Measuring the Distance to the Sun: First Tests

Content

  1. Equipment
  2. Klio, October 14, 1996
  3. Yerkes, October 14, 1996
  4. Klio, Yerkes and Semiramis until November 14, 1996
  5. Determination of the Orbits

Equipment

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Klio, October 14, 1996

We took several pictures of Klio on the Oldendorfer Berg between 19.15 UT and 20.15 UT. The exposure time was 20s. Two of the pictures are shown at the top of the project description. In spite of the short time difference the proper motion of the asteroid is clearly to be seen! For clarity we superposed the both pictures so that the stars coincide:

The both objects in the lower right edge are Klio moving retrograde.

Comparison of the ccd pictures with the map calculated by Guide 4.0 let us identify four of the stars in the pictures. The program then gave us the geocentric equatorial coordinates:

  1. GSC 2329 624: alpha = 2h43m 1.624s, delta = 33d11'53.77"
  2. GSC 2329 573: alpha = 2h43m 0.434s, delta = 33d11'03.91"
  3. GSC 2329 084: alpha = 2h42m46.190s, delta = 33d10'02.24"
  4. GSC 2329 812: alpha = 2h42m51.110s, delta = 33d08'45.82"
Measuring of the observed topocentric positions had approximately the following results (the results obtained with different programs differ slightly!):
  1. 19:16:56 UT: alpha = 2h42m47.740s, delta = 33d09'00.874"
  2. 20:10:01 UT: alpha = 2h42m45.567s, delta = 33d09'06.748"
The calculated geocentric positions are
  1. 19:16:57 UT: alpha = 2h42m47.518s, delta = 33d09'06.54", r = 1.028148 AU
  2. 20:10:01 UT: alpha = 2h42m45.377s, delta = 33d09'11.67", r = 1.028072 AU
Evaluation of these results with our program gives the first preliminary values of our own parallax of the sun:
  1. Combination of the observed topocentric with the calculated geocentric position:
  2. Combination of both pictures: The motion of Klio is not only due to its proper motion but is influenced by our own motion due to the earth's rotation during 44 minutes (try to verify that our positions are seperated by ???? km approximately!)!
Compared with the exact value pi = 8.794" all results of the first day differ less than 15 percent! We are lucky especially about the value resulting by combination of the two pictures: We got a quite good parallax measure during less then one hour using only roughly calculated geocentric positions.

If we are able to combinate simultanously taken pictures we will need only the corresponding geocentric distance which can be calculated even more easily.

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Yerkes, October 14, 1996

The picture below shows Yerkes at 19:29:26 UT. As with Klio we compared the ccd image with an output of Guide.40:
From these pictures we could identify the following stars:
  1. GSC 1796 0532: alpha = 3h14m01.790s, delta = 29d07'42.31"
  2. GSC 1796 0892: alpha = 3h14m02.661s, delta = 29d06'42.48"
  3. GSC 1796 0350: alpha = 3h13m59.846s, delta = 29d06'33.98"
  4. GSC 1796 0024: alpha = 3h13m50.150s, delta = 29d07'12.36"
  5. GSC 1796 1259: alpha = 3h13m48.470s, delta = 29d07'25.90"
  6. GSC 1796 0367: alpha = 3h13m44.680s, delta = 29d06'45.79"
The result for the topocentric coordinates is:

alpha = 3h14m01.068s, delta = 29d08'24.108"

The calculated geocentric position is:

alpha = 3h14m00.793s, delta = 29d08'26.130", r = 1.275044 AU

From these values we can derive the following measure for the sun's parallax: pi(Sun)=6.12". This value is not as good as for Klio. One reason may be the fact that the stars have too similar declinations not allowing a good astrometry.

This result is not very surprising for us: We know that the comparison of only one measured topocentric position with the calculated geocentric position is extremely sensitiv for errors!

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Klio, Yerkes and Semiramis until November 14, 1996

Today, we got the first contact to other groups. Therefore, we took the time to test our procedures: We now have got images and positions for the following days: On November 8, we got different positions of Yerkes, seperated by approximately 100 min. By these values we were again able to determine the distance to the sun (as described above). The best result:
pi(sun)=8.4arcsec
In this way, we are shure that the positions obtained at the Oldendorfer Berg are precise enough (and perhaps more than this) for our goal.

Now we are hoping to make and to get images taken simultanously with those of the observatory of La Silla, due to an observation proposal of Osnabrück! To make it easier to find the asteroids we give star maps in an additional paper.

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Determination of the Orbits

Klio

With the following topocentric positions
  1. Oct. 14, 1996, 19:17:07 UT: RA 2h42m47.740s, dec 33d 9' 0.874"
  2. Nov. 13, 1996, 20:14:06 UT: RA 2h 9m40.625s, dec 31d48' 8.617"
  3. Nov. 14, 1996, 18:26:40 UT: RA 2h 8m49.550s, dec 31d41'52.237"
(which we took as geocentric!) we got by means of the algorithm of Gauss the following orbital elements:

a = 2.361, e = 0.241, i = 9.309, kl = 327.940

Semiramis

With the following topocentric positions
  1. Nov. 8, 1996, 21:20:27 UT: RA 2h43m41.376s, dec 34d45'50.301"
  2. Nov. 13, 1996, 20:27:58 UT: RA 2h39m 5.268s, dec 33d51'13.477"
  3. Nov. 14, 1996, 18:39:53 UT: RA 2h38m16.977s, dec 33d40'22.863"
(which we took as geocentric!) we got by means of the algorithm of Gauss the following orbital elements:

a = 2.307, e = 0.241, i = 9.990, kl = 285.075

Yerkes

With the following topocentric positions
  1. Oct. 14, 1996, 19:29:36 UT: RA 3h14m 1.07s, dec 29d 8'24.11"
  2. Nov. 8, 1996, 21:03:06 UT: RA 2h49m35.70s, dec 29d38'27.92"
  3. Nov. 14, 1996, 18:01:09 UT: RA 2h43m20.97s, dec 29d25'57.00"
(which we took as geocentric!) we got by means of the algorithm of Gauss the following orbital elements:

a = 2.672, e = 0.215, i = 8.771, kl = 354.277

All of these elements are in surprisingly good agreement with those we got from Guide.40. Therefore, we will be able to calculate the necessary ephemeris data by means of self measured and calculated orbital elements. We hope that these data will be precise enouph, at least for the combination of positions measured by different observatories!

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update: November 19, 1996