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. 16. Of the Motion of Venus.

HAving done with the three superiour Planets, Saturn, Iupiter and Mars, we come to the two inferiour, Venus and Mer∣cury, the investigation of whose places is much after the same manner with the former, the difference is in the second inequali∣ty, occasioned by their motion under the earth, the Orbs of the other Pla∣nets being above it; that this difference may be the better discerned, we have added an example in each for the time before given.

The meane motions of Venus.

An. Christ.	Longit. ♀	Aphel. ♀	Node ♀
Yeares 1500	333. 11667	303. 97639	073. 28944
80	15. 48472	1. 12694	. 67028
6	270. 36028	. 08444	. 05028
Iuly	339. 65833	. 00806	. 00500
D 16	25. 63472	. 00062	. 00039
H 18	1. 20194
P 4564	. 03048
Meane Mot.	265. 48714	305. 19645	074. 01537
Aphel. Subt.	305. 19645	Rest Anom.	320. 29069

The Semidiameter of the orbe of Venus, in such parts of which the Earths orbe is 100. 000, by the computation of Bullialdus is 72398, her Eccentricity 575. The parts of her greatest inclination 4270. And the an∣gle it selfe 3. 38111. In the triangle therefore of the following Diagram M E H, we have three things given.

1. The halfe sum of the angles M E H and M H E 19. 85465, viz. the halfe complement of the meane Anomaly to a circle.

2. The side M E	144796
3. The side M H.	1150
Summe	145946 co. ar.	4. 8358079
Difference	143646	5. 1572934
Tang. halfe sum.	19. 85465	9. 5576273
Tangent halfe difference	19. 56560	9. 55072••6
Difference	. 28905 Angle M E H.
Differ. doubled	. 57810 Angle M B H.

or the Equation to be added to the mean longitude, because the Anomaly is more then a semicircle.

[illustration]

The meane Longitude of Venus

265. 48714

Equation adde

. 57810

The eccentrick place of Venus

266. 06524

Node subtract

74. 01537

Argument of latitude K L

192. 04987

To finde the distance of Venus from the Sun.

As the sine of M B H	0. 57810 co. ar.	1. 9961373
To the side M H	1150	3. 0606978
So the sine of H M B	39. 70931	9. 8054279
To the side B H	72822	4. 8622630

To finde the Reduction.

As the Radius
To the Cosine of the great inclina. X K L	3. 38111	9. 999••433▪
So tangent of K L	12. 04987	9. 329••295
To tangent of X K	12. 02950	9. 3285728
Difference	. 02037	Reduction.

Because the Argument of Latitude is more then 180, the Reduction must be subtracted from the eccentrick place.

The eccentrick place of Venus

266. 06524

Reduction subtract

. 02037

Eccentrick reduced

266. 04487

To finde the present inclination.

As Radius
To the greatest inclinat. E B.	4270	3. 6304••78
So sine of K L	12. 04987	9. 3196533
To the inclinat. X L	891	2. 9500811

Which are the parts of inclination agreeing to the common Radius 72398, but the distance of Venus from the Sun, 72822 being put for Radi∣us, the inclination will be 896.

As the common Radius D L	72398 co. ar.	5. 1402735
To Venus distance B H or A L	72822	4. 8622630
So is X L	891	2. 9508115
To X L	896	2. 9526176

To finde the distance corrected by Curtation.

As A L	7••822 co. ar.	5. 1377370
To Radius, so is X L	896	2. 9526176
To the sine of L A X	0. 70550	8. 0903546
As Radius
To A L	72822	4. 8622630
So Cosine of L A X	07055	9. 9999671
To A X	72816	4. 8622301

To finde the second inequality of Venus.

We must have given, 1. The angle N A S which is to be found by sub∣ducting the Suns place from the eccentrick of Venus reduced, or this from it so that less then 6 signes may remain, this remainer is the Anomaly of the orbe and the complement is the angle N A S, or the halfe is the halfe sum of the opposite angle.

[illustration]

Example.

The eccentrick of Venus reduced

266. 04487

The Suns true place

154. 07347

Anomaly of the orbe

111. 97140

Complement is N A S

68. 02860

Halfe Anomaly

55. 98570

These given with the sides N A and S A the Analogies are.

As the greater side S A	100895 co. ar.	4. 9961293
Is to Radius		10. 0000000
So is the lesser side N A	72816	4. 8622300
To the tangent of	35. 81815	9. 8583593
Adde	45.
As Radius
To cotangent	80. 81815	9. 2085475
So tang. halfe sum	55. 98570	10. 1707787
To tang. halfe diff.	13. 46926	9. 3793262
Summe	69. 45496 Angle A N S
Difference	42. 51644 Angle A S N

In the superiour Planets, Saturne, Iupiter, and Mars, the summe of these angles is the elongation, but in the inferiour Venus and Mercury there difference is the Elongation sought, and in our Example is to be ad∣ded to the Suns place, because the Suns place was subtracted from the Eccen∣trick of Venus reduced.

[illustration]

Suns true place

154. 07347

Elongation A S N add

42. 51644

True place of Venus

196. 58991

To finde the distance of Venus from the Earth.

As the sine of A N S	69. 45496 co. ar.	0. 0285403
To the side A S	100895	5. 0038707
So sine of N A S	68. 02860	9. 9672296
To the side S N	99917	4. 9996406

To finde the latitude of Venus from the Earth.

As the side S X	9991. 7 co. ar.	5. 0003594
Is to Radius		10. 0000000
So is X L	896	2. 9526176
To the tangent of X S L	0. 51417	7. 9529770
which is the South latitude of Venus.