Measuring the Distance to the Sun:
Ephemeris Data of some Minor Planets

We are looking for some other groups of students, amateur astronomers or pupils, respectively, who are interested in measuring the parallax of some minor planet by means of ccd imaging. We hope we will get some pictures taken at exactly at the same time and we will then try to determine the parallax and then to calculate the sun's parallax.

That means we hope to become able to measure und to calculate the Astronomical Unit by our own!

This document contains

  1. some remarks refering to our choice of four minor planets,
  2. three pictures showing the paths of these for asteroids, during October and November and the parallax effect of Klio,
  3. orbital elements and ephemeris data of Toutatis,
  4. orbital elements and ephemeris data of Semiramis,
  5. orbital elements and ephemeris data of Klio and
  6. orbital elements and ephemeris data of Yerkes.
The ephemeris data make it possible to find the asteroids with the telescope. But, because of their quick proper motion it may be difficult to find them to times which differ from those given below. When we will have found other groups to cooperate with we will fix some days and times for simultanous measurements. We will then publish ephemeris data in more detail, if necessary.

"Our" Minor Planets

Up to now we have selected the following minor planets because they are near to the earth (approx. 1-2 AU) during October and November 1996 and of different magnitude (Semiramis approx. 10.7mag, Klio approx. 11.7mag, Yerkes approx. 14.5 mag). Toutatis was proposed in the first announcement of AOL. It will come extremely near to the earth (downto 0.02 AU), but it will then be very difficult to find and photograph it because of its inferior conjunction with the sun (15.0mag - 21.0mag).

The orbital elements and ephemeris data given below we calculated with GUIDE 4.0 .

Three Pictures

1) trails of three asteroids , 2) trail of Toutakis , 3) parallax effect of Klio

If you click on one of the little pictures you will get a large version of it.

The third picture help you to imagine the magnitude of the parallax effect of a near by object. It shows you two pictures of Klio on 1996 Oct 1.0 (number 84 near the center), one of them taken (that means calculated with Guide 4.0 but we hope to make pictures by ourselves and to get others!) from Koblenz (latitude +50 degrees) the other from a city with latitude -50 degrees. The picture has a width of about 8 arcminutes! The stars are labeled with the numbers of the GSC (Guide Star Catalogue). In order to be able to determine the position of the asteroid it is necessary to find at least three stars of known position on the picture!

4179 Toutatis

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Orbital Elements of Toutatis 

date           epoch       semi-maior axis, eccentricity, inclination, longitude of the ascending node, longitude of the perihelion, mean anomaly
1996 Sept 24.0 2450350.5   2.5151           0.633959      0.467525     128.6601                         43.1015                      348.1266
1996 Nov 13.0  2450400.5   2.5159           0.634086      0.467512     128.6465                         43.0982                      0.4824
1997 Jan 2.0   2450450.5   2.5121           0.633579      0.469679     128.2071                         43.0354                      12.8727

Ephemeris Data of Toutatis 1996 Oct 1.0 - 1996 Dec 10.0 

Datum                  RA             Deklination       r      delta   mag
----                   --             -----------       -      -----   ---
 1 Okt 1996            19h01.65680m   S23 44.665'       1.084   0.325 15.5
 3 Okt 1996            19h01.34663m   S23 48.271'       1.070   0.317 15.5
 5 Okt 1996            19h01.19261m   S23 51.790'       1.057   0.310 15.5
 7 Okt 1996            19h01.17951m   S23 55.261'       1.044   0.302 15.5
 9 Okt 1996            19h01.29021m   S23 58.734'       1.031   0.294 15.4
11 Okt 1996            19h01.50551m   S24 02.263'       1.019   0.285 15.4
13 Okt 1996            19h01.80375m   S24 05.909'       1.008   0.277 15.4
15 Okt 1996            19h02.16026m   S24 09.745'       0.997   0.268 15.4
17 Okt 1996            19h02.54650m   S24 13.854'       0.986   0.258 15.4
19 Okt 1996            19h02.92801m   S24 18.340'       0.977   0.248 15.4
21 Okt 1996            19h03.26887m   S24 23.302'       0.968   0.238 15.4
23 Okt 1996            19h03.52453m   S24 28.877'       0.960   0.228 15.4
25 Okt 1996            19h03.64618m   S24 35.212'       0.952   0.217 15.4
27 Okt 1996            19h03.57916m   S24 42.478'       0.945   0.207 15.4
29 Okt 1996            19h03.26141m   S24 50.873'       0.939   0.196 15.4
31 Okt 1996            19h02.62068m   S25 00.628'       0.934   0.184 15.4
 2 Nov 1996            19h01.57019m   S25 12.023'       0.930   0.173 15.4
 4 Nov 1996            19h00.00273m   S25 25.394'       0.926   0.161 15.4
 6 Nov 1996            18h57.78249m   S25 41.146'       0.923   0.150 15.4
 8 Nov 1996            18h54.73301m   S25 59.770'       0.922   0.138 15.5
10 Nov 1996            18h50.61847m   S26 21.855'       0.921   0.126 15.6
12 Nov 1996            18h45.11382m   S26 48.091'       0.921   0.115 15.7
14 Nov 1996            18h37.75670m   S27 19.244'       0.922   0.103 15.9
16 Nov 1996            18h27.86922m   S27 56.034'       0.923   0.092 16.1
18 Nov 1996            18h14.42978m   S28 38.762'       0.926   0.080 16.5
20 Nov 1996            17h55.86536m   S29 26.270'       0.929   0.070 17.2
22 Nov 1996            17h29.74516m   S30 13.171'       0.934   0.059 18.4
24 Nov 1996            16h52.49864m   S30 42.963'       0.939   0.050 21.2
26 Nov 1996            15h59.95294m   S30 14.228'       0.945   0.043 25.5
28 Nov 1996            14h50.96432m   S27 31.370'       0.952   0.037 18.7
30 Nov 1996            13h34.08603m   S21 37.931'       0.959   0.035 14.8
 2 Dez 1996            12h24.84426m   S13 47.802'       0.967   0.037 12.9
 4 Dez 1996            11h31.64005m   S 6 27.889'       0.976   0.043 12.2
 6 Dez 1996            10h53.25426m   S 0 46.727'       0.986   0.050 12.0
 8 Dez 1996            10h25.25041m   N 3 24.329'       0.996   0.059 11.9
10 Dez 1996            10h04.65985m   N 6 25.581'       1.007   0.068 12.0

584 Semiramis

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Orbital Elements of Semiramis 


1996 Sept 24.0 2450350.5   2.3737  0.233690 10.717362  282.5048    6.9709   12.8918
1996 Nov 13.0  2450400.5   2.3737  0.233697 10.717374  282.5047    6.9763   26.3633
1997 Jan 2.0   2450450.5   2.3738  0.233714 10.717384  282.5046    6.9815   39.8331

Ephemeris Data of SEMIRAMIS 1996 Oct 1.0 - 1996 Dec 10.0 

Datum                  RA             Deklination       r      delta   mag
----                   --             -----------       -      -----   ---
 1 Okt 1996            03h09.85453m   N36 45.045'       1.850   1.037 11.1
 3 Okt 1996            03h09.75688m   N36 52.527'       1.852   1.026 11.1
 5 Okt 1996            03h09.48263m   N36 58.772'       1.854   1.016 11.1
 7 Okt 1996            03h09.03278m   N37 03.719'       1.857   1.006 11.0
 9 Okt 1996            03h08.40982m   N37 07.306'       1.859   0.997 11.0
11 Okt 1996            03h07.61778m   N37 09.475'       1.862   0.988 10.9
13 Okt 1996            03h06.66237m   N37 10.170'       1.864   0.980 10.9
15 Okt 1996            03h05.55110m   N37 09.340'       1.867   0.972 10.9
17 Okt 1996            03h04.29322m   N37 06.942'       1.870   0.965 10.8
19 Okt 1996            03h02.89963m   N37 02.942'       1.872   0.959 10.8
21 Okt 1996            03h01.38248m   N36 57.315'       1.875   0.953 10.7
23 Okt 1996            02h59.75480m   N36 50.050'       1.878   0.948 10.7
25 Okt 1996            02h58.03036m   N36 41.142'       1.881   0.944 10.7
27 Okt 1996            02h56.22357m   N36 30.599'       1.884   0.941 10.6
29 Okt 1996            02h54.34953m   N36 18.438'       1.887   0.938 10.6
31 Okt 1996            02h52.42420m   N36 04.689'       1.891   0.936 10.6
 2 Nov 1996            02h50.46427m   N35 49.395'       1.894   0.936 10.6
 4 Nov 1996            02h48.48710m   N35 32.614'       1.897   0.936 10.5
 6 Nov 1996            02h46.51035m   N35 14.420'       1.901   0.936 10.5
 8 Nov 1996            02h44.55176m   N34 54.901'       1.904   0.938 10.5
10 Nov 1996            02h42.62889m   N34 34.159'       1.907   0.941 10.5
12 Nov 1996            02h40.75888m   N34 12.310'       1.911   0.944 10.5
14 Nov 1996            02h38.95810m   N33 49.484'       1.915   0.949 10.5
16 Nov 1996            02h37.24180m   N33 25.818'       1.918   0.954 10.6
18 Nov 1996            02h35.62365m   N33 01.458'       1.922   0.960 10.6
20 Nov 1996            02h34.11547m   N32 36.551'       1.926   0.968 10.6
22 Nov 1996            02h32.72719m   N32 11.243'       1.930   0.976 10.7
24 Nov 1996            02h31.46703m   N31 45.674'       1.933   0.985 10.7
26 Nov 1996            02h30.34178m   N31 19.980'       1.937   0.995 10.8
28 Nov 1996            02h29.35704m   N30 54.292'       1.941   1.005 10.8
30 Nov 1996            02h28.51742m   N30 28.734'       1.945   1.017 10.9
 2 Dez 1996            02h27.82654m   N30 03.421'       1.949   1.029 10.9
 4 Dez 1996            02h27.28709m   N29 38.463'       1.954   1.043 11.0
 6 Dez 1996            02h26.90089m   N29 13.960'       1.958   1.057 11.1
 8 Dez 1996            02h26.66888m   N28 50.004'       1.962   1.072 11.1
10 Dez 1996            02h26.59154m   N28 26.677'       1.966   1.087 11.2

84 Klio

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Orbital Elements of Klio 

1996 Sept 24.0 2450350.5   2.3619  0.236887  9.340495  327.8295  342.3826   27.8824
1996 Nov 13.0  2450400.5   2.3619  0.236885  9.340470  327.8291  342.3880   41.4548
1997 Jan 2.0   2450450.5   2.3620  0.236894  9.340464  327.8282  342.3943   55.0245

Ephemeris Data of KLIO 1996 Oct 1.0 - 1996 Dec 10.0 


Datum                  RA             Deklination       r      delta   mag
----                   --             -----------       -      -----   ---
 1 Okt 1996            02h52.84189m   N32 05.859'       1.922   1.073 11.9
 3 Okt 1996            02h51.84447m   N32 18.556'       1.926   1.065 11.9
 5 Okt 1996            02h50.68156m   N32 30.146'       1.930   1.057 11.9
 7 Okt 1996            02h49.35783m   N32 40.568'       1.934   1.050 11.8
 9 Okt 1996            02h47.87960m   N32 49.763'       1.939   1.043 11.8
11 Okt 1996            02h46.25480m   N32 57.677'       1.943   1.037 11.7
13 Okt 1996            02h44.49304m   N33 04.260'       1.947   1.032 11.7
15 Okt 1996            02h42.60564m   N33 09.471'       1.951   1.028 11.7
17 Okt 1996            02h40.60549m   N33 13.277'       1.956   1.024 11.6
19 Okt 1996            02h38.50680m   N33 15.658'       1.960   1.021 11.6
21 Okt 1996            02h36.32478m   N33 16.603'       1.965   1.019 11.6
23 Okt 1996            02h34.07510m   N33 16.113'       1.969   1.018 11.5
25 Okt 1996            02h31.77376m   N33 14.201'       1.974   1.018 11.5
27 Okt 1996            02h29.43696m   N33 10.889'       1.978   1.018 11.5
29 Okt 1996            02h27.08114m   N33 06.207'       1.983   1.020 11.5
31 Okt 1996            02h24.72298m   N33 00.200'       1.988   1.022 11.5
 2 Nov 1996            02h22.37936m   N32 52.923'       1.992   1.025 11.5
 4 Nov 1996            02h20.06710m   N32 44.442'       1.997   1.030 11.5
 6 Nov 1996            02h17.80278m   N32 34.838'       2.002   1.035 11.5
 8 Nov 1996            02h15.60241m   N32 24.198'       2.007   1.041 11.5
10 Nov 1996            02h13.48128m   N32 12.622'       2.012   1.048 11.5
12 Nov 1996            02h11.45378m   N32 00.218'       2.016   1.056 11.6
14 Nov 1996            02h09.53315m   N31 47.099'       2.021   1.065 11.6
16 Nov 1996            02h07.73117m   N31 33.384'       2.026   1.075 11.7
18 Nov 1996            02h06.05791m   N31 19.193'       2.031   1.085 11.7
20 Nov 1996            02h04.52157m   N31 04.643'       2.036   1.097 11.8
22 Nov 1996            02h03.12857m   N30 49.849'       2.041   1.109 11.8
24 Nov 1996            02h01.88378m   N30 34.915'       2.046   1.123 11.9
26 Nov 1996            02h00.79084m   N30 19.943'       2.051   1.137 12.0
28 Nov 1996            01h59.85238m   N30 05.025'       2.056   1.152 12.0
30 Nov 1996            01h59.07025m   N29 50.250'       2.061   1.168 12.1
 2 Dez 1996            01h58.44549m   N29 35.698'       2.067   1.184 12.1
 4 Dez 1996            01h57.97842m   N29 21.444'       2.072   1.201 12.2
 6 Dez 1996            01h57.66870m   N29 07.556'       2.077   1.219 12.3
 8 Dez 1996            01h57.51537m   N28 54.094'       2.082   1.238 12.3
10 Dez 1996            01h57.51713m   N28 41.115'       2.087   1.258 12.4

990 Yerkes

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Orbital Elements of Yerkes 

1996 Sept 24.0 2450350.5   2.6699  0.213876  8.771425  354.2654    3.0472   19.2916
1996 Nov 13.0  2450400.5   2.6700  0.213887  8.771353  354.2649    3.0538   30.5823
1997 Jan 2.0   2450450.5   2.6701  0.213907  8.771274  354.2638    3.0603   41.8712

Ephemeris Data of YERKES 1996 Oct 1.0 - 1996 Dec 10.0 

Datum                  RA             Deklination       r      delta   mag
----                   --             -----------       -      -----   ---
 1 Okt 1996            03h20.44987m   N27 56.251'       2.158   1.352 14.8
 3 Okt 1996            03h19.94671m   N28 08.605'       2.160   1.339 14.8
 5 Okt 1996            03h19.29532m   N28 20.375'       2.163   1.326 14.7
 7 Okt 1996            03h18.49659m   N28 31.522'       2.166   1.314 14.7
 9 Okt 1996            03h17.55247m   N28 42.007'       2.168   1.303 14.7
11 Okt 1996            03h16.46598m   N28 51.790'       2.171   1.293 14.6
13 Okt 1996            03h15.24131m   N29 00.834'       2.174   1.283 14.6
15 Okt 1996            03h13.88392m   N29 09.100'       2.176   1.274 14.5
17 Okt 1996            03h12.40050m   N29 16.556'       2.179   1.266 14.5
19 Okt 1996            03h10.79896m   N29 23.171'       2.182   1.259 14.5
21 Okt 1996            03h09.08813m   N29 28.919'       2.185   1.252 14.4
23 Okt 1996            03h07.27754m   N29 33.778'       2.188   1.247 14.4
25 Okt 1996            03h05.37734m   N29 37.733'       2.191   1.242 14.3
27 Okt 1996            03h03.39824m   N29 40.770'       2.194   1.238 14.3
29 Okt 1996            03h01.35160m   N29 42.882'       2.197   1.236 14.3
31 Okt 1996            02h59.24953m   N29 44.065'       2.200   1.234 14.2
 2 Nov 1996            02h57.10487m   N29 44.327'       2.203   1.233 14.2
 4 Nov 1996            02h54.93115m   N29 43.679'       2.206   1.233 14.2
 6 Nov 1996            02h52.74239m   N29 42.145'       2.209   1.234 14.2
 8 Nov 1996            02h50.55292m   N29 39.754'       2.213   1.236 14.1
10 Nov 1996            02h48.37724m   N29 36.545'       2.216   1.239 14.1
12 Nov 1996            02h46.22980m   N29 32.566'       2.219   1.244 14.2
14 Nov 1996            02h44.12483m   N29 27.874'       2.223   1.249 14.2
16 Nov 1996            02h42.07593m   N29 22.531'       2.226   1.255 14.2
18 Nov 1996            02h40.09584m   N29 16.608'       2.229   1.262 14.3
20 Nov 1996            02h38.19608m   N29 10.176'       2.233   1.271 14.3
22 Nov 1996            02h36.38692m   N29 03.309'       2.236   1.280 14.4
24 Nov 1996            02h34.67742m   N28 56.080'       2.240   1.290 14.4
26 Nov 1996            02h33.07561m   N28 48.563'       2.243   1.301 14.5
28 Nov 1996            02h31.58865m   N28 40.829'       2.247   1.313 14.5
30 Nov 1996            02h30.22284m   N28 32.949'       2.251   1.326 14.6
 2 Dez 1996            02h28.98371m   N28 24.992'       2.254   1.340 14.6
 4 Dez 1996            02h27.87596m   N28 17.025'       2.258   1.355 14.7
 6 Dez 1996            02h26.90348m   N28 09.112'       2.262   1.371 14.7
 8 Dez 1996            02h26.06934m   N28 01.314'       2.265   1.387 14.8
10 Dez 1996            02h25.37609m   N27 53.689'       2.269   1.404 14.9

update:

1996 Nov 5, 15.00 MEZ