On the famous Oort table

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Written by dr Piotr A. Dybczyński, Astronomical Observatory Institute of the A.Mickiewicz University , Poznań, Poland.

On the famous Oort table (news at the bottom)

In the middle of XX century, famous Dutch astronomer, Ian Hendrik Oort (1900-1992) published his well known paper, entitled The structure of the cloud of comets surrounding the Solar System and a hypothesis concerning its origin.

Oort original table

The most important argument for the existence of the so called Oort Cloud of comets was a small table, reproduced here from the original paper.

He took 19 comets with well determined original orbits and simply counted the number of comets in small intervals if the inversed semi-major axis.

However, nowadays it is difficult to find out, which 19 comets Oort used.

In his paper Oort stated:

"Among the so-called long-period comets there are 22 for which, largely by the work of Elis Strömgren, accurate calculations have been made of the orbits followed when they were still far outside the orbits of the major planets 1. Approximate calculations of the original orbits by Fayet 2 are available for 8 other comets with well-determined osculating orbits. For the present limiting ourselves to the comets for which the perturbations were rigorously determined, and excluding 3 for which the mean error of the reciprocal major axis, 1/a, is larger than 0.000100, the values of 1/a for the remaining 19 comets are distributed as shown in Table I."

In the footnotes he specified:

1.A list of these is given by Sinding, Danske Vidensk. Selsk., Mat.-Fys. Medd. 24, Nr 16, 1948, or Publ. o. Mindre Medd. Köbenhavns Obs. Nr 146. Van Biesbroeck's orbit for comet 1908 III has been added to this list.

2. These, Paris, 1906; also in Ann. Paris, Mim. 26.A, 1910.

It seems legitimate to understand the above as follows: eight comets for which "approximate" original orbits were calculated by Fayet in 1906 were too inaccurate from the Oort's point of view. He limited himself to 21 comets listed in the Sinding (1948) paper, for which original orbits were calculated by Strömgren and added to them 22nd one (1908 III), calculated by Van Biesbroeck (no reference here). From that list of 22 comets he excluded three, with the 1/a determination error greater than 0.0001 AU-1, and the remaining 19 constitute the body of Table I.

Table from Sinding paper
Table from page 4
of the quoted Sinding paper (1948).

Unfortunately Sinding presented only 1/aosc i 1/aorig values, without their determination errors, so it is impossible to check directly, which 3 comets Oort removed from the list. I am sure that all three rejected comets were from the Sinding list - Oort added 1908 III not to reject it in the next step!

There is a note of Sinding concerning the comet 1910 I. He stated that its 1/aorig value is erroneous (therefore printed in brackets) due to an obvious error, and should be replaced with the correct value of +0.0006921.

Starting this 'investigation' I had no access to the source quoted by Sinding (Geelmuyden-Strömgren, Lærebog i Astronomi, 2. Udg., Oslo 1945, page 285), but in the earlier edition of the same book I found a list of 12 original cometary orbits with determination error of 1/a. These are: 1853 II, 1882 II, 1886 I, 1886 II, 1886 IX, 1890 II, 1897 I, 1898 VII, 1905 VI, 1902 III, 1910 I and 1914 V. From that list only two comets, namely 1882 II and 1910 I, have 1/a determination error greater than 0.0001 AU-1. It seems rather improbable, that Strömgren recalculated these two orbits again before the next book edition (however he added 9 new orbits). It seems even less probable that one of remaining 10 comets "increased" its 1/a determination error in this next edition. I think, that with a great level of certainty we can assume, that 1882 II and 1910 I were among three comets rejected by Oort and the remaining 10 were used to construct his table.

The number of unknowns decreased significantly so we can try to solve the puzzle.

Besides comet 1908 III we know exactly what 1/aorig values Oort used. Let's try to compare these values with the numbers in the Oort Table I.

As it concerns 1908 III, the oldest information I found, come from the paper by Marsden, Sekanina i Everhart, published in 1978. They obtained 1/aosc = -0.000711 ± 0.000007 and 1/aorig = +0.000174 AU-1 for that comet.

Let's start from the bottom of the Oort table:

  • For interval 0.00050 - 0.00075 fits only one comet: 1905 VI, with 1/aorig = +0.0006210
  • For interval 0.00025 - 0.00050 fits only 1886 II, with 1/aorig = +0.0003166
  • For interval 0.00020 - 0.00025 fit two comets: 1904 I and 1936 I. Bingo! One of them is the third comet rejected by Oort, since he counted only one comet in this interval of 1/aorig!

Let's continue our checking:

  • For interval 0.00015 - 0.00020 we cannot find any comet in the Sinding list, but... the comet 1908 III, having (according to Marsden, Sekanina and Everhart) 1/aorig = +0.000174 fits ideally!
  • For interval 0.00010 - 0.00015 fits only 1925 VII, having 1/aorig = +0.0001150
  • For interval 0.00005 - 0.00010 we need four comets... and voilá: 1853 III, 1886 IX, 1890 II and 1925 I fit perfectly.
  • Thus, as comets having 1/aorig < +0.00005 Oort counted FOR SURE: 1863 VI, 1886 I, 1889 I, 1897 I, 1898 VII, 1902 III, 1907 I, 1914 V, 1922 II and 1932 VI.
    You can count them: 10, as it should be !

The puzzle is almost solved.

For a contemporary reader we only should translate these old cometary designations to the modern ones. For many years it was possible to use the on-line interactive comet-name translator at MPC, but after the last upgrade of this site it stopped working. If you are interested, I have my own comet dictionary.

Finally, the 19 comets from the famous Oort Table were (almost surely) the following:

  1. 1853 III = C/1853 L1 Klinkerfues
  2. 1863 VI = C/1863 T1 Baeker
  3. 1886 I = C/1885 X1 Fabry
  4. 1886 II = C/1885 X2 Barnard
  5. 1886 IX = C/1886 T1 Barnard-Hartwig
  6. 1889 I = C/1888 R1 Barnard
  7. 1890 II = C/1890 F1 Brooks
  8. 1897 I = C/1896 V1 Perrine
  9. 1898 VII = C/1898 L1 Coddington-Pauly
  10. 1902 III = C/1902 R1 Perrine
  11. 1904 I = C/1904 H1 Brooks OR 1936 I = C/1935 Q1 Van Biesbroeck (but see below!)
  12. 1905 VI = C/1906 B1 Brooks
Tabela Strömgrena
Table from page 285
of the book Geelmuyden-Strömgren,
Lærebog i Astronomi, published at Oslo in 1945
  1. 1907 I = C/1907 E1 Giacobini
  2. 1914 V = C/1913 Y1 Delavan
  3. 1922 II = C/1922 U1 Baade
  4. 1925 I = C/1925 G1 Orkisz
  5. 1925 VII = C/1925 W1 Van Biesbroeck
  6. 1932 VI = C/1932 M2 Geddes
  7. 1908 III = C/1908 R1 Morehouse

The puzzle is completely solved

By courtesy of Miss Barbara Kerk, a librarian at the University of Chicago I have obtained a scan of the page 285 from a book: Geelmuyden-Strömgren, Lærebog i Astronomi, 2. Udg., Oslo 1945,. Indeed, there is a table there, containing 21 comets and presented are uncertainties of 1/a !

Jan Oort used this table "excluding 3 for which the mean error of the reciprocal major axis, 1/a, is larger than 0.000100", so he has to omit comets 1882 II, 1910 I, and 1936 I.

As you can see our 'investigation results' obtained so far were pretty correct and using this last table we can definitely exclude the comet 1936 I = C/1935 Q1 Van Biesbroeck.

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