Excellent pictures angeloneastralseed, but a couple of questions come to mind:
* How do you know the object is Elenin?
* What magnification factor did you use?
* How did you protect your eyes?
Okay, make that three questions

Just a quick, general caution:
observing the Sun through any unmitigated optical device like a telescope or binoculars will result in retina damage up to and including blindness (even looking at the Sun with the naked eye can do the same).--
Angel, your above calculation is mechanically correct, but the velocity is incorrect (speed and direction).
First, the speed of
Elenin is currently about 24 km/s (about 54,000 mph).
Second,
Elenin is traveling not in a straight-line, but in a curved path called a hyperbolic orbit. This means that its length of travel will be greater than a straight-line distance.
In both cases, its speed and direction are in constant change, although on its current segment that change may not be significant (it should be slightly slowing and turning).
If we had a straight-line distance between the Sun and the Earth and given
Elenin's current speed:
93,000,000 miles / 54,000 mph = about 72 days
--
Elenin's closet distance to the Sun will be 0.482 AU (on Sep 11, 2011 -- tomorrow)
Elenin's closet distance to the Earth will be 0.234 AU or (on Oct 16, 2011)
Distance covered (approximate because this assumes a straight-line): 0.482 AU - 0.234 AU = 0.248 AU = 44.8 million miles
Time interval (plus or minus 24 hrs): about 35 days or 840 hrs.
So the average speed of
Elenin between its closest approach to the Earth and its closest approach to the Sun is about:
44,800,000 miles / 840 hr = 53,000 mph
--
There is undoubtedly a simpler way to calculate the distance between two points on a hyperbolic arc, but am a bit pressed for time today. Will look into it later if no one else posts the formula first.