Time and Its Measurement

2. Time intervals have their root in astronomical observations. For example, the rotation of the earth about its axis could loosely define the _______________. The year is based upon one _______________ of the earth about the sun, while the moon's phase period gives logical understanding to the origin of the _______________. The sun, the moon, and the five planets which were observed during antiquity may have led to the establishment of the week.

APPARENT SOLAR TIME

3. The concept of a 24 hour day dates back to the ancient Egyptians who divided their sky into 24 nonequal and changing parts. The 24-hour clock used today, depends upon the position of the _______________ in the sky with respect to an observer's local meridian. The meridian is a great circle which intersects the horizon at the observer's south and north points, while also intersecting the zenith.

4. Using a (nighttime) star to facilitate time-keeping would be highly impractical. The sun and the reference star would soon be out of synchronization. The sun shifts its position eastward among the stars by about one degree per day as the result of earth's _______________. A solar day is equal to _______________ of clock time, but one rotation of the earth takes ____________________ of clock time. Time based on the successive transits of a star across the meridian would soon find the star and the sun out of phase. In just six months, day and night would be completely reversed causing continual disruptions to human activity. Time based upon the successive transits of a star on the meridian is called _______________ time. This is, however, not a strict definition.

5. To regulate our daily activities we are interested in having the _______________ returned to the same part of the sky in a uniform time interval. Therefore, we must add approximately _______________ to the sidereal day to allow the earth’s rotation to move the sun to its crossing position on the meridian.

6. The angle measured westward from the meridian along the celestial equator to the hour circle which contains the sun is referred to as the sun’s ____________________. Since this angle is measured as a function of time, it is stated in units of _______________, _______________, and _______________.

7. When the sun is on the meridian, its hour angle is _______________. As the earth rotates, the sun is carried towards the west. It eventually sets and continues its path beneath the horizon to reappear in the east and make its climb back to the meridian. During this interval, the sun's hour angle increases from zero to _______________, similar to army or military time.

8. Apparent Solar Time = Hour angle of the sun + 12 hours if the hour angle of the sun is between _______________ and _______________ hours.

9. If the hour angle of the sun is greater than 12, it will be necessary to subtract _______________ hours from the total to obtain the correct time.

10. The hour angle of the sun is 3 hours, 15 minutes. Based upon a military system of time-keeping (a 24 hour clock) the apparent solar time is _______________. With regards to a regular 12 hour clock the time is _______________. Don't forget the a.m. (ante meridiem) which means before the meridian or the p.m. (post meridiem) which means after the meridian if military is not being used.

11. The hour angle of the sun is 21 hour, 41 minutes. Stated as military time the apparent solar time is _______________. On a 12 hour clock this would correspond to _______________.

12. The apparent solar time is 19 hours, 16 minutes. The hour angle of the sun is _______________.

13. The apparent solar time is 9 hours, 12 minutes. The hour angle of the sun is _______________.

MEAN SOLAR TIME

14. The problem with the apparent solar day is that the time intervals of successive local meridian transits of the sun are never precisely the same. These changing intervals result from a variation in the earth’s orbital speed as it revolves around the sun in an elliptical path. In order to create uniformity in our time-keeping system, the apparent solar day is averaged to create the _______________ solar day.

15. The change in the length of the apparent solar day arises because the eastward movement of the sun is not uniform. This motion is a result of changes in the velocity of earth as it _______________ around the sun. The earth's orbital shape is _______________. This factor causes it to move faster when closer to the sun and slower when farther away. When the earth has a higher orbital velocity, the sun's eastward motion is GREATER/SLOWER (circle one).

16. A secondary reason why the eastward motion of the sun varies is due to its northerly and southerly change in _______________.

17. The sun's greatest daily eastward motion should occur when the earth is closest to the sun, giving the earth its highest orbital velocity. Another helpful effect would occur when the sun has a minimal daily change in declination and its entire component of motion along the ecliptic would be directed towards the east. This does occurs during the season of _______________.

18. Even though apparent solar time is vastly superior to sidereal time in monitoring our daily activities, it is still not uniform enough. Astronomers have therefore invented a fictitious sun called the _______________ sun. It is merely an imaginary point in the sky which moves uniformly along the celestial equator so that it will make successive transits of the meridian in precisely ______________________________.

19. Just like apparent solar time, mean solar time utilizes a 24 hour clock system equal to the ____________________ of the mean sun + or - 12 hours.

EQUATION OF TIME

20. The difference in time as measured by a sundial and a mechanical or digital clock is referred to as the _________________________. More precisely, it is apparent solar time - mean solar time. Think of the mean sun uniformly transiting a meridian. The apparent sun will sometimes transit first, and at other times of the year, it will transit after the mean sun.

21. If the apparent sun leads the mean sun, the equation of time is POSITIVE/NEGATIVE (circle one). If the apparent sun lags behind the means sun, the equation of time is POSITIVE/NEGATIVE (circle one). Below are found the approximate equations of time to the nearest minute for the first day of each month

Jan 1: - 3 Apr 1: - 4 Jul 1: - 3 Oct 1: +10

Feb 1: -13 May 1: + 3 Aug 1: - 6 Nov 1: +16

Mar 1: -12 Jun 1: + 3 Sep 1: - 1 Dec 1: +11

On Jan 1st the apparent sun transits the meridian about three minutes after the mean sun.

22. A very famous method of graphically depicting the equation of time is through a "figure 8" shaped diagram called an _______________.

LOCAL TIME

23. Until this point in our discussion, apparent solar time and mean solar time have been determined from the observer's meridian. There has been no attempt to standardize these times into zones. They are strictly local in nature, dependent upon one's _______________ position on earth.

24. Therefore if an individual moved west (causing the sun to move toward the east), time would get EARLIER/LATER (circle one). Just the opposite would be true if you moved east.

25. Since the sun returns to the same meridian in a 24 hour time period, it appears to complete a full circle (360 degrees) during this interval. Since there are 1440 minutes in a day, _______________ minutes of time are represented by each degree of sun movement across the sky. Another way of stating this concept is to say that the earth rotates ______________ degree every four minutes.

26. An astronomer notes the local time at his position of 104 degrees west longitude as 15:40 (3:40 p.m.). In Allentown, PA, located at 75 degrees west longitude, the local time would be _______________. Allentown is 29 degrees to the WEST/EAST (circle one) of 104 degrees west. When you go east, local time gets _______________. When you go west, local time gets _______________. For each longitude degree traveled east or west, local time changes by _______________

27. Greenwich, England is a reference position for calculating a worldwide time system based upon the local mean time at one meridian. Greenwich corresponds to a longitude position of _______________. The time at Greenwich can be referred to as Greenwich Mean Time or U T .

28. Local mean time = UT + longitude (east of Greenwich)

UT - longitude (west of Greenwich)

It is 00:12 UT (in Greenwich). The local time in Pittsburgh, Pennsylvania situated at 80 degrees west longitude would be _______________. If it were January 1st in Greenwich, the date in Pittsburgh would be _______________.

29. It is 00:12 (in Greenwich). The local time in Cairo, Egypt located at 31 degrees east longitude would be ______________. If it were January 1st in Greenwich, the date in Cairo would be _______________.

30. The difference in local time between any two places on the earth is simply their difference in _______________.

TIME ZONES

31. In the latter part of nineteenth century as travel by train became more common, confusion in scheduling occurred because it was necessary to consider the differences in local times (due to longitude changes) between rail stops as well as the time it would take to cover the distances between towns. The solution was the creation of time _______________ in 1883 where all locations would adhere to the ____________________ time of a particular standard meridian.

32. Although the boundaries of these time zones are legislated, their centers correspond to whole hour angles east and west of Greenwich. To the east of Greenwich there are _______________ standard time zone, but to the west there are only _______________. Since Greenwich is itself a standard time zone, this makes 24 in total.

33. In North America there are six standard time zones. From east to west they are named _______________, _______________, _______________, _______________, _______________, and _______________, (includes all of this state). Universal Time -10 hours represents the standard time in _______________.

34. Going east or west eventually brings about the addition or subtraction of a day at the location of the ______________________________. This line of demarcation at approximately 180 degrees, jogs back and forth so as not to bisect any land mass.

35. Crossing the IDL in a westward direction will cause the date to flip AHEAD/BEHIND (circle one) by one day.

36. You are on board a ship bound for Honolulu and have just brought in the New Year. The place is a mess with confetti, pompoms, streamers, broken balloons, and the like. The captain announces over the loudspeaker that the ship has just crossed the International Date Line. The passengers cheer, but you notice that the waiters look disappointed. Why? __________________________________________________________________________

__________________________________________________________________________

37. Many governments legislate the addition of an extra hour to the standard time of a zone during the summer months. This is called ____________________ time. This procedure, in effect, moves the zone one hour to the EAST/WEST (circle one). Therefore, instead of the sun rising at 4:30 a.m. and setting at 7:30 p.m., like it would in the Lehigh Valley if we were on Eastern Standard Time, the sun rises at _______________ and sets at _______________. The amount of daylight remains the same.

38. Daylight savings time brings human activities more in line with the time when the _______________ is visible.

39. Although the period of earth's rotation may seem to be uniform when compared to the extreme accuracy of atomic clocks, it is found that earth's rotational period is INCREASING/DECREASING (circle one) by about 1/1000th second per century.

40. The despinning of earth is the result of friction caused by the tidal bulge created by the moon's (differential) gravity acting on the earth. Because of earth's rotation, the tidal bulge is formed slightly AHEAD/IN BACK (circle one) of the moon's position. The effect is to _______________ the moon, causing it to spiral slowly away from earth. Since the angular momentum (total amount of spin) of the earth-moon system must be conserved, the earth's rotational period must become LONGER/SHORTER (circle one) as time goes on.

41. Since it is still the earth's rotation that we are most interested in, scientists occasionally adjust their atomic clocks by incrementing an addition _______________ second to bring their clocks in phase with the earth's rotation period.

SIDEREAL TIME

42. Solar time is based upon the repeated returns of the sun to one's local _______________. This does not correspond to the rotation period of the earth which is ________________ (hours and minute).

43. During the period of one earth rotation, the earth moves about one degree in a counterclockwise direction around the sun. This shifts the sun about one degree _______________ (direction as seen on a clock face) during this interval. With respect to direction among the stars, the sun moves EASTWARD/WESTWARD (circle one).

44. Therefore in order to return the sun back to the meridian, the earth must make one complete rotation plus continue through one degree of additional rotation to return the sun back to the meridian. This extra time takes approximately _______________.

45. However for a star, exactly one earth rotation will return it to exactly the same location in the sky. This is important for astronomical observations, for it gives astronomers an easy method for locating objects in the sky if they allow their observatory clocks to keep _______________ time rather than solar time.

46. Just like the 24 hours of clock time we use during the day, astronomers divide the rotation period of the earth into 24 hours of _______________ time. Each corresponding unit (hour, minute, second) is SHORTER/LONGER (circle one) than its corresponding period of clock time.

47. Solar is to sun as sidereal is to _______________! A star transiting (crossing) the meridian will be returned to the meridian in a period of one earth rotation or one _______________ day. In clock time this interval equals ____________________.

48. Sidereal time has a direct relationship with one of the components of the equatorial coordinate system called ____________________.

49. In the equatorial coordinate system the origin occurs at the ____________________ which is located at the intersection of the ecliptic and celestial equator. This is the position of the sun at the first moment of spring.

50. The hour angle that the vernal equinox is west of an observer's local meridian represents the _______________ time at that observer's position.

51. The hour angle of the vernal equinox also equals the circle of ____________________ crossing an observer's local meridian. When an observer knows the sidereal time at any particular clock time it automatically gives him/her the ____________________ meridian transiting due south and the objects which are visible in the sky at that moment.