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## Homework Statement

Mars orbits the sun at a mean orbital radius of 228 Gm ( 1 G = 10^9 m) and has an orbital radius of 687 days. Earth orbits the sun at a mean orbital radius of 149.6 Gm.

The earth-sun line sweeps out an angle of 360 during one earth year. Approximately what line is swept out by the Mars-Sun line during one Earth-year?

How frequently are Mars and the Sun in opposition (on diametrically opposite sides of the earth?)

## Homework Equations

365 days = 360 degrees for earth

687 days = 360 degrees for Mars

## The Attempt at a Solution

(360 degrees/ 687 days)x 365 day = 191 degrees for Mars sweeping.

That's cool. I get that.

It's the diametrically opposed part that I am having issues with comprehending. Yahoo answers gave a solution:

"Mars and the Sun are in opposition every T days where T is given by 1/T = 1/E - 1/M where E =365 days is the Earth year and M=687 days is the Mars year. This works out to T = 779 days, slightly more than 2 years. "

This works. But this formula seemed out of the blue to me. Where did they come up with this? Am I missing something really simple? (Probably...)

No need to solve the problem, it's on where they got that formula. Thank you very much.