How can we measure the distance to an asteroid? We need to know three things:
On March 4, 2005, at UT 02:45:00, astronomers at Gettysburg Observatory, in Gettysburg, PA, and at Yerkes Observatory, in Williams Bay, WI, measured the position of asteroid 1998WT. They found:
RA (J2000) Dec (J2000)
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Gettysburg 07:26:33.65 +00:46:13.7
Yerkes 07:26:34.69 +00:46:10.0
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difference -00:00:01.04 00:00:03.7
We can convert these differences in position into units of arcseconds. First, the difference in Right Ascension; this calculation is a little complicated, both because we have to convert from seconds of time into arcseconds, and because we need to include a factor for the Declination. The average Declination of the positions is about Dec = +00:46:12 = 0.77 degrees.
diff RA = (diff in seconds of time)*(15 arcsec/second of time)*cos(Dec)
= (-1.04 sec of time) * (15 arcsec/sec of time) * cos(0.77 degrees)
= -15.60 arcseconds
The difference in Declination is simple:
diff Dec = 3.7 arcseconds
The total shift in apparent position of the asteroid is therefore
2 2
total shift = sqrt ( (diff_in_RA) + (diff_in_Dec) )
2 2
= sqrt ( (-15.60 arcsec) + (3.7 arcsec) )
= sqrt ( 257 arcsec)
= 16.03 arcsec
What is the distance between the two locations on Earth?