For a work with a student here at Schiaparelli Observatory I decided to determine the distance of an asteroid by parallax, a good educational experiment.
Even with NEOs, it will be good to have the longest possible baseline, so I’ve asked the help of Robert Holmes from ARI Observatory, Illinois, USA (H21).
I chose NEO (Y5705) 2006 VB14, bright and of course visible at the same time from both observatories.
On 2012, Dec. 11 the sky was clear from both locations so we exposed the field for nearly half an hour with different exposure times to maximize the number of frames with the same exposure time. In the end I found several images taken at the exact second and I started to do the calculation of parallax.
Using Astrometrica I precisely determined the RA & DEC position of the asteroid on both images. Just an example from an image taken at 23.46.50 UT:
From 204: 02h 40m 18.83s – +26° 43′ 45.3″
From H21: 02h 40m 25.54s – +26° 43′ 52.5″
The parallax measured is 89” (+/- 1”).
To determine the effective distance between the two locations I’ve used the following formula:
cos (d) = sen (lat1) * sen (lat2) + cos (lat1) * cos (lat2) * cos (dlong)
where d is the angle between the observatories, lat1 is the latitude of 204, lat2 the latitude of H21 and dlong is the difference in longitude. Coordinates are the following:
204 – Schiaparelli
LAT1: 45° 52′ 04” N (45.86778° N) – LONG1: 08° 46′ 15” E (8.77083° E)
H21 – ARI
LAT2: 39° 27′ 20” N (39.45556° N) – LONG2: 87° 59′ 49” W (87.99694° W)
so d is 66.87440°
To have the distance D in km:
D = 2 * r * sin (d/2)
where r is the radius of the Earth and d the angle in degrees.
The result is 7,029 km.
Then, the distance of the asteroid (assuming the angle between the baseline and the bisector is 90°):
ASTD = D/tang (p)
where p is the parallax in degrees.
The final result was 16.290.000 km, in very good agreement (difference of only 0.77%) with the orbital distance (16.165.000 km).
Below you can find the image: