1. Eclipses Twice A Month? Animation
PHYS Astronomy
Eclipses Twice A Month? Animation
Why don’t we have eclipses every new and full Moon?

2. Moon’s orbit tilted 5° to ecliptic plane
PHYS Astronomy
Moon’s orbit tilted 5° to ecliptic plane
- Crosses ecliptic plane only at the two nodes
- Eclipse possible only when full/new occur near nodes

3. PHYS Astronomy
Moon’s Orbital Tilt

4. Conditions for Eclipses
PHYS Astronomy
Conditions for Eclipses
The moon’s orbit is inclined against the ecliptic by ~ 50.
A solar eclipse can only occur if the moon passes a node near new moon.
A lunar eclipse can only occur if the moon passes a node near full moon.

5. PHYS Astronomy
Eclipse Seasons
Eclipse season - a period in a given year during which the Earth-Sun line falls near the line of nodes of the Moon’s orbit, so that lunar and solar eclipses can take place - happens twice a year

6. PHYS Astronomy
Eclipse Seasons
If New Moon takes place within about 17° of a node, then a solar eclipse will be visible from some location on Earth.
The Sun makes one complete circuit of the ecliptic in days
average angular velocity is 0.99° per day.
takes 34.5 days for the Sun to cross the 34° wide eclipse zone centered on each node.
Moon's orbit with respect to the Sun has a mean duration of days so there will always be one and possibly two solar eclipses during each 34.5-day interval when the Sun passes through the nodal eclipse zones.
These time periods are called eclipse seasons

7. Moon’s Orbital Precession Animation
PHYS Astronomy
So eclipses should be easy to predict - every six months at nodes when Moon crosses the ecliptic. However, the Moon’s orbit also precesses making prediction difficult.
Moon’s Orbital Precession Animation
Eclipse seasons recur every days (~19 days earlier each year) and last about 24 days for lunar eclipses and about 37 days for solar eclipses.

8. PHYS Astronomy
Predicting Eclipses
Solar eclipse one of the most awe inspiring events in human history - difficult for ancients to predict because of orbital precession and narrow region of occurrence.
Surviving records shown Babylonians and tancient Chinese were able to predict solar eclipses as early as 2500 BC.
In China, solar eclipses thought to be associated with emperor’s health and success - failing to predict one meant putting him in danger. Legend has it that 2 astrologers, Hsi and Ho, were executed for failing to predict a solar eclipse. Historians and astronomers believe that the eclipse that they failed to forecast occurred on October 22, 2134 BC, which would make it the oldest solar eclipse ever recorded in human history.
First historical solar eclipse date known to be predicted - May 28, 585 BC.But Greek historian Herodotus wrote that Thales of Milete predicted an eclipse in a year when the Medians and the Lydians were at war. Date thus precisely known. Opposing armies in Turkey massing for battle - eclipse frightened them so much, they put down their weapons and signed a treaty. Used for dating of historical events.

9. PHYS Astronomy
Saros Cycle
Combination of changing dates of eclipse seasons (Lunar orbital precession) and 29 1/2-day cycle of lunar phases - solar eclipses occur in 18 year, 11 1/3 day cycle - saros cycle.
Eclipses repeat
- after one saros cycle, moon and nodes of its orbit return to same place wrt the sun
- one saros contains 223 lunar months
- changes location on Earth because of the extra 1/3 day - moves 8 hours of longitude west of the previous eclipse
- repeats in same location after 3 saros cycles

10. Paths of Total Solar Eclipses
PHYS Astronomy
Paths of Total Solar Eclipses
Paths of same color represent successive saros cycles.

11. PHYS Astronomy

12. Solar Eclipses Through 2027
PHYS Astronomy
Solar Eclipses Through 2027

13. Annular Eclipse of September 1, 2016
PHYS Astronomy
Annular Eclipse of September 1, 2016

14. Total Eclipse of August 21, 2017
PHYS Astronomy
Total Eclipse of August 21, 2017

15. PHYS Astronomy
Tides
The gravitational attraction of the Moon varies as the square of the distance (Newton’s Law of Gravitation) - gravity stronger on side facing the Moon than on opposite side. The Moon pulls the ocean water towards it on facing side - creates tide - and pulls the Earth away from the ocean water on the other side - reason for tides twice a day. Time of tides varies by 50 min per day - Moon at its highest point every 24 hrs 50 min because Moon orbits Earth while Earth rotates.

16. The Sun also causes tides - why are they weaker than the Moons’?
PHYS Astronomy
The Sun also causes tides - why are they weaker than the Moons’?
Neap tides - when Moon’s and Sun’s gravitational forces work at right angles
Spring tides - when Moon’s and Sun’s gravitational forces add up

17. PHYS Astronomy
Tidal Bulge
Because the Earth rotates, friction drags the tidal bulges off of the Earth-Moon line.

18. PHYS Astronomy
Tides

19. The Moon pulls on tidal bulge - slows Earth’s rotation
PHYS Astronomy
The Moon pulls on tidal bulge - slows Earth’s rotation
The excess mass in Earth’s tidal bulge exerts a gravitational attraction on the Moon that pulls the Moon ahead in its orbit - Moon moves farther away - Conservation of Angular Momentum

20. The Tidally-Locked Orbit of the moon
PHYS Astronomy
The Tidally-Locked Orbit of the moon
The Earth also exerts tidal forces on the moon’s rocky interior.
 It is rotating with the same period around its axis as it is orbiting Earth (tidally locked).
 We always see the same side of the moon facing Earth.

21. Astronomical Time Periods
PHYS Astronomy
Astronomical Time Periods

22. Definitions of a Day Sidereal Day
PHYS Astronomy
Definitions of a Day
Sidereal Day
Time from one transit of a star across the meridian to the next.
Related to the Stars
Apparent Solar Day -
Time from one transit of sun across the meridian to the next.
From one high noon to the next
Related to the sun
Mean Solar Day
Time between successive transits of mean sun.
Average of apparent solar days over one year.
Defined to be 24 Hours

23. PHYS Astronomy
Sidereal Day
Sidereal - “related to the stars” - the time it takes for any star to make a circuit of the sky - about 23 hours 56 minutes. Measure of the Earth’s rotation - varies about 1 second in 45,000 years. Today defined relative to an ensemble of extra-galactic radio sources.

24. PHYS Astronomy
Solar Day
The time it takes for the Sun to make one circuit around the local sky - length varies over course of year (up to 25 seconds longer or shorter) but averages 24 hours.

25. Why is a Sidereal Day Shorter than a Solar Day?
PHYS Astronomy
Why is a Sidereal Day Shorter than a Solar Day?
One full rotation represents a sidereal day - but while orbiting the Sun, Earth travels in its orbit (about 1 degree per day). So the Earth must rotate slightly farther to point back at the Sun - solar day.

26. PHYS Astronomy
Mean Solar Day
Length of solar day varies over course of year - averages about 24 hours - mean solar day.
Two reasons for variance.:
1. Earth's orbit is not a perfect circle - it’s an ellipse - Earth moves faster when it is nearest the Sun and slower when it is farthest from the Sun.
2. Earth's axial tilt - the Sun appears to move at an angle to equator during the year - apparently moves fast or slow depending on whether it is apparently far from or close to the equator. Apparent solar days are shorter in March and September than they are in June or December.
Solar day may differ from a mean solar day by as much as nearly 22 s shorter to nearly 29 s longer. Because many of these long or short days occur in succession, the difference builds up to as much as nearly 17 minutes early or a little over 14 minutes late. Discrepancy called Equation of Time - leads to analemma - shape of Sun’s yearly path in the sky.

27. PHYS Astronomy
The Analemma
Images of the Sun at same time at day intervals over the course of a year:
Altitude variation due to annual north-south oscillation of the Sun’s declination angle - axial tilt
East-west spread due to variation in Sun’s motion wrt to the stars - axial tilt and ellipticity
Distortion of figure 8 due to ellipticity of Earth’s orbit.
In northern hemisphere - if Sun’s position east of where your watch indicates it would be, Equation of Time is negative. If Sun to the west, the Equation of Time is positive.

28. PHYS Astronomy
The analemma shows where the sun is at any given time of day, on any day of the year - it rises, crosses the sky, and sets. From northern latitudes, the analemma slants upward and to the left at "sunrise" and upward and to the right at "sunset". (The analemma is vertical at local noon.)
Why do the earliest sunset, latest sunrise, and shortest day of the year occur on different dates?

29. PHYS Astronomy
Latest sunrise occurs when the last part of the analemma rises - this doesn’t happen when the sun is "at the bottom" of the analemma (December 21st) but a few days later (January 3th). Earliest sunset occurs when the first part of the analemma sets below the western horizon. Again, occurs a few days (December 8th) before the sun reaches "the bottom" of the analemma (December 21st). Same reasoning for solstice.

30. Often printed on globes and…
PHYS Astronomy
Often printed on globes and…
Turned vertical, the analemma can be used to determine solar declination and Equation of Time
sundials