Posted: Jun 06, 2011 2:45 pm
A back-of-the-envelope (literally!) calculation suggests to me that this is nowhere near close enough for Melancholia to take the Earth out of its solar orbit and put it into orbit around Melancholia instead, but it would surely disrupt the Earth's existing orbit significantly.
Bit hazy on the detail: haven't really done this celestial mechanics stuff beyond a fairly elementary level!
The figure you give for Melancholia's speed relative to the Earth is very close to the Earth's orbital speed around the Sun: so, as Melancholia crossed the Earth's path (assuming it crossed ahead of the Earth), they would be fast approaching each other during the manoeuvre.
Bit hazy on the detail: haven't really done this celestial mechanics stuff beyond a fairly elementary level!
The figure you give for Melancholia's speed relative to the Earth is very close to the Earth's orbital speed around the Sun: so, as Melancholia crossed the Earth's path (assuming it crossed ahead of the Earth), they would be fast approaching each other during the manoeuvre.