Astronomia Britannica exhibiting the doctrine of the sphere, and theory of the planets decimally by trigonometry, and by tables : fitted for the meridian of London ... / by John Newton ...

CHAP. 7. To calculate the Suns true place and distance from the Earth.

HAving composed tables of the Suns middle motions, according to the directions of the last Chapter, his true place in the Zodi∣ack, and distance from the earth may thus be found.

1 Write out the Epocha next before the given time and seve∣rally under that, set the motions belonging to the years, moneths, and days compleat, and to the houres and scruples current, every one under his like (onely remember that in the Bissextile year, after the end of Febru∣ary,

the dayes must be increased by an Unite) then adding them alto∣gether, the summe shall be the Suns meane motion for the time given.

Example.

Let the time given be May the 12th. houre 11 parts 15 before noon at London in the Bissextile yeare 1656, and the Suns place to be soughts The numbers are thus,

		Suns Longitude	Suns Apogeon
		Deg.	parts	Deg.	parts
The Epocha	1640	291.	24777	96.	22265
Years comp.	15	359.	37294		23686
April	118.	27760		519
Dayes	12	011.	82776		52
Houres	23		94458
Scruples	15		616
Suns Mean Longitude	421.	87681	96.	46522

2 Subtract the Apogaeum from the Mean Longitude, there rests the mean Anomaly.

Example.

The Suns mean longitude

421. 67681

Apogaeum substract

96. 46522

Rest mean Anomaly

325. 21459

Whose complement to a Circle

34. 78541

is the angle A M E in the Ellipsis.

And the complement of A M E to a semicircle is the angle E M H 145. 21459.

The side M E	200000
The side M H	3568
The summe	203568 co. ar.	4. 6912905
Differ.	196432	5. 2932122
Tang. ½ summe of the opposite angles	17. 39270	9. 4958787
	17. 39270
Tang. ½ Differ	16. 81799	9. 4803814
Differ	57471 is the angle M E H.
Difference doubled	1. 14942 is the angle M B H

3 The mean Anomaly being above 180 deg. the Aequation found must be added to the sunsmeane longitude, so have you the Suns true place.

[illustration]

Example.

The Suns meane longitude

421. 67681

Aequation adde

1 14942

The Suns true place

422. 82623

or 2 Signes 2 degrees 82623 parts of a degree

 

Lastly, to find his distance from the earth, I say,

As the sine of M B H	1. 14942 co▪ ar.	1. 6977118
Is to the side M H	3568	3. 5524249
So is the sine of B M H	34. 78541	9. 7562590
To the side B H		5. 0063957
or distance required	101483

Thus we have found the Suns place by calculation, we will now shew how to reduce the Suns mean longitude to his true, by the Table of Ae∣quations of the Suns excentrick.

The Suns Anomaly in this example is

325. 21459

The Aequation of 325 is

1. 15566

326

1. 12648

Difference is

02918

Now then I say if one deg. co. ar.

5.

Give 2918

3. 4650853

What shall 21459

4. 3316095

The answer is 6••6

2. 7966948

Aequation of 325 deg.

1. 15566

Part proportional subt.

626

Aequation equated

1. 14940

The Snns mean longitude

61. 67681

Aequation adde

1. 14940

Suns true place

62. 82621

And in like manner the Logarithme of the Suns distance from the Earth will be found to be 5. 0063633, which being more necessary then the di∣stance it self, in the calculation of the places of the other planets, we have as most convenient placed in the table.