Astronomy Principles and Practice Fourth Edition.pdf

440 Practical projects
Table 24.2. Observations of Saturn, August 2000–January 2001.
α
δ
Date h m s ◦ ′ ′′ λ
August 1 3 50 45 17 59 10 61·◦28
September 1 3 56 45 18 11 50 60·◦86
October 1 3 56 03 18 04 21 60·◦67
November 1 3 49 03 17 39 37 58·◦95
December 1 3 39 17 17 09 04 56·◦57
January 1 3 31 09 16 47 04 54·◦59
Now the observed shift in right ascension, α, will be made up of the parallactic shift, α p ,and
the orbital shift, α 0 . Thus,
α = α p + α 0
giving
α p = α − α 0 .
Care should be taken with regard to the algebra, since α p is essentially a negative quantity while
α 0 is positive.
Having found α p , equation (24.14) gives the Moon’s distance in Earth radii. If use is made of
the polar equation for the ellipse, namely
avaluefora can then be calculated.
r = a(1 − e2 )
1 + e cos ν
24.7 Planetary orbits
Positional data of the planets can be obtained by making regular observations over periods of weeks to
months as they execute their orbits. From the data, estimates of the planets’ distances can be made.
The same observations may also be made using a planetarium. Some machines provide sufficient
accuracy for reasonable quantitative results to be obtained. A planetarium provides a useful means
of concentrating into a few minutes a planet’s annual movements against the stellar background.
Differences between the inner and outer planets are quickly noted. All the terms such as elongation,
phase angle, direct and retrograde motion, conjunctions, quadrature, stationary points, etc, can be
demonstrated and appreciated in the course of an observing session.
24.7.1 The outer planets
The distances of the outer planets, Jupiter and Saturn, can be determined fairly easily by noting their
positions, say once per month, over the period of opposition. This may be done either by a planetarium
demonstration, by plotting the positions on a star map from direct observations or by obtaining the
celestial coordinates from the AA.
A scheme for an exercise with Saturn and a set of results is given in table 24.2.
From the values of right ascension and declination (α, δ) the corresponding value for the ecliptic
longitude, λ, may be calculated by using equation (8.10), namely
tan λ =
sin α cos ε + tan δ sin ε
. (24.19)
cos α