THE ASTEROID RING BETWEEN MARS AND JUPITER.
The mean distances of the minor planets between Mars and Jupiter vary
from 2·20 to 3·49. The breadth of the zone is therefore 20,000,000
miles greater than the distance of the earth from the sun; greater
even than the entire interval between the orbits of Mercury and
Mars. Moreover, the _perihelion_ distance of some members of the
group exceeds the _aphelion_ distance of others by a quantity equal
to the whole interval between the orbits of Mars and the earth. The
_Olbersian_ hypothesis of the origin of these bodies seems thus
to have lost all claim to probability.[30] Professor Alexander's
theory of the disruption of a primitive discoidal planet of great
equatorial diameter, is less objectionable; still, however, it requires
confirmation. But whatever may have been the original constitution
of the ring,[31] its existence in its present form for an indefinite
period is unquestioned. Let us then consider some of the effects of
its secular perturbation by the powerful mass of Jupiter.
_Portions of the ring in which the periods of asteroids would be
commensurable with that of Jupiter._--The breadth of this zone is
such as to contain several portions in which the periods of asteroids
would be commensurable with that of Jupiter. As in the case of the
perturbation of Saturn's ring by the interior satellites, the tendency
of Jupiter's influence would be to form gaps or chasms in the primitive
ring.
The mean distance of an asteroid whose period
is 1/2 that of Jupiter =3·2776
That of one whose period is 1/3 of Jupiter's =2·5012
" " 2/5 " =2·8245
" " 2/7 " =2·2569
" " 3/7 " =2·9574
" " 4/9 " =3·0299
For the purpose of facilitating the comparison of these numbers with
the mean distances of the asteroids and of observing whether any order
obtains in the distribution of these mean distances in space, we have
arranged the minor planets, in the following table, in the consecutive
order of their periods:
Periods and Distances of the Asteroids.
+------------+-------------+-----------+---------+
| ORDER OF | NAME. | DISTANCE. | PERIOD. |
| DISCOVERY. | | | |
+------------+-------------+-----------+---------+
| 8 | Flora | 2·2014 | 1193 d |
| 43 | Ariadne | 2·2034 | 1194·6 |
| 72 | Feronia | 2·2654 | 1245·4 |
| 40 | Harmonia | 2·2677 | 1247·3 |
| 18 | Melpomene | 2·2956 | 1270·4 |
| 80 | Sappho | 2·2971 | 1271·6 |
| 12 | Victoria | 2·3342 | 1302·6 |
| 27 | Euterpe | 2·3468 | 1313·2 |
| 4 | Vesta | 2·3613 | 1325·3 |
| 84 | Clio | 2·3618 | 1325·8 |
| 30 | Urania | 2·3655 | 1328·9 |
| 51 | Nemausa | 2·3657 | 1329·0 |
| 9 | Metis | 2·3858 | 1346·0 |
| 7 | Iris | 2·3863 | 1346·5 |
| 60 | Echo | 2·3931 | 1352·2 |
| 63 | Ausonia | 2·3949 | 1353·8 |
| 25 | Phocea | 2·4008 | 1358·8 |
| 20 | Massilia | 2·4144 | 1365·5 |
| 67 | Asia | 2·4217 | 1376·5 |
| 44 | Nysa | 2·4234 | 1378·0 |
| 6 | Hebe | 2·4244 | 1379·0 |
| 83 | Beatrice | 2·4287 | 1382·5 |
| 42 | Isis | 2·4400 | 1392·2 |
| 21 | Lutetia | 2·4411 | 1393·0 |
| 19 | Fortuna | 2·4416 | 1393·5 |
| 79 | Eurynome | 2·4437 | 1395·3 |
| 11 | Parthenope | 2·4519 | 1402·4 |
| 17 | Thetis | 2·4737 | 1421·1 |
| 46 | Hestia | 2·5262 | 1466·5 |
| 89 | | 2·5498 | 1487·2 |
| 29 | Amphitrite | 2·5544 | 1491·2 |
| 5 | Astræa | 2·5772 | 1511·2 |
| 13 | Egeria | 2·5775 | 1511·4 |
| 14 | Irene | 2·5860 | 1519·0 |
| 32 | Pomona | 2·5868 | 1519·6 |
| 91 | | 2·5958 | 1527·5 |
| 56 | Melete | 2·5959 | 1527·7 |
| 70 | Panopea | 2·6129 | 1543·0 |
| 53 | Calypso | 2·6188 | 1548·0 |
| 78 | Diana | 2·6236 | 1555·3 |
| 23 | Thalia | 2·6280 | 1568·0 |
| 37 | Fides | 2·6414 | 1570·0 |
| 15 | Eunomia | 2·6436 | 1572·6 |
| 85 | Io | 2·6466 | 1573·0 |
| 50 | Virginia | 2·6491 | 1575·0 |
| 88 | Thisbe | 2·6553 | 1580·0 |
| 26 | Proserpina | 2·6561 | 1581·1 |
| 66 | Maia | 2·6635 | 1587·8 |
| 73 | Clytie | 2·6666 | 1590·5 |
| 3 | Juno | 2·6707 | 1594·2 |
| 75 | Eurydice | 2·6707 | 1594·2 |
| 77 | Frigga | 2·6719 | 1595·3 |
| 64 | Angelina | 2·6805 | 1603·0 |
| 34 | Circe | 2·6865 | 1608·3 |
| 58 | Concordia | 2·7014 | 1622·0 |
| 54 | Alexandra | 2·7123 | 1631·6 |
| 59 | Elpis | 2·7131 | 1632·3 |
| 45 | Eugenia | 2·7218 | 1640·1 |
| 38 | Leda | 2·7401 | 1656·8 |
| 36 | Atalanta | 2·7458 | 1662·0 |
| 71 | Niobe | 2·7501 | 1665·8 |
| 82 | Alcmene | 2·7547 | 1670·0 |
| 55 | Pandora | 2·7591 | 1674·0 |
| 41 | Daphne | 2·7657 | 1679·9 |
| 1 | Ceres | 2·7663 | 1681·0 |
| 2 | Pallas | 2·7696 | 1683·5 |
| 39 | Lætitia | 2·7740 | 1687·6 |
| 74 | Galatea | 2·7777 | 1690·9 |
| 28 | Bellona | 2·7785 | 1691·6 |
| 68 | Leto | 2·7836 | 1696·3 |
| 81 | Terpsichore | 2·8591 | 1765·7 |
| 33 | Polyhymnia | 2·8653 | 1770·6 |
| 47 | Aglaia | 2·8812 | 1786·4 |
| 22 | Calliope | 2·9092 | 1812·4 |
| 16 | Psyche | 2·9233 | 1826·0 |
| 69 | Hesperia | 2·9707 | 1871·1 |
| 61 | Danaë | 2·9837 | 1882·4 |
| 35 | Leucothea | 3·0040 | 1904·2 |
| 49 | Pales | 3·0825 | 1976·6 |
| 86 | Semele | 3·0909 | 1984·7 |
| 52 | Europa | 3·1000 | 1993·6 |
| 48 | Doris | 3·1094 | 2002·7 |
| 62 | Erato | 3·1297 | 2022·3 |
| 24 | Themis | 3·1431 | 2035·3 |
| 10 | Hygeia | 3·1512 | 2043·2 |
| 31 | Euphrosyne | 3·1513 | 2044·6 |
| 57 | Mnemosyne | 3·1565 | 2048·4 |
| 90 | Antiope | 3·1576 | 2049·4 |
| 76 | Freia | 3·3864 | 2276·2 |
| 65 | Cybele | 3·4205 | 2310·6 |
| 87 | Sylvia | 3·4927 | 2384·2 |
+------------+-------------+-----------+---------+
REMARKS ON THE FOREGOING TABLE.
1. The first two members of the group, Flora and Ariadne, have very
nearly the same mean distance. Immediately exterior to these, however,
occurs a wide interval, including the distance at which seven periods
of an asteroid would be equal to two of Jupiter.
2. On the _outer_ limit of the ring Freia, Cybele, and Sylvia have also
nearly equal distances, and are separated from the next interior member
by a wide space including the distance at which two periods would be
equal to one of Jupiter, and also that at which five would be equal to
one of Saturn.
3. Besides these extreme members of the group, our table contains
eighty-six minor planets, all of which are included between the
distances 2·26 and 3·16; the mean interval between them being 0·0105.
The distances are distributed as follows:
2·26 to 2·36 6 minimum.
2·36 to 2·46 19 maximum.
2·46 to 2·56 4 minimum.
2·56 to 2·66 16 }
2·66 to 2·76 16 } maximum.
2·76 to 2·86 8
2·86 to 2·96 4 } minimum.
2·96 to 3·06 3 }
3·06 to 3·16 10 maximum.
The clustering tendency is here quite apparent.
4. The three widest intervals between these bodies are--
(_a_) between Leucothea and Pales 0·0785,
(_b_) " Leto and Terpsichore 0·0755,
(_c_) " Thetis and Hestia 0·0525;
and these, it will be observed, are the three remaining distances,
indicated on a previous page, at which the periods of the primitive
meteoric asteroids would be commensurable with that of Jupiter. Now,
if the original ring consisted of an indefinite number of separate
particles moving with different velocities, according to their
respective distances, those revolving at the distance 2·4935--in
the interval between Thetis and Hestia--would make precisely three
revolutions while Jupiter completes one. A planetary particle at this
distance would therefore always come in conjunction with Jupiter in
the same parts of its path: consequently its orbit would become more
and more eccentric until the particle itself would unite with others,
either exterior or interior, thus forming an asteroidal nucleus, while
the primitive orbit of the particle would be left destitute of matter,
like the interval in Saturn's ring.
5. If the distribution of matter in the zone was originally nearly
continuous, as in the case of Saturn's rings, it would probably break
up into a number of concentric annuli. On account, however, of the
great perturbations to which they were subject, these narrow rings
would frequently come in collision. After their rupture, and while
the fragments were collecting in the form of asteroids, numerous
intersections of orbits and new combinations of matter would occur, so
as to leave, in the present orbits, but few traces of the rings from
which the existing asteroids were derived. A comparison, however, of
the elements of Clytie and Frigga shows a striking similarity; and
Professor Lespiault has pointed out a corresponding likeness between
the orbits of Fides and Maia. For these four asteroids the nodal
lines and also the inclinations are nearly the same; while the periods
differ by only a few days. It is probable, therefore, that they are all
fragments of the same narrow ring. Finally, as they all move nearly in
the same plane, they must at some future time approach extremely near
each other, and perhaps become united in one large asteroid.