Astronomy Principles and Practice Fourth Edition.pdf

Problems—Chapter 12 165
with an observed angular velocity ω 2 . If the ratio ω 1 /ω 2 is 10·25, calculate the approximate height of the
spacecraft above the Moon’s surface (in lunar radii) assuming (i) the spacecraft’s orbital motion is retrograde
to the Moon’s direction of rotation, (ii) the spacecraft’s orbital period to be very short compared with the
Moon’s period of rotation.
13. The planet Jupiter, orbital period 11·86 years, was in opposition on 1968, February 10th. When was it next
in conjunction Calculate when it was in opposition in 1969. In what year after 1969 is there no opposition
How frequent are such years
14. At opposition a superior planet, heliocentric distance b AU, has a geocentric angular velocity against the
stars of −ω 1 degrees per day. At the next quadrature, the measured value is +ω 2 degrees per day. Show that
ω 2
ω 1
= 1 b
( b − 1
b 1/2 − 1
15. Neglecting the sizes of Venus and the Earth, show that a transit of Venus across the Sun’s disc lasts about
8 hours. Take the synodic period of Venus to be 584 days, its orbital radius as 0·723 AU and the Sun’s
angular diameter to be 32 ′ .
)
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