Physics 134
Quiz 1 Solutions
1/24/12
Imagine that the Earth suddenly reversed the direction in which it spins, rotating from
East to West at the same rate at which it now spins West to East. Answer the following
questions on how Astronomy would change:
1. The apparent rotation of the celestial sphere would
(a) Remain unchanged as it is now
(b) Reverse direction but maintain same rate of rotation
(c) Reverse direction and speed up slightly
(d) Maintain same direction as now but speed up slightly
The apparent rotation of the celestial sphere is due to Earth’s spin. If Earth reversed
the direction in which it spins, the apparent rotation of the celestial sphere would
also be reversed. Stars would rise in the West and set in the East. Its rate would be
unchanged, since we postulate that rate of Earth’s spin would not change. Thus the
length of the sidereal day would be unchanged.
Answer is b.
2. The length of a mean solar day would
(a) Remain unchanged
(b) Be longer by 4min than it is now
(c) Be shorter by 8min than it is now
(d) Be longer by 12min than it is now
The difference between mean solar day and sidereal day is due to Earth’s orbital
motion. Currently, since spin and orbit are in the same direction, solar day is longer
by about 4min than sidereal day. With spin and orbit in opposite directions, solar
day would be shorter than sidereal day by about four minutes. That would make it
about 8min shorter than the current solar day.
The answer is c.
3. Seasonal climate changes would
(a) Remain unchanged
(b) Become more extreme
(c) Become less extreme
(d) Reverse position, so that winter stars would be those now visible in summer, etc.
Seasonal climate changes are due to the tilt of Earth’s axis relative to its orbital
motion. Neither of these properties changes in the scenario described so seasonal
climate changes would not be affected at all.
The answer is a.
4. The star Castor in Gemini lies 52 light-years from Earth. Appropriately, Castor is
a binary star. As seen from Earth, the two stars comprising the binary system are
separated by 3.9 arc-seconds in the sky. What is the distance between the two stars,
in light-years?
This is an opportunity to use the small-angle formula. The members of the Cator
binary system are separated by α = 3.9” in the sky, and lie at a distance D = 52 ly
from Earth, so the distance between them is
d=
3.0
α
D=
× 52 ly = 7.56 × 10−4 ly .
206265”
2062625
5. Castor lies at R.A. 7h 35m , Declination +31◦ 53m . The other twin (also a binary, of
course), Pollux, is located at R.A. 7h 45m , Declination +28◦ 02m .
(a) Which of the two stars will transit (cross the local meridian, reaching its highest
point in the sky) earlier tonight? By how much?
A star transits when sidereal time is equal to its RA. With its earlier RA, Castor
will transit earlier, by 10 min.
(b) If we look for each star at the moment it transits, which will be higher in the
sky?
The distance of a star from our Zenith at transit is the difference between the
star’s Declination and our latitude. Castor, with Declination 31◦ 53m will come
within about 4◦ of our Zenith, while Pollux, with Declination 28◦ 2m will be 8◦
from the Zenith at its highest point. Yet again, the answer is Castor. Ah, sibling
rivalry..
We are located at latitude 36◦ N and longitude 79◦ W .