ASTRONOMY.
277
nets: and is therefore called a mean conjunction : but becausean interior planet and the Earth are really carried in elliptic orbits,in which then motions are sometimes swifter and sometimes slower,the true conjunctions may happen some days either sooner or laterthan what these rules will give. The time of the true conjunctionis to be computed from that of the mean con junction in the follow-ing manner: Find by astronomical tables the places of the planetand the Earth in the ecliptic, from which we shall have the dis-tance of the two as seen from the Sun ; compute also for the sametime the angular motions of these two planets for any given time,supp ise six hours; the difference of these two motions will givethe access of the planet to the Earth , or its recess from it in sixhours. As this difference is to the arc between the places of theinferior planet and Earth at the time of a mean conjunction, sois six hours to'the time between the mean conjunction and the true.This time added to, or subtracted from, the time of the meanconjunction, according as the planet is in antecedence or con-sequence from the Earth , shews the time of their true conjunc-tion.
Example, Required the mean and true time of the true su-
perior conjunction of Venus to happen in May, 1813, according toj De Ea Lande’s Tables in the Third Edition of his Astronomy.
; We must begin by determining the mean places of the Sun and! Venus for the beginning of May, as follows: To the Epoch of; the Sun ’s mean longitude for 1813, 9S. 9° 45' 12'',1, add his| mean motion for May, 3S. 29° 15' 48"; the sum (omitting 12 signs)IS. 9° T 0", 1 is the Sun ’s mean longitude for the mean noon of! May 1. Also, 6S. 12° 14' 52", the epoch of the mean longitude ofj \ enus for 1813, being added to 6S. 13° 51' 45", her mean motion| for May 1, gives OS. 26° 6' 37" for her mean place at the begin-j ning of the month. The mean place of the planet being sub-; traded from that of the Sun , because she has not yet arrived at| her superior conjunction, gives 12° 54' 23", 1, the distance she isj from an opposition to the Earth, as seen from the Sun . And 36'59",477739, the relative diurnal motion of © and 9 , is to 1 day',as 12° 54'23", 1 is to 20 days, 22h. 25m. 19", 12, which beingadded to May 1, gives May 22, at 25m. 19", 12 past ten, in theforenoon, for the mean time of the mean superior conjunction ofVenus . In order to reduce the mean to the true conjunction,the Sun’s true place as well as that of Venus , must be ascertainedat tl>e time of the mean superior conjunction, as below:
Calculation of Q's true place an May 22, at 10/(. 25m. 19", 12, morning, Parisian time, or at lO/i. 15m. 59", 12, mean time at Greentcieh.
Epoch of Q’s mean long. 1813-..
( May 21.
) 22 hours.
h 25 minutes.
V 19,12 seconds....
His motion for
0’s mean place at proposed time...Elliptic equation of ©’s orbit.
O.
Equation arising from < If. .
t 2 .
First equation of $ .
Secondequation of $ .
Nutation Equation.
Secular Equation.
O’s true place.
©’s mean place.
0’s Apcgee. j j)
U
2
$
S
Nut.
s> 0 ' "
9 9 45 12,1
4 18 58 34,6
54 12,6
1 1,60,8
s. 0 ' "
3 9 42 31
0 24
937
775
31
453
354
2
257
241
2
720
181
967
24
606
21
1 29 39 1,7
+ 1 13 7,3
- 6,0
— 8,40,0
+ 3,3
0,2
— 12,0
1,5'
3 9 42 551 29 39 1,7
743
809
500
901
991
627
t
10 19 56 6,7
©’s mean Anomaly.
The 0’s mean Anomaly gives 14' 24",36 for his motion insix hours.
2 0 51 44,2
Calculation of the true Heliocentric Place of Venus at the Time of her mean superior Conjunction in order to determine her real
Distance from an Opposition to the Earth, as seen from the Sun .
Mean Long. 9
Aphelion of 9
Long, of 9’sfi
s. 0
4 25 9 1
1 17 5 51
7 15 54 21
1 28 7
1 40
1,3
s. 0 ' "
10 8 36 12
0 10 32
19
s. 0 ' "
2 14 52 8
0 6 43
12
1 29 39 1,3
— 44 21,3
10 8 47 3
1 29 39 1,3
2 14 59 3
1 28 54 40
1 28 54 40,0+ 1 36
3 20 . 51 58,3
11 13 55 37
V
9’s mean Anom.
-y~—- ^ |
$ dist. from £X (
!
_1
1 28 56 16
Epoch of J for 1800.
Her Motion in 13 Years.
Do. - for May 21.
- 22 Hours.
- 25 Minutes..
- 19", 12......
9’s mean Long, at proposed TimeEquation of Orbit of 9.
9’s place in her Orbit..
VOL. 1.—NO. 18.
4 B
Calculation