Telling Time - astronomy.ohio-state.edukstanek/AY1140/Notes/AClass04_2018.pdf · 1 Telling Time A Warm Up Exercise The ecliptic is a) The annual path of the Earth across the celestial

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Telling Time

A Warm Up Exercise

The ecliptic is

a) The annual path of the Earth across the celestial sphere

b) The extension of the Earth’s equator

c) The annual path of the Sun across the celestial sphere

d) When the moon covers the sun

A Warm Up Exercise

In Columbus, the longest night of the year occurs close to

the

a) Fall Equinox

b) Summer Solstice

c) Spring Equinox

d) Winter Solstice

A Warm Up Exercise

In Columbus, the longest night of the year occurs close to

the

a) Fall Equinox

b) Summer Solstice

c) Spring Equinox

d) Winter Solstice

Keeping track of Time

•All of our time-keeping conventions are

astronomically based:

– Years are based on the apparent annual solar motion

due to the Earth’s orbit around the Sun.

– Months are based on the cycle of the Lunar Phases

(“Month” derives from “Moon”).

– Days are based on the apparent daily solar motion

as the Earth rotates on its axis.

Dividing the Day

•We divide the Day into 24 equal hours, with each day beginning at midnight.

•This wasn’t always the case:

–The day began at dawn (sunrise).

–Equal division of Day and Night into 12 hours.

–The length of the hour was different for day and night (except at the Equinoxes).

•Worked fine for sundials.

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Equal Hours

•The invention of mechanical clocks in the 1300s led to a need for equal hours:

–Ensured the clocks read true in the morning.

–Simplified clock design.

•Medieval clocks were large and complex:

–Erected in towers in cities for everyone to see.

–Led to a standardization of time keeping

–Personal timepieces came only later.

Oldest surviving clock in

England – Salisbury

Cathedral (1386)

These clocks were used

only to chime bells (no

hands) and were only

accurate to about 30

minutes per day

Dividing the Hour

•Until 1500s, clocks only kept time to the quarter hour.

•Further division of the hours was needed as clocks became more complex.

–1 hour was divided into 60 minutes.

–1 minute was divided into 60 seconds.

•Seconds didn’t become common until the 1670s (39-inch pendulum clocks).

Solar Time

•The Day is measured using the Sun.

•Local Solar Noon:

–Occurs when the Sun is on your meridian.

•Mean Solar Day:

–The time between successive Noons.

•Noon depends on your longitude:

–Person 15º east of you sees noon 1 hour earlier.

–Person 15º west of you sees noon 1 hour later.

Sidereal Time

• Sidereal Time is measured relative to the “fixed stars”.

• As the Earth rotates through 1 day, it moves about 1º

along its orbit around the Sun.

–As seen with respect to the stars, the Earth has move for an

extra 4 minutes in order for the Sun to return to the observer’s

meridian (noon).

• Stars rise 4m earlier each night measured against solar

(civil) clocks.

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NoonT=0h

T=23h 56m 04s

(Sidereal Day)

T=24h

(Solar day)

Not to Scale

Standard Time

•Invention of long-distance railroads and telegraph networks required standardized time keeping:

– Coordination of interstate railroad schedules.

– Telegraph lines linked many widely separated longitudes instantaneously, but needed to coordinate them.

•Small differences in local solar time began to matter.

Time Zones

•Charles Dowd (1883):

– Divided the Earth into Time Zones by longitude from the Prime Meridian.

– Basic time zones are 15º of longitude apart (360º/24h = 15º/hour)

– Each time zone keeps local solar time for a fixed reference longitude.

– All longitudes within that zone use “Zone Time”instead of local solar time.

The Motion of the Moon

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A Warm Up Exercise

The ecliptic is

a) The annual path of the Earth across the celestial sphere

b) The extension of the Earth’s equator

c) The annual path of the Sun across the celestial sphere

d) When the moon covers the sun

SCP

NCP

CEq

Winter

Solstice

Summer

Solstice

Vernal

Equinox

Autumnal

Equinox

“O! Swear not by the moon, the inconstant moon

That monthly changes in her circled orb,

Lest that thy love prove likewise variable.”

William Shakespeare,

Romeo & Juliet, II, 2

Our Nearest Celestial Neighbor

•The Moon is a natural satellite of the Earth.

•Its orbit around the Earth is elliptical:

–~5% deviation from circular.

–The orbit is tilted by 5º from the Ecliptic.

•Mean Distance: 384,400 km

–Perigee (Closest Approach): 363,300 km

–Apogee (Maximum Distance): 405,500 km

–Appears ~11% larger at Perigee than at Apogee

The Moons Orbit is Elliptical

(closest point on orbit)/(furthest point on orbit) = 0.9

Which means the angular size of the moon changes by the same factor since

(angular size)=(moon diameter)/(distance)

It will be 11% bigger at perigee (closest approach) than apogee (most distant point).

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Synchronous Rotation

•The Moon rotates at the same rate it revolves:

• Completes 1 rotation in the same time it takes to complete 1

orbit (revolution) around the Earth.

•Always keeps the same face towards us.

• Near Side: hemisphere facing towards us

• Far Side: hemisphere facing away from us

•Caused by tidal coupling between the Earth and Moon.

• The Moon is “tidally locked” to the Earth

•Example of a “resonance”

Lunar Near Side

Full Moon(Lick Observatory Photo)

Lunar Far Side

Historic image returned

by the Soviet Luna 3

Spacecraft in October 1959.

Lunar Far Side

Far-side image

returned by the Galileo

Spacecraft during a fly-by

enroute to Jupiter (Dec 1990)

Case I – The Moon Is Not Rotating

start ¼ orbit

½ orbit¾ orbit

Case II – Tidal Locking -- The Moon Spins as Fast

as It Orbits

start ¼ orbit – moon rotated by 90o

Moon rotating in the

same direction and at

the same rate as the

orbit

¾ orbit – moon rotated by 270o½ orbit – moon rotated by 180o

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Why is it called “Tidal Locking”?

The “tidal locking,” as the name suggests, is a result of the tidal

effects produced by the Earth on the Moon

If the Moon were rotating faster or slower, the Earth would

produce time varying tidal deformations in the moon.

These deformations produce frictional forces that either slow the

rotation rate (if rotating faster than synchronously) or speed up the

rotation rate (if rotating slower than synchronously)

When tidally locked, the tidal deformations do not vary with time

so there is no friction and the rotation rate stops changing

The Moon’s Orbit Is Slowly Expanding

It expands by 3.8 cm per year

Phases of the Moon

•The Moon produces no visible light of its own

– It shines only by reflected sunlight

– Surface is very dark, only ~7% reflective

•During the month, we see a complete cycle of Phases:

– The sunward hemisphere is fully lit.

– The opposite hemisphere is dark.

– The phase of the Moon is the fraction of the sunlit hemisphere

visible to us.

New Moon Full Moon

Waning Crescent

Last Quarter

Waning Gibbous

Waxing GibbousWaxing Crescent

First Quarter

The Moon’s Phases

EarthThis Way

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New & Full Moon

•New Moon:

–Moon and Sun are on the same side of the sky.

–Near side is in total darkness.

–Moon and Sun rise together.

•Full Moon:

–Moon is opposite the Sun in the sky.

–The near side is fully illuminated.

–Moon rises as the Sun sets.

Quarter Moon

•Earth, Moon, & Sun are at right angles:

–Half of the near side is illuminated

–Half of the far side is illuminated

•First Quarter:

–Between New Moon and Full Moon.

•Last Quarter:

–Between Full Moon and New Moon.

Waxing & Waning

•Waxing: increasing illumination

–Waxing Crescent: after New Moon

–Waxing Gibbous: just before Full Moon

•Waning: decreasing illumination

–Waning Gibbous: just after Full Moon

–Waning Crescent: before New Moon

What you can see strongly depends on the phase

For a 1st quarter moon, for example, the moon will always be

visible at sunset, and then sets at midnight (it rose at noon).

Moonrise, Moonset...

•You don’t see all moon phases at all times

–Never see a crescent moon at midnight.

–Never see the last quarter moon at sunset.

–Never see a full moon during the day.

•Times of rising and setting depend on the Earth-

Sun-Moon configuration as viewed from the

surface of the rotating Earth.

•When in doubt, draw a picture!

The View from the Moon

•Question:

What would an astronaut on the Lunar near side see

during one month?

•Answer:

– See the Earth neither rise nor set, but stay nearly

fixed at the same position in the sky.

– See the Earth rotate on its axis once every 24h.

– See the Earth go through phases.

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The earth as viewed from the Apollo 17

landing site in the Taurus-Littrow valley.

Earth Phase Movie

https://www.youtube.com/watch?v=YQfm2icwtDk

Sidereal Period

•The time for the Moon to complete one orbit around the

Earth with respect to the stars.

–Moon’s Sidereal period = 27.3 days

–Also called the “Sidereal Month”

•Measure by watching its motions against the

background stars – returns to the same constellation

•The phase at the end of a sidereal month is DIFFERENT

from the phase at the start

1999 October 2

1999 October 29

Moon in Gemini

27.3 days apart

Same Background Stars

but,

Different Phases

Synodic Period

•The time between successive New Moons.

– Moon’s Synodic period = 29.5 days

– Also called the “Synodic Month”

•This is the month used in Lunar Calendars:

– The Islamic calendar starts and ends on the New

Moon, signaled by the first appearance of the

Waxing Crescent moon.

Sidereal vs. Synodic Months

New

Moon

T=0d

T=27.3d

(Sidereal)

T=29.5d

(Synodic)

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MonthsThe synodic period (full moon to full moon)

is 29.5 days

The sidereal period (one complete orbit) is

27.3 days

The difference is the same issue as for sidereal and mean solar days – the

earth moved along its orbit, in this case by

360o(29.5days/365days) = 29o

So the moon must turn by

360o+29o= 389o

to go from new moon to new moon, so the real sidereal period is

(29.5d)(360o/389o)= 27.3 days

The Calendar

Key Ideas:

•Our calendars are based on the motions of the Sun

and Moon.

•Two Basic Types of Calendars:

–Lunar Calendars

–Solar Calendars

•The Julian & Gregorian Calendars

•A.D., B.C., Y2K and all that...

Dividing the Year

•The first major division of the year is into seasons:

–Equinoxes & Solstices divide the year into quarters

–Sometimes called “Quarter Days”

Solstice & Equinox Holidays

•Winter Solstice:

– Christmas, Yuletide, Saturnalia

•Vernal Equinox:

– Easter, Passover, Eoestre (Saxon)

•Summer Solstice:

– Midsummer (viz. Midsummer Night’s Dream)

•Autumnal Equinox:

– Mabon (Welsh festival)

Months & Weeks

•The year is also divided into 12 months.

–Why? 12.4 lunar synodic periods (cycles of phases) during a year.

–“Month” derived from the word “Moon”

•Months are divided into Weeks:

–The week is traditionally divided into 7 days

–Seven for the 7 moving bodies (“planets”) visible to the naked eye (Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn)

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Roman Anglo-Saxon English Spanish

Sol Sun Sunday Domingo

Luna Moon Monday Lunes

Mars Tiw Tuesday Martes

Mercurius Woden Wednesday Miercoles

Jupiter Thor Thursday Jueves

Venus Freya Friday Viernes

Saturnus Saturn Saturday Sabado

Thirty days hath September,

April, June, and November,

February has twenty-eight alone

All the rest have thirty-one.

Excepting leap year — that’s the time,

When February’s days are twenty-nine.

Anonymous (16th c.)

Lunar Calendars

•The phases of the moon provide a convenient way to keep track of time.

–Phases are easily visible and distinctive.

–Our word for “month” derives from “moon”

–Lunar month is 29.5 days long.

–12 lunar months is 354 days.

•Oldest recognizable ancient calendars are lunar calendars.

The Earliest Lunar Calendar?

Markings carved onto a bone tool thought to

depict the phases of the moon.28,000 BC (Dordogne, France)

Abri Blanchard Bone

The Metonic Cycle

• The 354d lunar year is 11d short of the 365d solar year.

–Causes the seasons to drift among the months.

• Babylonians discovered the Metonic Cycle:

–235 lunar months is almost exactly 19 solar years

–(235)(29.531 days) = 6939.79 days

–(19)(365.256 days) = 6939.86 days

• The Babylonians built a complex, but very precise

hybrid luni-solar calendar based on the Metonic Cycle.

Lunar Calendars in Use Today

•Islamic Calendar

• Purely lunar calendar, 354d in the calendar year.

• Months occur in different seasons.

•Jewish Calendar

• Luni-solar calendar.

• Interpolate an extra 13th month every few years to keep the

calendar aligned with the seasons.

• Repeats on the 19-year Metonic cycle.

•Chinese & Japanese calendars.

• Also Luni-solar calendars

• 29 or 30 day months plus leap months to keep things matched to

the seasons

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Solar Calendars

•Solar Calendars mark time by the Seasons

–Tie the calendar to the Equinoxes and Solstices.

•Arrival of seasons often has practical and/or cultural importance:

–Knowing when to plant or harvest.

–Annual flood of the Nile Valley.

–Religious festivals associated with specific seasons (e.g., Easter and Christmas)

Egyptian Solar Calendar

• The Egyptians developed the first recorded solar

calendar in 3000 BC.

–Divided year into 12 months of 30d each

–Added an extra 5 days to make up 365d.

–Year began when the star Sirius rose exactly in line with the

rising Sun (“Heliacal Rising”). This corresponded with the

annual Nile flood.

• By 300 BC, they measured a year as 365.25d, only 11m

14s longer than the true value.

The Julian Calendar (46 BC)

•Julius Caesar asked the Alexandrine astronomer Sosigenes to reform the Roman calendar.

•He started with the solar year of 365.25d:

– Year divided in 12 months of 30 and 31d, adding up to 365 days.

– Every 4 years, add a day to February to make 366 days.

–“Leap Year” makes up the difference between 365.25 and 365 days per year.

Annus confusionis

•Caesar started the calendar in 46 BC

–Added 80 extra days to 46 BC

–46 BC had 445 days in it!

•Caesar called 46 BC:

Ultimus annus confusionis

(“The final year of confusion”)

•The Romans called it

Annus confusionis

(“The year of confusion”)

Missed it by that much...

•Sosigenes and the others knew, however, that the year was not exactly 365.25 days long.

•True solar year is about 365.242199…. days:

– Calendar gets ahead about 1d every 128 years.

– Causes a slow slip of the seasons against the dates of the Julian Calendar.

•By the Middle Ages the slip became large.

A Moveable Feast

• In 325 AD, the Council of Nicaea established a formula

to compute the date of Easter.

–Most important holy day in Christianity.

–Important to celebrate it on the correct day.

• Council adopted a fixed March 21 equinox:

–Easter is the first Sunday after the first full moon of the Vernal

Equinox.

–But, it must not coincide with Passover.

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Gregorian Calendar Reform

•By the 1570’s, the Julian Calendar was out of

alignment with the seasons by 10 days.

–Easter was being computed incorrectly, and so

celebrated on the wrong day.

–Other important holy days were also being celebrated

on the wrong days.

•Pope Gregory XIII appointed a commission to

develop an improved calendar.

A New Leap Year Formula

•An elegant formula was invented by Aloysius Lilius

(Luigi Lilio), an Italian physician:

–Keep the Julian formula for leap years, but

–A century year is not a leap year unless it is divisible by 400.

–2000 is a leap year, but not 1700, 1800, & 1900

•Removes 3 days every 400 years:

–Eliminates all but ~3 hours of error per 400 yrs

The Lost Ten Days

•Gregory instituted the new calendar in 1582

–Took 10 days out of October 1582 to realign the calendar

with the seasons.

–The day after October 4, 1582 was October 15.

•Adopted by Catholic countries within 2 years:

–Some rioting over the “lost days”, especially over payment of

rents and taxes.

•Adopted all over continental Europe by 1700.

Just like the metric system?

England (and the colonies) refused to accept this reform for 170

years, finally adopting it in 1752

Wednesday September 2, 1752 was immediately followed by

Thursday September 14, 1752

This made a mess of some people’s birthdays – for example,

George Washington was born on February 11, 1731 (Julian).

After the reforms it was February 22, 1732 (Gregorian). How did

the year change? It was common in the colonies to use March 24

or 25 (alternating) as the New Year (matching the solar equinox,

roughly), but after the reform it was switched to the standard

January 1.

The Eastern (Orthodox) Churches adopted the Gregorian calendar

only in 1923, 337 years later.

Still off by a little bit...

• The Gregorian Calendar formula is equivalent

to a year of 365.2425 days.

• This is ~0.0003 days longer than the length of

the true solar year (365.2422 days).

– Gets ahead of the true solar year by 1 day every

3327 years.

– The Gregorian Calendar will be ahead of the true

solar year by 1 day in 4909 AD.

A.D. and B.C.

•Anno Domine (A.D.) system of dates

–Invented by Dionysus Exiguus (Dennis the Short) in 531 AD.

–Starts counting years from the birth of Christ, or 1 AD.

–Has no year zero (no zero used in European mathematics until

the 11th or 12th century).

•B.C. (Before Christ) not introduced until 1627

–Before 1 AD is 1 BC

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The Millennium (or not)

• Jan 1 2001 was the start of the 3rd Millennium A.D.

• But,

–Most 3rd Millennium celebrations were held on January 1, 2000

• These dates are of historical rather than astronomical or

physical significance.