astronomy 217 T e l l i n g T i m e o n a

S p i n n i n g O R B

Time is RevolutionEach of the Earth’s motions results in a distinct “clock” tuned to the period of that motion.1) rotation around axis produces the day.2) Earth-Moon orbit produces the month.3) revolution around Sun produces the year.4) precession of the pole produces the Great Year.

Solar DayThe rising and setting of the sun are natural markers for the day. However the variation in the length of the day make sunrise and sunset make very irregular time keepers.The upper transit, the passage of the sun across the local zenith meridian, AKA noon, is a more reliable marker.

Sunrise

Sunset

Month

The solar day is defined to be the length of time for the Sun to return to your celestial meridian.

Two effects cause the actual solar day to deviate over the course of the year.1) The Earth’s slightly elliptical orbit causes the Earth to move faster in winter and slower in summer.

2) The projection of the solar motion onto the Celestial Equator causes the Sun to move slower near the equinox by cos(23.5°)~.9.

Appa

rent

-Mea

n So

lar T

ime

Mean Solar Time

To work around these variation, we define the mean solar day to be average length of solar day.

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utes

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AnalemmaIf you were to take a picture of the sun each day at the same time over the course of a year, you’d get a figure 8 on the sky. This is called the analemma.This image shows the ruins at Ancient Nemea in Greece, but the shape of the figure would be similar in Knoxville, because of the similar latitude.

Credit & Copyright: Anthony Ayiomamitis

Universal TimeHistorically, every locality had it’s own local time, based on the solar upper transit at local noon. In the late nineteenth century, with railroads and telegraphs connecting many local times at higher and higher speeds, it became necessary to establish a common standard of time. Since the Prime Meridian was already established to run through Greenwich, England, Greenwich Mean Time (GMT) became the standard, or Universal time. It is now generally denoted UT (or UTC).Unfortunately, UT has no relation to the local noon, thus it is inconvenient as a local time away from the Prime Meridian. For example, today 11:30 AM at UTK is 3:30 PM UTC.

Time ZonesAs a compromise between a multitude of local times and a single universal times, 24 one hour wide time zones were devised as a local correction to the universal time. This allows the solar upper transit to occur near 12 pm.Ideally, each time zone is 360°/24 = 15° wideFor the Eastern Time Zone, local time is UT − 5 hr (except that it is UT − 4 when daylight savings time is in effect).

The center of this timezone is then at 5 * 15° = 75° W Longitude (Philadelphia, PA), and it ideally covers from 67.5° W (Bar Harbor, ME) to 82.5° W (Asheville, NC).

Real Time zones

Politics complicate the regular 15° timezones.

ExampleKnoxville is situated near the Western edge of the Eastern Time Zone at 84° W. What is the Mean Solar Time of the solar upper transit? Center of timezone is 75° W, so Knoxville is 9° west of center. 60 min. × 9°/15° = 36 min.So the answer is 12:36 pm.Can the Actual Solar Time of the upper transit be 12 noon?Maximum Deviations are −14 minutes in February and +14 minutes in October, so our astronomical noon varies from 12:22 pm to 12:50 pm EST.

Sidereal TimeAs the Earth rotates on its axis, it is also revolving around the Sun, thus it must rotate further to align with the Sun than it would to align with a distant star.We call the period between pointing at a fixed star the sidereal period. For the earth’s rotation, this is the sidereal day.This causes there to be one more sidereal day than solar day per year, thus the sidereal day is 1/365th shorter (~4 min.)

Credit: Hong Kong Space

The Moon-thTraditionally, the month is defined by the period of the Moon’s orbit. The lunar month is the time to complete the cycle of lunar phases (29.53 days).This is the average period of the Moon's revolution with respect to the sun, the synodic period.This is not the moon’s true orbital period.

Sidereal MonthAs with the day, the period of the moon’s rotation with respect to the fixed stars is less.

1

Psid=

1

Plun+

1

Pyear

Plun = 29.53 daysPyear = 365.24 daysso Psid = 27.32 days

The YearHistorically, the definition of a year is the interval between two successive returns of the Sun to the vernal equinox. This is called the tropical year, because the Sun is at the zenith on the tropic of Cancer on this anniversary. The tropical year has a length of 365.2422 mean solar days. The period of revolution of the Earth around the Sun as referenced to the distant stars is called the sidereal year. It has a length of 365.2564 mean solar days. The difference (1 part in 25,721) is due to the precession of the equinoxes.The sidereal year is the "true" year, but our calendar is based on the tropical year because the seasons, which are important to agrarian societies, are correlated with the tropical year.

SeasonsUltimately, the seasonal variations we experience are the result of the mis-alignment of the Earth’s rotational and orbital axes.More direct sunlight and additional hours of sunlight result in warmer summers. In fact the Earth is slightly closer to the Sun during January (147,098,290 km) than in June (152,098,232 km).

CalendarThe desire to predict and plan for the seasons caused most cultures to develop calendars to chart the year for agricultural and religious purposes, often devoting tremendous resources to the effort.

Counting the DaysThe astronomical challenge to calendar making is the non-integral mismatch between the Earth’s rotational and orbital periods, a fact well known to the ancients. By 330 BC (or earlier) the length of the years was known to be (365 + 1/4) days. By 120 BC, Hipparchus determined the tropical year to be (365 + 1/4 - 1/300) days, within 6 minutes of the modern value, by using sundials to determine the time between the recurrence of the equinoxes.

Leap DaysTo keep their calendars aligned with the seasons, many cultures adopted leap days (or months) to periodically bring their calendar into alignment with the Heavens.In 46 BC, Julius Caesar introduced a calendar with a leap day added to February every fourth year, for a 365 + 1/4 day average year (the Julian Calendar).Though accurate to better than 11 minutes per year, the errors in the Julian calendar added up over the centuries, amounting to 10 days by 1582 AD when Pope Gregory decreed a new calendar (the Gregorian Calendar).By dropping 3 leap days per 400 years, the Gregorian calendar achieves an accuracy of better than 30 sec./year.

Precession of the Equinoxes

Another discovery by Hipparchus of Nicea near 130 BC was a precession of the equinoxes. Hipparchus found a rate of precession >1° per century, or a period < 36,000 years).

The equinoxes move about 1° in 72 years or a period of roughly 26,000 yearsAs a result, the tropical year is about 20 minutes shorter than the sidereal year.

The cause of the precession of the equinoxes is a precession in the Earth’s rotational axis. As a result, the Earth’s Poles trace circles on the Celestial Sphere and the “Pole” star becomes time dependent.

Precession of the Pole

Vega

Polaris

Thuban

Errai

Alfirk

Alderamin

Rijl al Jathiyah

Rukbalgethi ShemaliRukh

Eltanin

Edasich

Oblate Earth

12,756 km 12,714 kmBecause it is rotating, the Earth is slightly flattened at the poles, forming an Oblate Spheroid.Because the Pole is inclined to the Ecliptic, there is an unbalanced component of the Sun’s gravity on the near bulge and a smaller component on the far bulge. This unbalanced force (plus a contribution from the Moon) on the rotating Earth, produces a torque that drives the polar precession.

Next TimeCelestial Motions orTracing Movement across the Sky.