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Direct Distance Measurement of NEOs by Parallax

 If a minor planet on a close approach to the Earth is viewed from places that are widely separated, it will not appear in quite the same position against the background stars from the two different sites (Figure 1)


Figure 1

This is due to parallax and is the same effect used to directly measure the distances to the nearest stars, but in that case, rather than use different observatories imaging at the same time, the Earth is allowed to move half way around its orbit, so that the baseline for the parallax measurement is as long as possible, i.e. the diameter of the Earth's orbit.

For NEO distance determination, the two observatories should be widely separated, the further apart the larger the measurable parallax effect will be but also, the fewer objects will be visible at the same time from both places. With two observatories literally half way around the Earth from each other, although the baseline would be as long as possible (the diameter of the Earth) the two sites would only be able to simultaneously observe objects that were visible at sunset from one site and also visible at sunrise from the other, drastically limiting the opportunities.

In November 2004 Monty Robson, the Director of the John J. McCarthy Observatory (IAU code 932) in Connecticut, USA made contact with the Great Shefford Observatory (J95) to suggest some simultaneous observing of NEOs, to directly determine their distance. The John J. McCarthy Observatory is sited in the grounds of the New Milford High School and is used for educational and research purposes.

The John J. McCarthy Observatory has a good track record of NEO range finding, the technique had been used to great effect by New Milford student Lisa Glukhovsky in 2003 with a project originally suggested by Monty Robson "A Rapid, Accurate Method of Determining the Distance to Near Earth Asteroids" which has won her many awards, including top prize at the 2003 Intel International Science and Engineering Fair.

New Milford High Junior wins big at science fairs
For this New Milford student, Asteroids + Smarts = $70,000

Simultaneous Imaging

After waiting for clear sky on both sides of the Atlantic, the collaboration between 932 and J95 kicked off on 26 November 2004 with simultaneous imaging of NEO 2004 VB, discovered at the start of that month by the LONEOS survey at Lowell Observatory. On 26th November this Apollo asteroid was at a distance of about 5.5m miles (8.8m Km) and closing, at magnitude +17 and moving at about 14"/min.


Field of view 6' x 4', North up
Parallax effect shifts the apparent position of 2004 VB by 1'57" in p.a. 65/245 between the two observatories.
Details:

John J. McCarthy Observatory (932):
Long. 73.4W, 41.5N, height above sea level 79m
0.4-m Schmidt-Cassegrain at f/6.6
Focal length 2690mm
SBig ST-10XME CCD binned 3x3, 1.56"/pixel
Five exposures of 10 seconds each.


Great Shefford Observatory (J95):
Long. 1.4W, 51.5N, height above sea level 100m
0.3-m Schmidt-Cassegrain at f/6.0
Focal length 1821mm
Apogee AP47p CCD binned 2x2, 3.01"/pixel
Image enlarged by x1.93
Five exposures of 14 seconds each.

Using the astrometry obtained simultaneously from the two stations and plugging the numbers into a spreadsheet developed by Dr Jeff Tarvin for the John J. McCarthy Observatory, the distance of 2004 VB was determined, with key results summarised in Table 1:


Table 1 (Results of direct distance determination for NEO 2004 VB on 26 Nov 2004)
Baseline distance (between observatories) 5,245.5 Km
Parallax angle 116.9"
Calculated distance to 2004 VB 8,771,756 Km = 22.84 LD
(Lunar Distances)
Actual distance to 2004 VB (from JPL ephemeris) 8,793,741 Km = 22.90 LD
Error in calculated distance 21,985 Km = -0.25%

In order to get simultaneous imaging from both sites it was found to help greatly by using an internet instant messaging application. Microsoft MSN Messenger was used but any of the commonly used IM applications would have done just as well, including Yahoo messenger, AOL Messenger etc.

Agreeing exposure policy beforehand is also a 'must' to obtain simultaneous imaging. We agreed to set exposure duration to whatever was optimal for our individual systems (in this case 10 seconds for 932 and 14 seconds for J95) but to centre the exposures at the start of each minute. 932 would therefore start the 10 second exposures at 55seconds past the minute, whereas at J95 the 14 second exposures would start at 53 seconds past the minute. One image would be obtained each minute until enough images had been obtained from both sides to allow good astrometry to be measured by using Astrometrica to track & stack individual images together.

Other benefits of (near) simultaneous imaging

In a second collaboration between 932 and J95 a newly discovered object on the NEO confirmation page was imaged from both observatories early on 3rd Dec 2004. The object was posted on the NEOCP as AR66046 on 2004 Dec 02 at 23:02 UT and listed as mag +17.7, moving at 14"/minute and with an uncertainty area of about 1x0.5.

A search was undertaken for the unconfirmed object from both observatories, with areas being divided up between the two observatories to speed the coverage of the entire uncertainty area. It was picked up first from J95 and subsequently a simultaneous imaging run was completed by both observatories, the results appearing on MPEC 2004-X06 with details of the newly designated Aten class NEO 2004 XJ showing three pairs of observations from 932 and J95 with exactly matching times!

Using these measurements, as an example of how having astrometry from two widely separated places tightens up the orbit determination from a very short arc, two orbits were calculated (using the excellent freeware program FindOrb from Bill Gray).

Orbit 1 was determined using the positions of 2004 XJ from J95 only. The residuals for the 932 positions were calculated from this orbit although these positions were not used in the orbit computation (Table 2).

Orbit 2 was then calculated using the positions from J95 as well as those from 932 and the residuals again calculated (Table 3).

As can be seen, although a very reasonable fit to the J95 positions is found with the first orbit, the distance to the object is not well determined and the residuals for the 932 positions are huge.

Adding in the 932 positions in the second orbit brings the residuals for all positions to very acceptable levels and the distance to the NEO is determined using positions over a time span of just 1h 45m to be just 0.2% different to that determined by JPL using all positions reported during the entire observed 13 day apparition (Table 4).


Table 2 (Orbit 1 using only using J95 positions):
Date RA residual Dec. Residual Observatory
2004 12 02.98280 -0.46 0.29 J95
2004 12 02.98643 0.33 -0.28 J95
2004 12 02.98982 0.12 0.04 J95
2004 12 03.01840 0.41 -0.40 J95
2004 12 03.03611 -20.14 -5.98 932
2004 12 03.03611 -0.43 0.23 J95
2004 12 03.03993 -20.17 -6.56 932
2004 12 03.03993 -0.17 0.31 J95
2004 12 03.05035 -0.17 0.25 J95
2004 12 03.05590 -19.77 -7.69 932
2004 12 03.05590 0.37 -0.43 J95

Table 3 (Orbit 2 using positions from both J95 and 932):
Date RA residual Dec. Residual Observatory
2004 12 02.98280 -0.40 0.30 J95
2004 12 02.98643 0.35 -0.29 J95
2004 12 02.98982 0.10 0.03 J95
2004 12 03.01840 0.23 -0.42 J95
2004 12 03.03611 0.20 0.14 932
2004 12 03.03611 -0.53 0.25 J95
2004 12 03.03993 0.03 -0.18 932
2004 12 03.03993 -0.24 0.34 J95
2004 12 03.05035 -0.10 0.34 J95
2004 12 03.05590 -0.18 -0.19 932
2004 12 03.05590 0.54 -0.31 J95

The distance from Earth as determined for the J95 position for Dec 03.03611 UT is shown below in Table 4:

Table 4 (Distance from Earth at 00:52 UT 03 Dec 2004)
Source #
Positions
Timespan Distance from Earth
(A.U.)
% error
(c.f. JPL orbit)
Orbit 1
(Only J95 positions)
8 1h 45m 0.0410 -13.0%
Orbit 2
(J95 & 932 positions)
11 1h 45m 0.0472 +0.2%
JPL
(All reported positions 
from all observatories)
75 13 days 0.0471 0%

This technique of simultaneous or near simultaneous imaging of nearby objects is a powerful one and can help in the initial determination of NEO orbits. As has been shown at the John J. McCarthy Observatory it is also a very useful educational tool. If you are interested in participating please contact Monty Robson by e-mail mail @ mccarthyobservatory.org (remove the blanks before mailing) or visit their web site at John J. McCarthy Observatory.

Check out the presentation delivered by Monty Robson and Peter Birtwhistle at the MACE 2006 meeting in Vienna: Direct determination of NEO distance by parallax, containing some of the material on this page. Be sure to select to display "Notes" so you can follow the dialogue used during the presentation. You will need to have a browser capable of displaying frames and to have Javascript enabled.

 

Great Shefford Observatory would like to thank Monty Robson for the initial invitation to collaborate on this project and his continuing great enthusiasm, without which none of the NEO distance determination described above would have happened. Further distance determinations are planned to be made between 932 and J95 when conditions are favourable.

All images from John J. McCarthy Observatory are used with permission. If you wish to use any of those images then please include an acknowledgement to the John J. McCarthy Observatory.

Footnote:

On 6th March 2005 we were very pleased to welcome Dr Jeff Tarvin, (author of the spreadsheet used in the range finding exercise) for a short visit to Great Shefford Observatory. Pictured below is Jeff (left) and Peter Birtwhistle in front of the observatory, both sporting John J McCarthy Observatory t-shirts!


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