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Astronomy Explained Upon Sir Isaac Newton's Principles / And made easy to those who have not studied mathematics cover

Astronomy Explained Upon Sir Isaac Newton's Principles / And made easy to those who have not studied mathematics

Chapter 61: Sun’s mean Motion and Anomaly.
By James Ferguson
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Science - Physics

About This Book

Aimed at readers without advanced mathematics, the author presents Newtonian astronomy in clear, practical terms, describing the solar system’s arrangement and demonstrating the Copernican model. Chapters explain planetary motions and phases, refute older geocentric ideas, and explore gravity as the physical cause of orbital behavior. The text treats light, refraction, atmospheric effects, and methods for measuring distances, time, and longitude, and it analyzes tides, eclipses, and the apparent motions of stars from different vantage points. Practical aids include tables, catalogs of eclipses, and descriptions of instruments and orreries used to illustrate the concepts.

Table XI. The Sun’s Equation at the time of New and Full Moon.

Sun’s Anom. Subtract Sun’s Anom.
0 1 2 3 4 5
Signs Signs Signs Signs Signs Signs
° H. M. H. M. H. M. H. M. H. M. H. M. °
0 0 0 1 44 3 2 3 32 3 5 1 48 30
1 0 4 1 47 3 3 3 32 3 3 1 45 29
2 0 7 1 50 3 5 3 32 3 2 1 42 28
3 0 11 1 53 3 7 3 32 3 0 1 38 27
4 0 14 1 57 3 9 3 32 2 58 1 35 26
5 0 18 2 0 3 10 3 31 2 56 1 31 25
6 0 22 2 3 3 12 3 31 2 54 1 28 24
7 0 25 2 6 3 14 3 31 2 52 1 24 23
8 0 29 2 8 3 16 3 30 2 50 1 21 22
9 0 32 2 11 3 17 4 30 2 48 1 17 21
10 0 36 2 14 3 18 3 30 2 45 1 14 20
11 0 40 2 17 3 19 3 29 2 43 1 11 19
12 0 43 2 20 3 20 3 29 2 40 1 7 18
13 0 47 2 22 3 21 3 28 2 37 1 4 17
14 0 50 2 25 3 22 3 27 2 35 1 0 16
15 0 54 2 28 3 23 3 26 2 32 0 56 15
16 0 57 2 30 3 24 3 25 2 29 0 52 14
17 1 0 2 32 3 25 3 24 2 26 0 49 13
18 1 4 2 35 3 26 3 23 2 23 0 45 12
19 1 7 2 38 3 27 3 22 2 21 0 41 11
20 1 11 2 40 3 28 3 21 2 18 0 38 10
21 1 14 2 43 3 28 3 20 2 15 0 34 9
22 1 17 2 45 3 29 3 19 2 12 0 30 8
23 1 21 2 47 3 29 3 18 2 10 0 26 7
24 1 24 2 49 3 30 3 17 2 7 0 23 6
25 1 28 2 51 3 30 3 15 2 4 0 19 5
26 1 31 2 54 3 31 3 13 2 1 0 15 4
27 1 34 2 57 3 31 3 11 1 58 0 11 3
28 1 38 2 59 3 31 3 9 1 55 0 7 2
29 1 41 3 1 3 32 3 7 1 52 0 4 1
30 1 44 3 2 3 32 3 5 1 48 0 0 0
Sun’s Anom. 11 10 9 8 7 6 Sun’s Anom.
Signs Signs Signs Signs Signs Signs
Add

Table XII. Equation of the Sun’s mean Place.

Sun’s Anom. Subtract Sun’s Anom.
0 1 2 3 4 5
Signs Signs Signs Signs Signs Signs
° ° ʹ ° ʹ ° ʹ ° ʹ ° ʹ ° ʹ °
0 0 0 0 57 1 40 1 56 1 42 0 59 30
1 0 2 0 59 1 41 1 56 1 41 0 57 29
2 0 4 1 0 1 42 1 56 1 40 0 56 28
3 0 6 1 1 1 43 1 56 1 39 0 54 27
4 0 8 1 2 1 44 1 56 1 38 0 52 26
5 0 10 1 4 1 45 1 56 1 36 0 50 25
6 0 12 1 6 1 45 1 56 1 35 0 48 24
7 0 14 1 7 1 46 1 55 1 34 0 46 23
8 0 16 1 9 1 47 1 55 1 33 0 44 22
9 0 18 1 10 1 48 1 55 1 32 0 42 21
10 0 20 1 12 1 48 1 54 1 30 0 41 20
11 0 22 1 14 1 49 1 54 1 29 0 39 19
12 0 24 1 15 1 50 1 54 1 28 0 37 18
13 0 26 1 17 1 51 1 53 1 26 0 35 17
14 0 28 1 18 1 51 1 53 1 25 0 33 16
15 0 30 1 20 1 52 1 52 1 23 0 31 15
16 0 31 1 21 1 52 1 52 1 22 0 29 14
17 0 33 1 22 1 53 1 51 1 21 0 27 13
18 0 35 1 24 1 53 1 51 1 19 0 25 12
19 0 37 1 25 1 54 1 50 1 18 0 23 11
20 0 39 1 27 1 54 1 49 1 16 0 21 10
21 0 41 1 28 1 55 1 49 1 14 0 19 9
22 0 43 1 29 1 55 1 48 1 13 0 17 8
23 0 45 1 30 1 55 1 47 1 11 0 14 7
24 0 46 1 32 1 56 1 46 1 10 0 12 6
25 0 48 1 33 1 56 1 46 1 8 0 10 5
26 0 50 1 34 1 56 1 45 1 6 0 8 4
27 0 52 1 35 1 56 1 45 1 5 0 6 3
28 0 54 1 36 1 56 1 44 1 3 0 4 2
29 0 55 1 38 1 56 1 43 1 1 0 2 1
30 0 57 1 40 1 56 1 42 0 59 0 0 0
Sun’s Anom. 11 10 9 8 7 6 Sun’s Anom.
Signs Signs Signs Signs Signs Signs
Add

Table XIII. Equation of the Moon’s Nodes.

Sun’s Ano. Subtract Sun’s Ano.
0 1 2 3 4 5
S. S. S. S. S. S.
° ʹ ʹ ʹ ʹ ʹ ʹ °
0 0 5 8 10 8 5 30
1 0 5 8 10 8 5 29
2 0 5 8 10 8 5 28
3 0 5 8 10 8 4 27
4 1 5 8 10 8 4 26
5 1 5 8 10 8 4 25
6 1 6 9 10 8 4 24
7 1 6 9 9 8 4 23
8 1 6 9 9 8 4 22
9 1 6 9 9 7 3 21
10 2 6 9 9 7 3 20
11 2 6 9 9 7 3 19
12 2 6 9 9 7 3 18
13 2 6 9 9 7 3 17
14 2 7 9 9 7 3 16
15 2 7 9 9 7 3 15
16 2 7 9 9 7 2 14
17 3 7 9 9 7 2 13
18 3 7 9 9 6 2 12
19 3 7 9 9 6 2 11
20 3 7 9 9 6 2 10
21 3 7 9 9 6 2 9
22 4 7 9 9 6 1 8
23 4 8 9 9 6 1 7
24 4 8 9 9 6 1 6
25 4 8 9 9 6 1 5
26 4 8 10 9 5 1 4
27 4 8 10 9 5 1 3
28 4 8 10 8 5 0 2
29 5 8 10 8 5 0 1
30 5 8 10 8 5 0 0
Sun’s Ano. 11 10 9 8 7 6 Sun’s Ano.
S. S. S. S. S. S.
Add

The above titles, Add and Subtract, are right when the Equation is applied to the Sun’s mean distance from the Node; but when it is applied to the mean place of the Node, the titles must be changed.

Tab. XIV. The Moon’s latitude in Eclipses.

Argument of Latit.
Moon fr. the Node. Sig. 0 N. A.
Sig. 6 S. D.
° ° ʹ ʺ °
0 0 0 0 30
1 0 5 15 29
2 0 10 30 28
3 0 15 44 27
4 0 20 59 26
5 0 26 13 25
6 0 31 26 24
7 0 36 39 23
8 0 41 51 22
9 0 47 2 21
10 0 52 13 20
11 0 57 23 19
12 1 2 31 18
13 1 7 38 17
14 1 12 44 16
15 1 17 49 15
16 1 22 52 14
17 1 27 53 13
18 1 32 54 12
N. D. Sig. 5 Moon fr. the Node.
S. A. Sig. 11
Argument of Latit.

This Table extends no farther than the limits of Eclipses. N. A. signifies North Ascending Lat. S. A. South Ascending; N. D. North Descending; and S. D. South Descending.

Table XV. The Moons Horizontal Parallax; the Semidiameters and true Horary motions of the Sun and Moon.

Anomaly of the Sun and Moon. Moon’s Horizontal Parallax. Sun’s Semidiameter. Moon’s Semidiamet. Moon’s horary Mot. Sun’s horary Mot. Anomaly of the Sun and Moon.
s ° ʹ ʺ ʹ ʺ ʹ ʺ ʹ ʺ ʹ ʺ s °
0 0 54 59 15 50 14 54 30 10 2 23 12 0
  6 54 59 15 50 14 55 30 12 2 23   24
  12 55 0 15 50 14 56 30 15 2 23   18
  18 55 4 15 51 14 57 30 18 2 23   12
  24 55 11 15 51 14 58 30 26 2 23   6
1 0 55 20 15 52 14 59 30 34 2 23 11 0
  6 55 30 15 53 15 1 30 44 2 24   24
  12 55 40 13 54 15 4 30 55 2 24   18
  18 55 51 15 55 15 8 31 9 2 24   12
  24 56 0 15 56 15 12 31 23 2 25   6
2 0 56 11 15 58 15 17 31 40 2 25 10 0
  6 56 24 15 59 15 22 31 58 2 26   24
  12 56 41 16 1 15 26 32 17 2 27   18
  18 57 12 16 2 15 30 32 39 2 27   12
  24 57 30 16 4 15 36 33 11 2 28   6
3 0 57 49 16 6 15 41 33 23 2 28 9 0
  6 58 10 16 8 15 46 33 47 2 29   24
  12 58 31 16 9 15 52 34 11 2 29   18
  18 58 52 16 11 15 58 34 34 2 29   12
  24 59 11 16 13 16 3 34 58 2 30   6
4 0 59 30 16 14 16 9 35 22 2 30 8 0
  6 59 52 16 15 16 14 35 45 2 31   24
  12 60 9 16 17 16 19 36 0 2 31   18
  18 60 26 16 19 16 24 36 20 2 32   12
  24 60 40 16 20 16 28 36 40 2 32   6
5 0 60 54 16 21 16 31 37 0 2 32 7 0
  6 61 4 16 21 16 34 37 10 2 33   24
  12 61 11 16 22 16 37 37 19 2 33   18
  18 61 16 16 22 16 38 37 28 2 33   12
  24 61 20 16 23 16 39 37 36 2 33   6
6 0 61 24 16 23 16 39 37 40 2 33 6 0

The gradual increase or decrease of the above numbers being so small, it is sufficient to have them to every sixth degree; the proportions for the intermediate degrees being easily made by sight.

Table XVI. The Sun’s mean Motion and Anomaly.

  Years of Christ beginning Sun’s mean Longitude from Aries. Sun’s mean Anomaly.
s ° ʹ ʺ s ° ʹ
O.S. 1 9 7 53 10 6 29 54
1301 9 17 42 30 6 16 58
1401 9 18 27 50 6 15 59
1501 9 19 13 10 6 14 59
1601 9 19 58 30 6 13 59
1701 9 20 43 50 6 12 59
N.S. 1753 9 10 16 52 6 1 38
1801 9 9 39 39 6 0 10
Old Style to the beginning of A. D. 1753; then New Style Years of Christ compleat Sun’s mean Motion. Sun’s mean Anomaly.
s ° ʹ ʺ s ° ʹ
  1 11 29 45 40 11 29 45
  2 11 29 31 20 11 29 29
  3 11 29 17 0 11 29 14
  4 0 0 1 49 11 29 58
  5 11 29 47 29 11 29 42
  6 11 29 33 9 11 29 27
  7 11 29 18 49 11 29 11
  8 0 0 3 38 11 29 55
  9 11 29 49 18 11 29 40
  10 11 29 34 58 11 29 24
  11 11 29 20 38 11 29 9
  12 0 0 5 26 11 29 53
  13 11 29 51 7 11 29 37
  14 11 29 36 47 11 29 22
  15 11 29 22 27 11 29 7
  16 0 0 7 15 11 29 50
  17 11 29 52 55 11 29 35
  18 11 29 38 35 11 29 20
  19 11 29 24 16 11 29 4
  20 0 0 9 4 11 29 48
  40 0 0 18 8 11 29 36
  60 0 0 27 12 11 29 24
  80 0 0 36 16 11 29 12
  100 0 0 45 20 11 29 0
  200 0 1 30 40 11 28 1
  300 0 2 16 0 11 27 1
  400 0 3 1 20 11 26 1
  500 0 3 46 40 11 25 2
  600 0 4 32 0 11 24 2
  700 0 5 17 20 11 23 2
  800 0 6 2 40 11 22 3
  900 0 6 48 0 11 21 3
  1000 0 7 33 20 11 20 3
  2000 0 15 6 40 11 10 7
  3000 0 22 40 0 11 0 10
  4000 1 0 13 20 10 20 13
  5000 1 7 46 40 10 10 16
  6000 1 15 20 0 10 0 19
  Months Sun’s mean Motion. Sun’s mean Anomaly.
  s ° ʹ ʺ s ° ʹ
  Jan. 0 0 0 0 0 0 0
  Feb. 1 0 33 18 1 0 33
  Mar. 1 28 9 11 1 28 9
  Apr. 2 28 42 30 2 28 42
  May. 3 28 16 40 3 28 17
  June 4 28 49 58 4 28 50
  July 5 28 24 8 5 28 24
  Aug. 6 28 57 26 6 28 57
  Sep. 7 29 30 44 7 29 30
  Oct. 8 29 4 54 8 29 4
  Nov. 9 29 38 12 9 29 37
  Dec. 10 29 12 22 10 29 11
Days. Sun’s mean Motion and Anomaly.
s ° ʹ ʺ
1 0 0 59 8
2 0 1 58 17
3 0 2 57 25
4 0 3 56 33
5 0 4 55 42
6 0 5 54 50
7 0 5 53 58
8 0 7 53 7
9 0 8 52 15
10 0 9 51 23
11 0 10 50 32
12 0 11 49 40
13 0 12 48 48
14 0 13 47 57
15 0 14 47 5
16 0 15 46 13
17 0 16 45 22
18 0 17 44 30
19 0 18 43 38
20 0 19 42 47
21 0 20 41 55
22 0 21 41 3
23 0 22 40 12
24 0 23 39 20
25 0 24 38 28
26 0 25 37 37
27 0 26 36 45
28 0 27 35 53
29 0 28 35 2
30 0 29 34 10
31 1 0 33 18

In Leap-years, after February, add one Day and one Day’s motion.

Sun’s mean Motion and Anomaly.