Time, Day, Month, and the Moon
Announcements
o  First Homework will start on Tue Sept 20st; due
on Thu, Sept 29th.
o  Accessible through SPARK
Assigned Reading
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Units 7 and 8
Goals for Today
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To discuss time and time keeping.
To discuss the day, and month
To Introduce the Moon and the Lunar
Phases
What is time?
Properties of Time
- Time has length.
- Time is believed to be continuous.
- Time is relative (not absolute).
- two people traveling at different speeds experience
the flow of time differently!
- Time may have a beginning.
- Time has a direction (unlike the spatial
dimensions).
Physical Time Direction
The Three arrows of time
1.
Thermodynamic: the direction in which disorder
increases
2.
Psychological: the direction in which we
remember the past and not the future
3.
Cosmological: the direction in which the
universe expands or contracts.
Stephen Hawking, A Brief History of Time
The Thermodynamic Argument
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The 2nd law of thermodynamics says that:
degree of disorder in
the entropy of an isolated system which is not in equilibrium will
tend to increase over time, approaching a maximum value at
equilibrium
This actually makes intuitive sense – imagine a jigsaw
puzzle on a vibrating table. Or an ice crystal melting.
So the direction of time can be determined by the
change in disorder in an isolated system that is not in
equilibrium.
Thermodynamic time
It measures `irreversible systems’ , i.e. systems (the
Earth, a gas balloon, you) for which doing an action in
one direction cost more `work’ than doing it in the
opposite direction.
A system that has performed an `irreversible’ action is
said to have increased its disorder
1.  Reversible: You drive from Amherst to Boston.
2.  Irreversible: You let air out of your bike’s tire.
Survey Question
Which of the following demonstrates a direction
to the flow of time?
1) the Earth rotates counter-clockwise
when viewed from above the North Pole
2) the Moon orbits the Earth
3) light travels from the Sun to us in 8 minutes
4) the lava flows out of a volcano.
Some ways to measure the passage of time …
Astronomical
- Appearance of seasons
- Appearance of constellations
- Appearance of Moon (phases)
- Rising and setting of the Sun
Mechanical
- The motion of a pendulum
- The vibration of a crystal
Atomic
- The decay of unstable isotopes
- The emission of radiation by all elements
Seconds (MKS)
Old Definition:
The hour / minute / second system
• Hour- 1/24 of a mean solar day
• Minute – 1/60 of an hour
• Seconds – 1/60 of a minute
New Definition:
Seconds now defined by one form of
radiation given off by the cesium atom
(9,192,631,770 Hz)
Day
Day = 1 full rotation of the Earth on its axis
Local Noon – sun crosses the celestial meridian
Ante meridiem (A.M.) and post meridiem (P.M.)
Sidereal day – consecutive meridian
crossings of a particular star (23:56:4)
Solar day – consecutive meridian
crossings of the Sun (noon to noon)
Four minutes longer than a sidereal day
(Solar day = 86,400 s)
Solar
86,400s
Sidereal
86,164s
Why are they different?
Solar and Sidereal Days
Need to rotate this much
more for 1 solar day
Direction to Noon
360º rotation
= 1 sidereal day
Survey Question
A sidereal day is 4 minutes shorter than a solar
day. If the Earth s spin were in the opposite
direction then a sidereal day would
1) not change
2) change, but still be shorter than a solar day
3) be longer than a solar day
4) be the same as a solar day
Backwards Solar and Sidereal Days
Need to rotate this much
less for 1 solar day
Direction to Noon
Rotating backwards!
360º rotation
= 1 sidereal day
Survey Question
If you put a sundial in your back yard, you want
to point the 0 point in which direction?
1) North
2) South
3) East
4) West
Time Zones in the U.S.
Local Noon changes
approximately one minute
for every 12 1/2 miles E-W
Solar local noon in
Northampton occurs about
45 seconds after it happens
in Amherst.
In general, time zones were created to synchronize
our schedules with the daylight and to make time
uniform over a large region (for the railroads).
In Michigan, there are days in the summer when it is still light out at
10:00pm!
Universal Time
Daylight Saving Time
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Just when things were getting easy …
Idea is to shift clock during the year to minimize the
use of artificial lights.
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Most of the world observes DST, with laws and regulations
dating back to the early 1900 s.
But non-uniformities can make this quite complicated
(Move to Arizona if you don t like setting your
watch!)
Year
Tropical Year – interval between spring equinoxes
365 days, 5 hours, 48 minutes, 46 seconds, or
365.24240 solar days
Sidereal Year – interval for the sun to return to same
apparent position relative to stars
365.2525636 m.s.d. (about 20 minutes longer than
tropical year) – precession of the Earth s rotation
axis (a.k.a precession of equinoxes)
Calendar year = 365 days (with leap year of 366 days
every 4 years except when century changes
unless century is divisible by 400)
Survey Question
The year 1900 was a leap year:
1) Yes
2) No
Month
Linked to the phases of the moon
Sidereal month – 27.33 days, two consecutive
crossings of any star
Synodic month – 29.5 days, new moon to
new moon
Calendrical month – 1/12 year, 28-31 days
The Egyptians are credited with the first 12
month solar year.
Sidereal and Synodic Month
Sidereal and Synodic Month
Sidereal month (27.33 days)
Synodic month –
complete cycle
of moon phases
(29.5 days)
Survey Question
If the Moon s orbit (radius) were twice as big
but the Moon went around at the same speed
as it currently does, the difference between a
sidereal month and
a synodic month would be
1) smaller
2) larger
3) the same
Earth & Moon
The Moon is ~1/4 of the
Earth in diameter and
~1 percent in mass.
The rotation of the Moon
and its revolution around
the Earth takes 27 days,
7 hours, and 43 minutes.
This is the Sidereal
Period of the Moon s
orbit.
The period of time it takes
the moon to go through
its cycle of phases is
called its synodic
period. This is 29.5
days – or one month.
We only see one face
of the moon!
Lunar Phases
•  Why can we see the Moon at all?
The Moon is
Illuminated by the
Sun!
Like planets, the moon does
not emit its own light.
sunlight
Survey Question
A third quarter moon is rising. What time is it?
1) sunset
2) sunrise
3) midnight
4) noon
Survey Question
A third quarter moon is rising. What time is it?
1) sunset
2) sunrise
3) midnight
4) noon
Earth Rising on the Moon
Apollo 11
Survey Question
In this picture of the Earth rising, what is the
predominant direction of the sun in relation to
the observer?
1) above the observer
2) below the observer
3) behind the observer
4) behind the Earth
Survey Question
In this picture of the Earth rising, what is the
predominant direction of the sun in relation to
the observer?
1) above the observer
2) below the observer
3) behind the observer
4) behind the Earth
Solar Eclipses
The Sun is physically 400 times larger than
the Moon.
Why can it be obscured by the Moon?
Angle diameter (in radians) = diameter/distance
Full circle = 2π (in radians)=360 degrees=360o
1o=60 arminutes = 60
1 = 60 arcseconds = 60
Angular Size
Some Examples:
Horizon to zenith (point overhead) 90o Your fist at arm's length 10o Sun or Moon seen from Earth 0.5o = 30' Smallest detail visible to naked eye 1' = 60'' Smallest detail visible by a single telescope from
Earth's surface: 1'' Angular size of Pluto: 0.15”
Betelgeuse (largest star) seen from Earth 0.004'' Geometry of Moon and Sun
•  Both the Moon and the Sun have angular diameter of about
0.5 degree, the exact value at a given time depending on the
exact distance.
•  Therefore, we can periodically have solar eclipses
Geometry of Solar Eclipses
Looking Back on an Eclipsed Earth; 1999 August 11 Credit: Mir Space Station Crew
Total and Annular Eclipse
Annular Eclipse
October 3, 2005
It takes about an hour for the
moon to cover the sun. Why?
The moon moves at an angular speed of
360 deg/(28x24 hr) = 0.5 deg/hr.
The angular size of the moon is about 0.5 deg.
How come there isn't an eclipse
every full moon and new moon?
The main reason is that the moon’s orbit is tilted from the
earth’s orbit.
However, twice a year the nodes of the moon’s orbit will
align with the Earth-Sun direction, and total eclipses will
be possible.
A total eclipse from a given point on the surface of the
Earth is not a common occurrence. For example, next
solar eclipse in the USA will occur on 21 August 2017;
the following one will be on 8 April 2024. Survey Question
The phase of the moon at a solar eclipse is?
a) new
b) 1st quarter
c) full
d) it depends on the year
Survey Question
The phase of the moon at a solar eclipse is?
a) new
b) 1st quarter
c) full
d) it depends on the year
Lunar Eclipse
(the Moon in the Earth’s Shadow)