Thursday, December 17, 2020

Planetary conjunctions

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.

DATA:

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

FORMULA:

F = Gm1m2/d2

RESULT

Gravitational attraction Earth-Mars:      4.2 x 1016 newtons
Gravitational attraction Earth-Jupiter 202 x 1016 newtons

Eccentricity
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.

Grounded said...

I'm honored that you found my pedestrian question worth exploring. If I may, impose further, what is the mass of Earth's Moon, and what is the mass of Earth's oceans. How does this equate with the resulting tidal effect of the Moon? Does it seem rather disproportionate, from what might be expected, or just what you might expect, expat?

expat said...

Moon: 7.342 x 10sup22 kg
Oceans: 1.35 x 10sup21 kg

I investigated tidal force a few years ago and discovered that the explanation of ocean tides is not nearly as simple as what we were taught at school. Here's the story.

Ground Ed said...

I'll have to chew on that a bit, expat. Did you write the Wikipedia article?

expat said...

No, that was a real astronomer.

Ground Ed said...

If Jupiter and Saturn were close enough for their combined gravitates to mutually attract a collision, are those planets gaseous enough to explode, and if so, would we feel the shock-waves on Earth?

expat said...

No, they would not explode but it would be an almighty collision. I don't think shock waves can propagate through a vacuum.