Download Homework PHY121 (Astronomy

Homework PHY121 (Astronomy - Physics)
Chapter 2: The Sky
Due 09/12/2003
RQ 2-3
Q: What characteristic do stars in a constellation or asterism share?
A:
Stars in a constellation or an asterism appear to be in about the same direction as seen from Earth.
They are part of a grouping of stars on the celestial sphere which has a shape which suggested a
particular object, animal or person to the people in ancient cultures. Most stars in such groupings,
however, only seem to be related to each other. In reality, they have very different distances to us.
If one would look at a given constellation, say Cassiopeia, which forms a big “W” on our sky,
from a distant planet which is orbiting for example γ Pers., Cassiopeia might be spread over a vast
part of that sky. It certainly wouldn’t appear as a “W” on that planet’s sky.
RQ 2-7
Q: What does the word apparent mean in apparent visual magnitude?
A:
The word apparent in apparent visual magnitude means that it is the magnitude of the star as it
appears to us when viewing the star from Earth. Apparent visual magnitude does not take into
account the effect of the star’s distance from Earth and of its color (temperature) on its brightness
as it appears to our eyes as we observe the star on our sky.
RQ 2-10
Q: If Earth did not rotate, could we define the celestial poles and celestial equator?
A:
When we say, “if the Earth did not rotate”, we mean that relative to space (i.e. to the rest of the
Universe) the Earth would not rotate. In that case, the sky would stand still. We would always see
the same stars on our sky. The only changes on our sky would come from the moving planets, the
Moon and the Sun.
Since our (real) equatorial system is defined by Earth’s rotation and by the apparent motions it
incurs on the stars, the “equatorial coordinate system” for our hypothetical, still standing Earth
would be quite different. Our (real) celestial poles are defined in such a way, that they are the only
two points on the sky which stand still during time. All stars seem to move along circles centered
on either of these two poles. The celestial equator lies in the plane which is perpendicular to a line
drawn from one pole to the other.
On a hypothetical non-rotating Earth, we would not be able to define a “pole” or “equator” in the
same way as we do on (the real and rotating) Earth.
Humans on a hypothetical, non-rotating Earth would probably choose the next obvious, periodic
change in the sky to define a coordinate system. Since the moon rotates every 29 days around
Earth, the plane in which the moon moves would probably define Earth’s equator. Another possible equator could be defined by the plane, in which all planets of the solar system move (the ecliptic). The sun would slowly move along this “equator” on the sky. One “day” on this Earth would
be as long as our year.
Problem 2-2
If two stars differ by 8.6 magnitudes, what is their intensity ratio?
Solution:
Use By the Numbers 2-1: It is
I
(mB – m A)
-----A = ( 2.512 )
IB
In our case, the stars differ by 8.6 magnitudes, therefore: m B – m A = 8.6 and we can calculate
their intensity ratio
I
( 8.6 )
= 2755
-----A = ( 2.512 )
IB
The intensity ratio of the two stars is ~2800.
Problem 2-3
Star A has a magnitude of 2.5; Star B, 5.5; and Star C, 9.5. Which is brightest? Which are visible
to the unaided eye? Which pair of stars has an intensity ratio of 16?
Solution:
The brightest of the 3 stars is star A, then comes star B and finally star C which is the dimmest of
the 3 stars. Our unaided eye can only see stars with magnitude ~6 or smaller (=brighter) and therefore we could only see the stars A and B without any optical instrument.
To find out, which pair of stars has an intensity ratio of 16, use By the Numbers 2-1: It is
I1
m 2 – m 1 = 2.5 log  ----- = 2.5 log ( 16 ) = 3
 I 2
Only for the stars B and A, the difference of the magnitudes is 3. Star A and B are the pair of stars
with an intensity ratio of 16.
Problem 2-5
If you are at a latitude of 35 degrees north of Earth’s equator, what is the angular distance from the
northern horizon up to the north celestial pole? from the southern horizon down to the south celestial pole?
Solution:
If you are at a latitude of 35 degrees north of Earth’s equator, the situation is as follows:
no
rth
Zenith
ce
N
les
tia
lp
ole
35o
North
Horizon
South
35o
so
uth
ce
les
tia
S
lp
ole
The angular distance from the northern horizon up to the north celestial pole is 35 degrees. The
distance from the southern horizon down to the south celestial pole is the same: 35 degrees. The
distance from the northern horizon up to the north celestial pole is always equal to the latitude at
which the observer stands.