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[Phys-L] planetary alignment



In the Mechanical Universe video, Navigating In Space, they discuss how
spacecraft are sent to the planets. When the Earth and a planet are
aligned, it's called an opportunity. For example, Mars has to be 44°
ahead of the Earth when this happens so that the craft can land on Mars
along a low-energy trajectory that intersects the orbits of Earth and
Mars. This opportunity happens about every two years. For Venus (-54°),
once every 19 months. And for Jupiter (97°), once every 13 months.

On a related note, I am wanting to know how often each planet is closest
to the Earth. Then it will appear largest (and brightest) in the sky. For
example, Jupiter's orbital period is 11.86 years. If Jupiter and the Earth
are at their closest position tonight, how long will it be until they
return to this closest position again?

Is there a simple formula to figure this out (given two different orbital
periods)? Or does anyone know of an online source that shows/calculates
this?