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It may be remarked further, that the smaller planets take the longer time to complete their rotations. An attempt has been made to explain this on the supposition that the motion in the orbit, and that on the axis, are the result of a single impulse. In this case the larger body would admit of a direction more favorable to a rotatory motion ; just as a foot-ball is more likely to turn on its axis, while it is impelled forward, than a batting-ball.

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The Sun, Mercury, Venus, Earth, Mars, Vesta, Juno, Ceres, Pallas, Jupiter. Saturn, Uranus,

Mean Diameters Mean Diameters of Surfaces of the Bulks of the Planof the Planels, the Planets, that of Planets, that of

ets, that of the in miles. the Earth being 1. the Earth being 1. Earth being 1. 881441

111.7851 12496.0 1396856.0
3036
0.3837
0.1472

0.0565
7590
0.9593
0.9202

0.8828 7912 1.0000 1.0000

1.0000 4140 0.5233 . 0.2738

0.1433 269 0.034 0.0012

0.00004 1393 0.176 0.0310

0.0055 1582 0.2 0.0400

0.008 2025 0.256 0.0655

0.0168
83937
10.8616
117.97

1281.3
79168
9.9831
99.66

99 1.9
35112
4.2630
18.77

77.5

XI. ORBITS OF THE PLANETS.

A FRUITFUL source of error, in the ancient systems of astronomy, was the supposition that the motions of the planets took place in circular orbits. Kepler laid the foundation of the present improved state of the science, by establishing the following propositions known by the name of Kepler's Laws.

1. The planets revolve in ovals or elliptical curves, the sun being in the focus of the ellipse.

2. The spaces passed over by a line drawn from the sun to the revolving body, in different parts of the orbit, are equal, when equal times are allowed. In other words, A planet, as it approaches nearer to the

sun, moves just so much faster, as to make the space passed over by the revolving radius, in a day, for instance, always the same.

3. If we take the times in which any two planets complete their revolution, and multiply each by itself; and then t'i + the r mean distances from the sun, a d multiply each by itself twice ; the two first results will have the same proportion to each other, as the two last; in other words, the squares of the times are as the cubes of the distances.

There are several particulars respecting a planet, given in the following tables, which being known, we are able to calculate its position or place at any time. These are termed the elements of a planet's orbit, and are as follows.

1. The time employed in making a complete circuit of the heavens, which is called the sidereal revolution.

2. The average distance of the planet from the sun, which is half the greatest diameter of the elliptical orbit. This is called the mean distance.

3. The eccentricity, or the proportion which the distance from the focus to the centre bears to the mean distance. This is subject to a slight change, the amount of which, for a century, is put down under the title of secular variation.

4. The position or mean longitude of the planet, for any given time, as the beginning of the century. This longitude is reckoned from the vernal equinox, or the 1st of Aries, as longitude on the earth is reckoned from any assumed meridian, as that of Greenwich. But celestial longitude is counted on the ecliptic, and only in one direction, namely, from west to east, in the direction of the planetary motions.

5. The position of the point of nearest approach of the planet to the sun, is called the perihelion (from two Greek words, which signify about the sun). This point is referred, also, to the 1st of Aries, and its position is determined, like that of the planet itself, by its distance from the vernal equinox, reckoned on the ecliptic. This distance is denominated the longitude of the perihelion. As the perihelion has a slow motion, its position is given for a particular time, or epoch, and also its change of position in a century, termed the secular variation.

6. The orbits of the planets not being coincident with, or parallel to the ecliptic, their oblique position with respect to the ecliptic, is of great importance in calculating their places. This is called the inclination of the orbit. Like the other elements, it is subject to a slight change; hence the inclination is given for a particular epoch, together with the alteration

in a century.

7. The two points in which the orbit of a planet cuts the ecliptic are called its nodes. That node, through which the planet passes in coming from the south to the north, is distinguished as the ascending node. The position of this point is determined, like that of other points, by its distance

from Aries. It is called the longitude of the ascending node. The node, in like manner, has a slight motion; accordingly its position is given for à particular epoch, together with the sidereal and secular variation, or change with respect to a star in a century.

TABLE OF THE ELLIPTICAL MOTION OF THE PLANETS.

3

Mercury
Venus
The Earth
Mars
Jupiter
Sati 11
Uranus

(1.) Sidereal Revolution.

Days.

Years.
87.9692580 or nearly.
224.7007869
365.2563835 1
686.979645S 2 nearly.
4332.5848212

12
10759.2198174 291
30686.8208296 84

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(2.) Mean Distance, or Half the Major Axis of the Orbit. Mercury

0.3870981 or 37,000,000 miles. Venus

0.7233316 69,000,000 The Earth

1.0000000 95,000,000 Mars

1.5236923 144,000,000 Jupiter

5.202776 490,000,000 Saturn

9.5387861 900,000,000 Uranus

19.182390 1900,000,000

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(3.) Ratio of the Eccentricity to the Mean distance, at the Beginning

of 1801, with the Secular Variation. The Sign indicates a Diminution.

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(4.) Mean Longitude, for the Minute which separates the 31st of Decem

ber, 1800, from the 1st of January, 1801, Mean Time at Paris.

.

Mercury
Venus
The Earth

163 56 27,0

10 44 21.6 100 09 13.0

.

64 66 69.9

Mars
Jupiter
Saturn
Uranus

112 12 51.3
135 19 05.5
177 48 01.1

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(5.) Mean Longitude of the Perihelion, for the same Epoch, with the

Sidereal and Secular Variation. The Sign - indicates a Retro-
grade Motion.
Mercury

74 21 16.9

9 43.5 Venus

128 43 53.1 - 4 27.8 The Earth

99 30 05.0 19 39.8 Mars

332 23 56.7 26 22.4 Jupiter

11 03 31.4 11 3.9 Saturn

89 09 29 6 32 17.1 Uranus

167 32 06.0 3 59.3

(6.) Inclination of the Orbit to the Ecliptic, at the Beginning of 1801,

with the Secular Variation of the Inclination to the true Ecliptic. Mercury

7 00 09.1

18.2 Venus.

3 23 28.5

4.6 The Earth

0 00 00.0

0.0 Mars

1 51 06.2

0.2 Jupiter

1 18 51.3

22.6 Saturn.

2 29 35.7

15.5 Uranus

0 46 28.4

3.1

.

(7.) Longitude of the Ascending Node, at the Beginning of 1801, with

the Sidereal and Secular Motion. Mercury

45 57 30.9 13 Venus

74 54 12.9 31 10 The Earth

00 00 00.0 00 00 Mars

48 00 03.5 38 48 Jupiter

98 26 18.9 26 18 Saturn

111 56 37.4 37 46 Uranus

72 59 35.5 59 58

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(3.) Ratio of the Eccentricity to the Mean Distance. Ceres

0.078439 Pallas

0.241648 Juno .

0.257848 Vesta

0.089130

.

Ceres
Pallas
Juno
Vesta

(4.) Mean Longitude at the Beginning of 1820.

123 09 41.4 108 18 28.7 200 09 32.4 278 21 45.1

(5.) Longitude of the Perihelion at the same Epoch. Ceres

147 67 311.5 Palla3

121 07 04.3 Juno

53 33 46.0 Vesta

249 33 24.4

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Ceres
Pallas
Juno
Vesta

(6.) Inclination of the Orbit to the Ecliptic.

10 37 26.3 34 34 55.1 13 04 09.7 7 08 09.0

(7.) Longitude of the Ascending Node, at the Beginning of 1810. Ceres

78 53 245 Pallas

172 39 26.8 Juno

171 07 40.4 Vesta

103 13 18.2

XII. SYNODIC REVOLUTIONS OF THE PLANETS:

Each of the planets, after a certain period, returns to the same position with regard to the sun. This period is called the synodic revolution, from two Greek words, which signify, to come together. It is readily found from the motion of the planet, compared with the apparent motion of the

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