Observational
Astronomy
1911.231:
HW #3
Due
Thu 2/9
1.
Phases of the Moon
New Moon: Near
side completely dark.
Waxing Crescent: Western
part of near side lit between 0% and 50% by direct sunlight.
First Quarter: Western
part of near side lit 50% by direct sunlight.
Waxing Gibbous: Western
part of near side lit between 50% and 100% by direct sunlight.
Full Moon: Near
side completely lit by direct sunlight.
Waning Gibbous: Eastern
part of near side lit between 50% and 100% by direct sunlight.
Last Quarter: Eastern
part of near side lit 50% by direct sunlight.
Waning Crescent: Eastern
part of near side lit between 0% and 50% by direct sunlight.
As the Moon orbits the Earth, the angle between the Sun and Moon as measured
from the Earth changes. As the angle changes,
the directly lit portion of the Moon rotates by the same angle. The amount of the lit portion that is visible
from Earth changes because of this.
(A drawing would explain this even better)
2.
View from
the Moon.
a.
A New Earth. It would be
daylight.
b.
No because the Moon has a rotation that is synchronized with its
orbit around the Earth.
c.
During a solar eclipses on Earth, a
Mooninite would observe a shadow from the Moon
covering a small part of the Earth.
During a lunar eclipse, a Mooninite would observe
the Earth completely covering the Sun and a faint red glow from the atmosphere
of the Earth.
3.
Definition
of a Day.
A solar day is determined by the length of time between meridian crossings of the Sun, while the sidereal day is determined by the motion of the stars. The mean time between meridian crossings of the Sun is 24 hours, and the sidereal day is 23 hours 56 minutes. The difference is a result of the motion of the Sun against the background stars of about 1 degree per day.
4.
Definition
of a Month.
A synodic
month is the period of time between new moons (i.e., the time for the phase
cycle to repeat, 29.5 days). The
sidereal month is the time it takes the Moon to orbit around the Earth as
measured against the background stars (27.3 days). The difference of 2.2 days is due to the fact
that as the Earth orbits the Sun, the Sun moves about 27 degrees against the
background stars.
5.
Length of
the Year.
The tropical year is the time
between vernal equinoxes, but the sidereal year is the time it takes the Earth
to orbit once relative to the background stars.
The Earths precession causes the celestial equator and the equinoxes to
move along the ecliptic.
6.
Telling
Time.
Apparent solar time is equal to the actual
hour angle of the Sun + 12 hours.
The mean solar time is the average hour angle of the Sun + 12 hours, where 12
noon is based on the average time between meridian crossings occurring every 24
hours.
Universal Time (UT) is the mean
solar time at a longitude of 0 degrees (Greenwich England)
Standard time is the solar time
based on your time zone (typically differs from UT by and integer number of
hours)
Daylight savings time is one hour
ahead of your standard time and is used between April and October in this
country.
7.
l
= -25 degrees (south)
h = 90 - | delta - l |
At Equinoxes, delta = 0
h = 90 - | 0 + 25 | degrees = 90 25 degrees =
65 degrees
At Summer Solstice, delta = +23.5 degrees
h = 90 - | 23.5 + 25 | degrees = 90 48.5
degrees = 41.5 degrees
At Winter Solstice, delta = -23.5 degrees
h =
90 - | -23.5 + 25 | degrees = 90 1.5 degrees = 88.5 degrees
8.
d = +38.8 degrees, h = 75
degrees to the south.
h = 90 - | delta - l |
75 = 90 - | 38.8 l |
| 38.8 l | = 15
38.8 l = 15 or 38.8
l = -15
l = 38.8 15 = 23.8 or l = 38.8 + 15 = 53.8
Because meridian crossing is to the south, choose the more northern latitude:
l = 53.8 degrees (north)
9.
Lost at Sea I.
·
Sun: alpha = 0 hours, delta = 0°, EqT =
-7 min (from figure in lecture slide)
·
h = 75° in the south, ast = 12 hours
·
UT = 22 hours
a.
What is your latitude?
d = +0 degrees, h = 75
degrees to the south
h = 90 - | delta - l |
75 = 90 - | 0 l |
|-l| = 15 l = 15 degrees (north) or l = -15 degrees (south)
Latitude is 15 degrees north (southern meridian crossing)
b.
What is your longitude?
ast = 12 hours
mst = ast EqT = 12 hours (-7 min) = 12:07 (you could skip this step)
mst = UT + lambda
lambda = mst UT = 12:07 22:00 = -9:53 (-10 hours would be OK)
lamda = - 9*15 degrees - 53/4 degrees = -148
degrees = 148 degrees W (150 degrees OK)
c.
Near
10.
Lost at Sea
II
·
Sun: alpha = 6 hours, delta = +23.5°, EqT
= -3 min
·
h = 67.5° north, ast = 12:00
·
UT 06:00.
a.
What is your latitude?
d = +23.5 degrees, h = 67.5
degrees north
h = 90 - | delta - l |
67.5 = 90 - | 23.5 l |
|23.5 - l| = 22.5
23.5 - l = 22.5 or
23.5 - l = -22.5
l = 1 or l
= 46.0
Latitude is 1 degree north (northern meridian crossing)
b.
What is your longitude?
ast = 12 hours
mst = ast EqT = 12 hours (-3 min) = 12:03 (you could skip this step)
mst = UT + lambda
lambda = mst UT = 12:03 6:00 = 6:03 (6 hours would be OK)
lamda = 6*15 degrees + 3/4 degrees = +90.75
degrees = 90.75 degrees E (90 degrees OK)
c.
11.
Lost at Sea
III.
·
mst = 0:00
·
Polaris h = 67° in the north.
·
UT = 01:00.
a.
Your latitude is equal to the altitude of Polaris +/- 0.75 degrees
67° North
b.
mst = UT +
lambda
lambda = mst UT = 0:00 01:00 = -1 hour
lambda = -15 degrees = 15 degrees W
c.
Near
12.
Sidereal
Time.
a.
mst = 16:00,
but ast = mst + EqT = 16:00 00:07 = 15:53
so that HAsun = 3 hours 53 min (4 hours OK)
RAsun = 0 hours on the spring equinox.
LST = HA + RA = 3:53 + 0:00 = 3:53
LST = 3:53 (4:00 would be OK)
b.
LST = 19:30, RA = 18:37 for Vega
HA = LST RA = 19:30 18:37 = +0:53
Last meridian crossing about 53 minutes ago, next meridian crossing 23 hours 3
minutes
c.
HA = +3 hours, LST = 8:15
RA = LST HA = 8:15 3:00 = 5:15
RA = 5 hours 15 minutes