A comment in line with my sine vs cycloid thinking :
http://science.slashdot.org/story/13/02/15/1747226/asteroid-2012-da14-approaches?utm_source=rss1.0mainlinkanon&utm_medium=feed
Re:are we sure it has nothing to do with DA14? (Score:4, Informative)
by Clueless Moron (548336) on Friday February 15, @02:51PM (#42914591)
No... if that meteorite was in an orbit 30,000km radius from DA14 (which it
would have to have been in order to hit Russia when it did), its orbital
velocity would necessarily have to be very low. As in, so slow it would take
millenia to complete even one orbit. Since DA14 is moving at a whopping
30km/second relative to Earth, anything orbiting it that far out would be
moving in virtually the same direction and speed with respect to us.
In short, there's no way that meteorite could have been orbiting DA14
- - - - - -
I plugged the best numbers I could find into a spreadsheet.
The asteroid of mass m1 passes d1 above earth, with velocity v1
For the meteor to just graze earth 16 hours ahead of the asteroid, it must be
d2 = time*velocity ahead of it.
We then have a right triangle with sides d1 and d2 ... hypotenuse d3 = radius
of orbit.
Ignoring the mass of the meteor, we have the period 2 pi * sqrt( d3^3 / G m1 )
Indeed, it gives an orbital period of 153 millenia -- so they're pretty much
travelling in the same direction. No cycloid motion.
Asteroid 2012 DA 14 and Russian meteorite
v1 2013.2.15:A
v1 30km/sec 30000m/sec Velocity of asteroid relatve
to earth
d1 27000km 27000000m Distance from surface of
earth
t2 16hrs 57600secs Meteor ahead of asteroid
(hours)
d2 1728000000m v1*t2 Meteor ahead of
asteroid (m)
d3 1728210925 sqrt(d1^2 + d2^2) Radius of
meteor orbit
m1 130000tonnes 130000000kg Mass of asteroid
G 6.7E-11 G gravitational
constant
t2 4.83674E+15 orbital period seconds = 2 *
pi * sqrt ( d3 / G m1)
1.34354E+12 hrs
55980833311 days
153372146.1 years
