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Mean Time / Apparent Time

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Mean Time / Apparent Time

Presented By: Mate O

- Navigational Astronomy Lecture 1 & 2
- Mean Time / Apparent Time Lecture 3
- Time Zones, Zone Description, Chronometer Time Lecture 4
- The Earth, Celestial, And Horizon Coordinate System Lecture 5 & 6
- The Spherical Triangle Lecture 7
- Circle of Equal Altitude Intercept Lecture 8
- Time Diagram, Right Ascension Lecture 9
- The Nautical Almanac, Finding GHA, LHA, and Dec.Lecture 10 & 11
- Instruments For Celestial NavigationLecture 12
- Sight Reduction of the Sun, Stars, Planets, MoonLecture 13- 15
- Plotting and Advancing / Retarding the Assumed PositionLecture 16
- Calculating Time of Meridian Passage (LAN) Lecture 17
- Calculating Latitude at Meridian PassageLecture 18
- Calculating Time of Sunrise/ Sunset/ Twilight Lecture 19
- Star Shooting Schedule / Pub. 249 Lecture 20
- Azimuth and AmplitudesLecture 21 – 24
- Polaris – Azimuth and Latitude ByLecture 25
- Star – Finder – Stars, Planets, Selecting the 3 best Stars Lecture 26
- The Complete Day’s Work Lecture 27 & 28

The Earth’s Rotation On Its Axis Causes The Sun And Other Celestial Bodies to Appear to Move Across the Sky From East to West Each Day

Time

- Solar Time
- Time Based Upon the Earth’s Rotation in Relation to the Sun
- One Rotation Takes 24 Hours

- Sidereal Time
- Time Based Upon the Earth’s Rotation in Relation to the Stars
- One Rotation Takes 23 Hours 56 Minutes

- The Reason for the Difference is the Use of Different Reference Points. Because the Earth Is Revolving Around the Sun and Not the Stars, It Takes the Earth 4 Extra Minutes Each Day to Rotate to the Sun Because It Has Moved in Its Orbit Around the Sun. This Is Not the Case for the Earth’s Rotation Relative to the Stars. Which We Can Consider an Infinite Distance Away

Considered Infinite Distance

S

E

Parallel Rays of Light

Insignificant Angle

E

Needs To Rotate 4 Extra Minutes For Sun To Be Directly Over Head Again, Not So For The Stars

Time

Considered Infinite Distance

S

E

Insignificant Angle

E

Needs To Rotate 4 Extra Minutes For Sun To Be Directly Over Head Again Not So For The Stars

Mean Sun vs. Apparent Sun

- Two Suns?
- Yes and No. There Is Only One Real Sun, It’s the One We Can Seeand is Referred to As the “Apparent Sun”

- Mean Sun
- The Mean Sun Was Created to Keep Track of Time Because the Apparent Sun Does Not Appear to Move at a Constant Speed Across the Sky

In a 24 Hour Day the Sun* Should Move at a Constant Rate of 15° of Longitude Every Hour. 15° X 24 Hours = 360°

But Because the Earth’s Rotational Speed, and Revolution Speed Around the Sun Are Not Constant, and Because the Path of the Real Sun Is Not ALong the Celestial Equator but Rather Along Its Ecliptic the Apparent Sun Does Not Move at a Constant Rate

* Note the Sun Is Not Moving - It’s the Earth’s Rotation Which Is Causing the Sun to Appear to Move

Solution

Solution:

Create A Fictitious Sun Which Moves at a Uniform Speed Equal to the Average Speed of the Apparent Sun Along the Ecliptic. This Provides a Uniform Measure of Average Apparent Time = 15° Per Hour

Mean Sun

Apparent Sun

Fictitous

Constant Moving15° Per Hour

Real

Not Constant – Can Be Ahead or Behind The Mean Sun

Equation of Time: Ex. #1

The Equation of Time is the Time Difference Expressed in Minutes and Seconds That the Apparent Sun Is Ahead or Behind the Mean Sun. The Difference Never Exceeds About 16.4 Minutes.

* The Equation of Time and the Time of Meridian Passage of the Apparent Sun Can Be Found in the Daily Pages of the Almanac

Central Meridian

Equation of Time8m 10 sec.

1200 – 00s

+ 8-10s

Ans. 1208-10s

Mean Sun

Apparent Sun

The Mean Sun Will Be Over The Central Meridian At 1200 Always

The Apparent Sun Is Lagging Behind by 8m 10s. So Meridian Passage of the Sun Will Be 1208 - 10s

Equation of Time: Ex. #2

The Equation of Time Is 6m – 30 Sec. The Apparent Sun Is Ahead or (Leading) the Mean Sun. What Will Be the Time of the Sun’s Meridian Passage?

Central Meridian

1200 – 00s

-6-30s

Ans. 1153-30s

ApparentSun

6m 30 sec.

Mean Sun

The Mean Sun Will Be Over the Central Meridian at 1200 Always

The Apparent Sun Is 6m 30s Ahead of the Mean Sun, So It Will Cross Before 6m 30 Sec. Before 1200

Equation of Time: Ex. #3

Determine the Time of Upper and Lower Meridian Passage of the Sun on Jan 1, 1981

Upper Passage

12h

1200 – 00s+3m 38sec

Ans. 1203-38

Behind

Lower Passage

00h

0000 – 00s+3m 24sec

Ans. 0003 – 24s

Behind

- Determine the Time of Upper and Lower Meridian Passage of the Sun on Dec 25, 1981

Upper Passage

1200 – 00s+0m07s

Ans. 1200-07

* The Dividing Line Separates Between When the Sun Is Ahead or Behind the Mean Sun. We Know From This Diagram That All the Equations of Time Below the Dividing Line Are Behind Because Mer. Pass. On Dec 23rd Is 1159.

* Note How the Almanac Rounds Mer. Pass. To the Nearest Minute

Lower Passage

0000 – 00s+0m 08sec

Ans. 2359 – 52s

If It Takes the Earth 24 Hours to Rotate 360° Then We Can Subdivide the Earth’s Rotation Into Time/Arc Equivalents

Converting Time to Arc

1 Day=24 Hours=360° Rotation (Arc)

60 Min=1 Hour=15° Arc

4 Min=1° Arc=60’ Arc

60 Sec=1 Min=15’ Arc

4 Sec=1’ Arc=60” Arc

1 Sec=15” Arc=.25’ Arc

Therefore, Any Time Interval Can Be Expressed As an Equivalent Amount of Rotation, and Vice Versa

Converting Arc to Time: Ex. #1

Convert 14h 21 m 39s to Arc

- 14h x 15=210° 00’ 00”
- 21m / 4=005° 00’ 00” (remainder 1m)
- 1m x 15=000° 15’ 00”
- 39s / 4=000° 09’ 00” (remainder 3s)
- 3s x 15=000° 00’ 45”
- Total14h 21m 39s = 215° 24’ 45” Arc

Converting Arc to Time: Ex. #2

Convert 334° 18’ 22” to Time Units, Using the Nautical Almanac Arc To Time Conversion Table

Arc Time

334° 00.00m= 22h 16m 00s

18.25m=00h 01m 13s

334° 18’ 22” = 22h 17m 13s

Converting Arc to Time

060°W

045°W

030°W

1100 ZT

1200 ZT

1300 ZT

Time and Longitude

- If the Sun Is Directly Overhead of an Observer Then 1 Hour Later the Sun Would Be 15° West of the Observer (Because the Earth Has Rotated)
- Therefore, Places to the East Have Later Times Than the Observer and Places to the West Have Earlier Times
- The Difference in Time Between Two Places Is Equal to the Difference in Longitude Between Their Meridians, Expressed in Units of Time Instead of Arc