Shadowless Moments
Do you know what Lāhainā Noon is? It is also known as a zero-shadow
day.
In Kerala, this year, we
have shadowless days from the 10th to the 23rd of April 2024 and the 19th of
August to the 1st of September 2024.
10-04-2024 was a zero-shadow day for people living in Thiruvananthapuram,
Kerala, India.
In this article, I included a brief explanation of this phenomenon.
I took three objects to observe the variations of shadow between 11.35
am - 12.40 pm on 10th April 2024. I took the side-view and front-view images to
observe the shadow. At around 12.25, shadows disappeared, and it was under the
object itself. After 12.30, I could see the shadow on the left side of the
objects.
It is a
semi-annual tropical solar phenomenon, and we can observe it twice a year for
locations in the tropics.
The light rays will fall
vertically relative to an object on the ground and cast no observable shadow
[2] when they reach overhead
We can observe a zero-shadow day twice a year.
- Earth's axial tilt has a link to the zero-shadow day, which causes the planet to be at its zenith, or directly overhead, at specific latitudes.
- The Tropic of Cancer experiences it at the summer solstice, while the Tropic of Capricorn witnesses it during the winter solstice.
The date varies by location. [3] The Bishop Museum in Hawaiʻi coined the
term Lāhainā Noon. [4]
Details
The subsolar point travels through the tropics. Locations between the Tropic of Cancer and the Tropic of Capricorn receive the sun's direct rays overhead before and after the summer solstice.
Lāhainā Noon can occur anywhere from 12:16 to 12:43
noon. At that time, objects that stand straight up cast no outward shadow.
Chosen in a contest sponsored by the Bishop Museum
in the 1990s, Lāhainā Noon was the selected appellation because lā
hainā (the old name for Lāhainā, Hawaii) means cruel sun in the
Hawaiian language. [7] The ancient Hawaiian name for the event was kau
ka lā I ka lolo, which translates as the sun resting on the
brain.[5][8]
In popular culture
- Honolulu possesses a unique sculpture called Sky Gate, created by artist and landscape architect Isamu Noguchi.
- Most of the year, except during Lāhainā Noon, it makes a curvy, twisted shadow on the ground.
- During Lāhainā Noon, the height-changing ring casts a perfect circular shadow on the ground. [13]
- Axial tilt is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane. [22]
- It differs from orbital inclination.
- Two axes point in the same direction, then the axial tilt is zero degrees.
The rotational axis is the imaginary line that passes through the North and the South Pole.
- Earth's orbital axis is the line perpendicular to the imaginary plane through which it revolves around the Sun. Earth's axial tilt is the angle between these two lines.
Throughout an orbital period, the tilt usually does not change considerably, and the orientation of the axis remains the same relative to the background of stars.
- Because of this, one pole is pointed more toward the Sun on one side of the orbit and away from the Sun on the other side- cause of the seasons on Earth.
1 Based on the planet's north pole,
defined by the direction of Earth's north pole.
2 Based on the planet's positive pole,
defined by the right-hand rule.
- The
International Astronomical Union (IAU) defines the north pole of
a planet as that which lies on Earth's north side of the invariable plane
of the Solar System;[2] under this system, Venus is tilted 3° and rotates
retrograde, opposite that of most of the other planets. [23][24]
- The IAU also uses the right-hand rule to define a positive pole[25] [26]to determine orientation. Using this convention, Venus is tilted 177° ("upside down") and rotates prograde.
The ancient Greeks had good obliquity measurements since about 350 BCE when Pytheas of Marseilles measured the shadow of a gnomon at the summer solstice. [27] About 830 CE, the Caliph Al-Mamun of Baghdad directed his astronomers to measure the obliquity, and the Arab world used the result for many years. [28] In 1437, Ulugh Beg determined the Earth's axial tilt as 23°30′17″ (23.5047°). [29]
- During the Middle Ages, it was a belief that both precession and Earth's obliquity oscillated around a mean value, with a period of 672 years, an idea known as trepidation of the equinoxes.
Perhaps this was incorrect [30], and the first to realize that the obliquity was decreasing at a relatively constant rate was Fracastoro in 1538. [31] The first accurate, modern, western observations of the obliquity were probably those of Tycho Brahe from Denmark in about 1584.[32] The observations by several others, including al-Ma'mun, al-Tusi,[33] Purbach, Regiomontanus, and Walther, could have provided similar information.
Seasons
The axis of Earth remains oriented in the same direction concerning the background stars regardless of where it is in its orbit.
Earth's axis remains tilted in the same direction
concerning the background stars throughout the year (regardless of where it is
in its orbit) due to the gyroscope effect.
- One pole will be directed away from the Sun at one side of the orbit, and half a year later, this pole will be towards the Sun.
- It is the reason for Earth's seasons.
- Summer occurs in the Northern Hemisphere when the north pole is toward the Sun.
- Variations in Earth's axial tilt can influence the seasons and are likely a factor in long-term climatic change
Oscillation
Short term
We can calculate the exact angular value of the
obliquity by observation of the motions of Earth and planets over many years.
Astronomers produce new fundamental ephemerides as the accuracy of observation
improves and as the understanding of the dynamics increases, and from these
ephemerides, including the obliquity, are derived.
Annual almanacs are published listing the derived
values and methods of use. Until 1983, mean obliquity for any date was
calculated based on the work of Newcomb, who analyzed the positions of the
planets until about 1895.
ε = 23°27′8.26″ − 46.845″ T − 0.0059″ T2
+ 0.00181″ T3
where ε is the obliquity,
and T is the tropical centuries from B1900.0 to the date in
question. [34]
From 1984, the Jet Propulsion Laboratory's DE
series of computer-generated ephemerides took over as the fundamental ephemeris
of the Astronomical Almanac. Obliquity based on DE200, which analyzed
observations from 1911 to 1979, was calculated:
ε = 23°26′21.448″ − 46.8150″ T − 0.00059″ T2
+ 0.001813″ T3
where hereafter T is Julian
centuries from J2000.0.[35]
They updated JPL's fundamental ephemerides
continually. For instance, according to the IAU resolution in 2006 in favor of
the P03 astronomical model, the Astronomical Almanac for 2010
specifies:[36]
ε = 23°26′21.406″ − 46.836769″ T − 0.0001831″ T2
+ 0.00200340″ T3 − 5.76″ × 10−7 T4 − 4.34″ × 10−8 T5
These expressions for the obliquity are for high
precision over a relatively short period, perhaps ± several centuries. [37] J.
Laskar computed an expression to order T10 good to 0.02″ over 1000
years and several arcseconds over 10,000 years.
ε = 23°26′21.448″ − 4680.93″ t − 1.55″ t2
+ 1999.25″ t3 − 51.38″ t4 − 249.67″ t5 −
39.05″ t6 + 7.12″ t7 + 27.87″ t8 +
5.79″ t9 + 2.45″ t10
where here t is multiples of
10,000 Julian years from J2000.0.[21]
These expressions are for the so-called mean obliquity,
free from short-term variations. Periodic motions of the Moon and Earth in its
orbit cause much smaller (9.2 arcseconds) short-period (about 18.6 years)
oscillations of the axis of Earth, known as nutation, which adds a periodic
component to Earth's obliquity. [38][39] The true or
instantaneous obliquity includes this nutation. [40]
Long term
Studies are there for the long-term changes in
Earth's orbit and its obliquity using numerical methods to simulate Solar
System behavior over several million years. For the past 5 million years,
Earth's obliquity has varied between 22°2′33″ and 24°30′16″, with a mean period
of 41,040 years. This cycle is a combination of precession and the term in the
motion of the ecliptic. For the next 1 million years, the cycle will carry the
obliquity between 22°13′44″ and 24°20′50″.[41]
- The moon has a stabilizing effect on Earth's obliquity.
- However, more recent numerical simulations [44] made in 2011 indicated that obliquity might not be unstable even in the absence of the moon.
- It varies only by about 20–25°.
The position of the Sun in the sky is a function of:
- Time and the geographic location of observation on Earth's surface.
- Earth's rotation about its axis causes diurnal motion so that the Sun appears to move across the sky in a Sun path that depends on the observer's geographic latitude.
- The time when the Sun transits the observer's meridian depends on the geographic longitude.
To find the Sun's position for a given location at
a given time, one may proceed in three steps as follows:[47][48]
1.
Calculate the Sun's position in
the Wecliptic coordinate system,
2.
Convert to the equatorial
coordinate system.
3.
Convert to the horizontal
coordinate system for the observer's local time and location.
It is the coordinate system used to calculate the
position of the Sun in terms of solar zenith angle and solar azimuth
angle.
To depict the Sun's path, we can use these two
parameters. [49]
This calculation is significant in astronomy,
navigation, surveying, meteorology, climatology, solar energy, and sundial
design.
Earth
Earth's orbital plane is known as the ecliptic plane, and Earth's tilt is known to astronomers as the obliquity of the ecliptic, being the angle between the ecliptic and the celestial equator on the celestial sphere. [6] Its notation is by the Greek letter ε.
- Earth currently has an axial tilt of about 23.44°.[7]
- This value remains about the same relative to a stationary orbital plane throughout the cycles of axial precession. [8]
- But the ecliptic (i.e., Earth's orbit) moves due to planetary perturbations, and the obliquity of the ecliptic is not a fixed quantity.
- It is decreasing at about 46.8″ [9] per century.
What is the subsolar point?
- The subsolar point on a planet is the point where the Sun's rays strike the planet perpendicular to its surface (position is directly overhead). [1]
Imagine you are on a planet with an orientation and
rotation same as that of the Earth.
Then, the subsolar point will appear to move
westward at 1600 km/h speed. However, it will also move north and south between
the tropics over a year.
- The subsolar point meets the Tropic of Cancer on the June solstice and the Tropic of Capricorn on the December solstice.
- The subsolar point crosses the equator twice during equinoxes in March and September.
- It happens twice yearly, once in each hemisphere (Northern and Southern). [1]
The summer solstice occurs during the hemisphere's
summer. In the Northern Hemisphere, this is the June solstice (20 or 21 June).
In the Southern Hemisphere, this is the December solstice (21 or 22 December).
Since prehistory, the summer solstice has been a significant time of year in
many cultures, and it is the season of festivals and rituals. [1]
- Earth's maximum axial tilt toward the Sun is 23.44° On the summer solstice.[7]
- Likewise, the Sun's declination from the celestial equator is 23.44°.
- The zenith [11] is an imaginary point directly above a particular location on the celestial sphere.
- The zenith is the highest point on the celestial sphere.
Angles and planes of a celestial sphere (image source: Wikipedia)
Origin
The word zenith derives from an
inaccurate reading of the Arabic expression samt al-ras, meaning
direction of the head or path above the head. [12]
The shadows of trees are the shortest on Earth when the Sun is directly overhead (at the zenith) (image source: Wikipedia)
- The term zenith sometimes means the highest point, reached by a celestial body on its daily apparent path around a point. [14]
In a scientific context, the zenith is the
direction of reference for measuring the zenith angle, the angle between a
direction of interest (e.g. a star) and the local zenith - that is, the
complement of the altitude angle.
- The Sun reaches the observer's zenith when it is 90° above the horizon, and this only happens between the Tropic of Cancer and the Tropic of Capricorn.
At a given location during the day, the Sun reaches
its nadir also, at the antipode of that location, twelve hours from solar noon.
- In astronomy, with the horizon perpendicular to the zenith, the altitude in the horizontal coordinate system and the zenith angle are complementary angles.
- We can determine the astronomical meridian by the zenith. [18]
Meridian
- In astronomy, the meridian is the great circle passing through the celestial poles, the zenith and nadir of an observer's location.
A zenith telescope is designed to point straight up
at or near the zenith and used for precision measurement of star positions, to
simplify telescope construction, or both. The NASA Orbital Debris Observatory
and the Large Zenith Telescope are zenith telescopes that use liquid mirrors.
These telescopes could only point straight up. [20]
- Meridian contains the north and south points on the horizon and is perpendicular to the celestial equator and horizon.
- We can determine the celestial and geographical meridians by the pencil of planes passing through the Earth's rotation axis.
- For a location not at a geographical pole, there is a unique meridian plane in this axial pencil through that location.
- The intersection of this plane with Earth's surface is the geographical meridian, and the intersection of the plane with the celestial sphere is the celestial meridian for that location and time.[19][21]
Analemma
- It shows an image of the Sun's apparent motion during a year.
- An analemma is a graph of the Sun's declination, usually plotted vertically against the equation of time, plotted horizontally.
- Usually, the scales are equal distances on the diagram, representing equal angles in both directions on the celestial sphere.
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37. ^ Explanatory Supplement (1961), sec. 2C
38. ^ "Basics of Space Flight, Chapter 2". Jet Propulsion Laboratory/NASA. 29 October 2013. Retrieved 26 March 2015.
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