11 m3 kg-1 s-2
Earth mass 5.97 x 1024 kg
Mars mass 6.42 x 1023 kg
Jupiter mass 2.00 x 1027 kg
Earth-Mars av. dist. 78 x 109 m
Earth-Jupiter av. dist 628 x 109 m
F = Gm1m2/d2
Gravitational attraction Earth-Mars: 4.2 x 1016 newtons
Gravitational attraction Earth-Jupiter 202 x 1016 newtons
The orbit of Mars is sufficiently eccentric (0.09) that its closest approach to Earth is 55 x 109 m. It's possible for a conjunction to coincide with closest approach, but that still wouldn't be enough to overcome Jupiter's dominance.