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Asteroid TC4 Earth capture

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Based on the recent 'graze' of TC4 is there anybody that can answer if it would be possible for Earth to capture such an object.  I did do a course whereby we calculated this for Sun grazing comets but I have forgotten how to do it. Is it a matter of distance from Earth and the kinetic energy of the asteroid? Escape velocity? I would be very interested in seeing the working. How close would such an object need to graze us?

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Starting to pick at this over a coffee... found two graphics to start with:



Source: http://www.telegraph.co.uk/news/0/asteroid-2012-tc4-pass-damn-close-earth-tomorrow-give-rare-chance/

Each time it has come round, the orbit changes due to the graze with earth, but it's still orbiting the sun, not us.


From the same article:


 4.5 miles a second... 27,000 miles 


From https://en.wikipedia.org/wiki/Escape_velocity:


On the surface of the Earth, the escape velocity is about 11.2 km/s ... at 9,000 km altitude in "space", it is slightly less than 7.1 km/s.

4.5 miles/second happens to be very close to 7.1 km/s, so if it had passed just under 9km, its velocity would have been < escape velocity at that height and we'd have nabbed it...? Don't know if that's right or how to do the maths, but interesting to be able to calculate the change in orbit due to such a graze.



Edited by furrysocks2
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