Of the Planets in general

The Sun, the sole Fountain of Light and Heat, is plac’d in the common Focus of all the primary Orbits, and nearly in the Center of the System, with a Rotation round his own Axis from West to East in the Space of 25 Days 6 Hours.

His Diameter is in round Numbers, nearest¹ 763,000 Miles, (how this is found will be shewn hereafter), and the Obliquity of his Axis to the Plane of the Ecliptic is about 83 Degrees.

Round him and their common Center of Gravity, the several Planets form their Motions, revolving in elliptical Orbits, and are observed to complete their respective Periods, with Regard to the fixt Stars, nearly as follows:

• ♄ 10759.275
• 🜨 365.2565
• ♃ 4332.514
• ♀ 224.6176
• ♂ 686.9785
• ☿ 87.9692

These Times are all found by the return of the Planets, in their Heliocentric Motion, to the same Point in the Heavens amongst the zodiacal Stars.

The mean, or rather middle, Distances of all those Planets from the Sun’s Center, with respect to one another, have been determined, by the Help of Trigonometry comparing many Observations together, to be very nearly thus:

By Kepler

• ☿ 38806
• ♀ 72400
• ♂ 152350
• ♃ 519650
• ♄ 951000

By Bullialdus

• ☿ 38585
• ♀ 72398
• ♂ 152350
• ♃ 522520
• ♄ 954198

Mean Distance of the earth in like Parts 100000.

Kepler found out, and Sir Isaac Newton has since demonstrated, that the Squares of the periodic Times, and the Cubes of the mean Distances of the Planets bear to one another a reciprocal Analogy, and from this the above Numbers have been proved to be very near the Truth. (viz.)

As the Square of the periodic Time of any one Planet,
Is to the Square of the periodic Time of any other Planet;
So is the Cube of the mean Distance of the former Planet,
To the Cube of the mean Distance of the Latter.

Thus confirmed,

The mean Distance of the Earth being supposed 100000 Parts, its Cube will be 1,000,000,000,000,000, and the periodic Time 365^d. 5^h. 48^m. reduced into Minutes is 525968.5, and squared is 276642862992.25; of Venus the periodic Time is 224d. 16^h. 49^m. 27^s., the Minutes 323569.4, and squar’d is 104679156616.36.

Now
As the Square of 525968.5, which is 276642862992.25
Is to the Square of 323569.4, which is 104697156616.36
So is the Cube of 100000 which is 1,000,000,000,000,000
To \(\frac{104697156616360000000000000.00}{276642862992.25}\)

Which will be 378456019012834.7; the Cube Root of which is 72333.3 Venus’s mean Distance from the Sun.

In like Manner, the Square of Mars’s periodic Time in Minutes, being 97839026137562.5 the Cube of his mean Distance will be found 3537446267659410; the Root as per Table, and so of all the rest, Viz.

These Numbers found by the above proportional Properties, and so nearly agreeing with the former, deduced from Observation, is a sufficient Proof of the great Truth of our present Theory of the Planets Motions.

The Planets being observed in different Parts of their Orbits to move faster and slower, and to be much farther distant from the Sun at one time than at another, are found by Calculation, and confirmed by the Laws of Gravity, to circumvolve in elliptical Curves. And,

Their Orbits have been determined nearly as follows:

	The Transverse Semi-diameter	The Conjugate	Excentricity
Of Mercury	38710	37881	7970
Of Venus	72333	72331	517
Of The Earth	100000	99985	1732
Of Mars	152369	151715	14100
Of Jupiter	520110	519506	25050
Of Saturn	953800	952230	54700

These Numbers being reduced to English Miles, by having given the Radius of the Orbis Magnus in Diameters of the Earth; which last is known, and the former easily found by Calculation; tho’ at present not quite so exact as we may hope for at the next Transit of Venus over the Sun, by reason of the great Difficulty in observing the true Parallax of very distant Bodies.

The various Distances of the Planets from the Sun, in round Numbers will come out as follows:

Of	In Perihelion	The Mean	In Aphelion	Excentricity
Mercury	25,280,000	32,000,000	38,720,000	6,720,000
Venus	58,587,000	59,000,000	59,413,000	413,000
The Earth	79,623,000	81,000,000	82,377,000	1,377,000
Mars	111,561,000	123,000,000	134,439,000	11,439,000
Jupiter	403,648,000	424,000,000	444,352,000	20,352,000
Saturn	734,265,000	777,000,000	819,735,000	42,735,000

The Diameter of {

• Mercury
• Venus
• The Earth
• Mars
• Jupiter
• Saturn

} Is found to be {

• 4,240
• 7,900
• 7,970
• 4,440
• 81,000
• 61,000

Miles.

Saturn is encompassed with two Rings, which together are like the Horizon of an artificial Globe; their Distance from Saturn is nearly 24,500 Miles, and both together 12,000 Miles broad. But more of this in its proper Place.

We come at these Magnitudes from the Solution of a right angled Triangle, having first given the apparent Diameters of the Planets, and secondly their Distance from us: Thus,

As Radius, or Sine of 90 Degrees,
Is to the Logarithm of the Planet’s Distance;
So is the Sine of half the Angle of Appearance,
To the true Semi-diameter of its Body.

From what is known above, Mr Whiston computes the superficial Areas of the Planets to be nearly, in round Numbers, as follows:

• Of The Sun
• Of The Saturn
• Of Jupiter
• Of Mars
• Of The Earth
• Of Venus
• Of Mercury

• 1,813,200,000,000
• 14,000,000,000
• 20,000,000,000
• 60,000,000
• 200,000,000
• 200,000,000
• 55,000,000

} Square Miles.

At the same time he computes their Solidities to be,

These Bodies are all represented in Proportion to one another upon the great Scheme; but, to know exactly how many times one contains another, cube any two of their Diameters, and divide the greater by the lesser. (See Euclid, B. 12. Prop. 18.)

Thus the Sun will be found to contain the Earth above 867568 times.

From the various Inequality of the planetary Motions, and their Distance from us, it is easy to conceive that their apparent Diameters can never be the same in all Positions; and, in all small and very remote Bodies, their visible Diameters nearly increase and decrease in the same Proportion as their Distances decrease or increase. But more mathematically: If the true Diameter of any Planet be given, and its Distance to any Part of its Orbit known; the Angle under which it will at any time be seen, may thus be found:

As the true Distance, or Vicinity of the Body,
Is to the Sine Radius, or 90 Degrees;
So is the real Semi-diameter,
To the Sine of the apparent One.

In this Manner it may be found, that the apparent Disk of the Sun to

And in general, the Phænomena of these Planets from the Earth, are as follows:

The Stars. 1. \( \overset{\mathrm{2ds.}}{\frac{6}{0}}\) 2. \( \overset{\mathrm{2ds.}}{\frac{5}{0}}\) 3. \( \overset{\mathrm{2ds.}}{\frac{4}{0}}\) 4. \( \overset{\mathrm{2ds.}}{\frac{3}{0}}\) 5. \( \overset{\mathrm{2ds.}}{\frac{2}{0}}\) 6. \( \overset{\mathrm{2ds.}}{\frac{1}{0}}\)

N.B. The Diameter of Saturn’s Ring in Apogeon, is 44^2ds. 48^3ds. in Perigeon 55^2ds. 12^3ds. and at a mean Distance of 50^2ds. but rejecting all the scatter’d Light will be little more than 42^2ds.:

To know how much one Disk is larger than another, square each apparent Diameter, and divide the greater by the less. (See Euclid B. 12. Prop. 2.)

Thus the Sun to Mercury will be found to appear 6,\(\frac{3}{10}\) times bigger than to use at the Earth.

All opaque Bodies, exposed to the direct Light of any radient Object, cast Shadows behind them; and if the radient Body be equal to the opaque one, the Shadow will be cylindrical (as at A in the Center Scheme); if less, the Shadow will increase, as at B; and if greater, diminish at C. Thus the Planets, being in themselves dark masses of terraqueous Matter, and Reflecting only the solar Light, carry along with them, in their Orbits, vast Voids in the Space opposite the Sun, which, if the Sun were either equal to, or less than, the Planetary Bodies, would obscure every Object in that direction, not having native Light of their own as far as the Stars. But this has never yet been done; for Jupiter in Syzygia has never yet eclipsed Saturn, nor Venus the Earth; consequently the Sun must be greater than either of them, and their Shadows conical. The Extent of these Privations of Light to every Planet is found by this Canon,²

As the Difference of the Semidiameters of the Sun and Planet,
Is to the Planet’s Distance from the Sun’s Center;
So is the Semidiameter of the Sun,
To the true Distance of the Shadow’s Point from his Center.

Out of which subtracting the Planet’s Distance from the Sun, there will remain the Length of the Shaodw: Thus,

Of	In Perihelion Miles	Mean Distance Miles	In Aphelion Miles
Mercury	141,266	178,817	216,367
Venus	- - - -	617,266	- - - -
The Earth	840,476	855,021	869,558
Mars	652,986	719,941	786,896
Jupiter	- - - -	50,357,700	- - - -
Saturn	- - - -	67,516,935	- - - -

Venus, Jupiter, and Saturn having, proportionally the least Excentricity, I have omitted their greatest and least Shadows, as being of no great Consequence.

The Planets, tho’ all of the same original Matter, yet differ very much in their Solidity, Union of Parts, or Hardness of their Composition; as Earth from Stone, or Stone from Glass; and this condens’d Mass, or real Quantity of Matter, is in all Bodies proportional to their relative Gravities, i.e. to their Force of Attraction or gravitating Powers. And through all the Planets where the Ratio of this Virtue is in Effect known, the Quantity of Matter is thus determined.

The Quantity of Matter in the Sun, is to the Quantity of Matter in the Earth, in a Ratio compounded of the triplicate Ratio of Mercury or Venus’s Distance from the Sun, to the Moon’s Distance from the Earth, and the duplicate Ratio of the periodic Time of the Moon, to that of Mercury or Venus, &c.

Hence the Ratio of the Quantity of Matter in the three Primary Planets, who have Secondaries, to the Quantity of Matter in the sun, will be found to be as follows.

• In the Sun is 227500
• In Saturn 94
• In Jupiter 220
• And in the Earth 1

This being found, the Density of Planets are to one another; in a Ratio compounded of the direct Ratio of their Quantities of Matter, and the invers Ratio of their Magnitudes, that is to say,

The Density of the Sun, is to the Density of the Earth, in a Ratio compounded of the Ratio of the Quantity of Matter in the Sun, to the Quantity of Matter in the Earth, and the Ratio of the Magnitude of the Earth, to the Magnitude of the Sun.

Hence the Density of the Sun will be, as 25.5
To 15, the Density of Saturn,
To 19, in Jupiter,
And to 100, in the Earth.

And their accelerating Gravity, or the Weight of equal Bodies, upon the Surfaces of each of them; which is in a Ratio compounded of the direct Ratio of their Masses of Matter, and the inverse Ratio of the Squares of the Distances from each respective Center, will be thus.

A Body at the Sun, weighing 10000 Ounces, Pounds, &c.
That same body would weigh at³

It is easy to conceive from the Laws of Gravity, that every Planet must have peculiar Sphere of Attraction of its own, whereby all heavy Bodies in these circumambient Regions, have a natural Tendency to their common Center; as a Stone, projected in the Earth’s Atmosphere, falls to the Earth again; and that there is always one Point betwixt any two Bodies, where Gravity ceases, and where a third would be at rest. Thus there is ever one Place betwixt the Sun and Earth, &c. where neither has Power to act, consequently, a Body there suspended would rest self-balanc’d and free from falling either Way.

To find this Point of Equilibrium, between any two Planets, whose Distance assunder, and Quantity of Matter is known, this is the Theorem.

Let A and B be the two Bodies given, and let Quantity of Matter in A to be to that in B, as 10,000 to 100.

A

100,

E

D

C

10

B

Lemma 1. At equal Distances from different Bodies, Gravity is as the Quantity of Matter.

Hence in the Point E, equally distant from A and B, andy Body, weighing 10,000 towards A, will weigh but 100 to B.

Suppose the Semi-distance AE, or EB, then the √² 10000, = 100, and CB be the Root of this Equal 10.

Lemma 2. Gravity to all Bodies decreases, as the Square of the Distance increases; & vice versa. Hence the same Body C will weigh 10,000 to B, that lately in E weigh’d 10,000 to A. Hence, in these two Points, E and C; Gravity is equal to both A and B: And since a third Point D must be found common to both, where Gravity to each will cease, for CD put x.

And as, by Lemma 2d, BC² : BD² :: AE² : AD² also by Euclid 5. bc : bd :: ae : ad, and consequently 10 : 10 + x :: 100 : 190 − x. Hence 1000 + 100x = 1900 − 10x and x will be found = \(\frac{900}{110}\) = 8.18.

By this will be found, that the Radius of the Sphere of Attraction to

The Distances of the Planets from the Sun are so very immense, that were their projectile Forces to cease, according to Mr Whiston,

And their Velocities round the Sun, are so very violent and rapid, (tho’ not perceptible to us); that in the Space of one Hour,

1. According to Mr Whiston.
2. Theorm. Let the Planet’s Distance from the sun be d; the Sun’s Semediameter e, and that of the Planet b. Then by Euclid of similar Triangles \(e-b\) : \(d\) :: \(e\frac{de}{e-b}\) and \(\frac{de}{e-b}-d\) = Length of the Shddow.
3. For the Demonstration of all these Quantities, see Gregory’s Astron. B. III. Prop. 48, 49, &c.
4. In respect of the Sun: But here we may present a Quere, which will admit of some Dispute; for sine the Point of equal Attraction betwixt the Earth and the Sun, falls here considerably within the Moon’s Orbit, we should be inclined to believe with Mr N. Facio, that our present Knowledge of the Sun’s Distance and Magnitude is not a little defective, and that the solar System is not near so extensive as we imagine. (See the Theory of the Earth and Moon.)