Astronomy

Given a date obtain latitude and longitude where is the sun zenith

Given a date obtain latitude and longitude where is the sun zenith



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Searching is easy to find terminator line (frontier between day and night) or the position of the sun in the sky given a position on the earth and a time; but I can't find how to obtain where is the zenith of the sun given a date (and time).

I need to obtain the center of the illuminated zone of the earth (latitude and longitude) at a given time. (Well, actually I need the opposite, the Nadir, but with one you can calculate easily the other).

Any knows the function?

Thank you.


What you're looking for is the latitude and longitude of the subsolar point.

Calculating it with accuracy is somewhat complicated. Here is a python library that has routines to do it for you: http://rhodesmill.org/pyephem/

You could also possibly query this information from other sites.

If you really want to work it out on your own, I suggest "Spherical Astronomy" by Robin M. Green published by Cambridge University Press as a starting point.


Javascript calculations here . Now you just need to port.

Edit: the calculations are in the source code of this page now.

Edit: here is a direct link to the source code. No need to go hunting through the html.

I know this post is old, but in case anyone is still looking.

CoordinateSharp is available as a Nuget package. It's a standalone packge that can handle sun as well as moon times.

It assumes DateTimes are always in UTC.

Lastly, you may need to reference the Celestial objects Sun/Moon .Condition if a date returns null. This occurs when the sun is up/down all day.

The library has changed dramatically since this post. It can now handle local times as well.

I used NAA javascript and c# to create this library in C#.

I tested it against these two sites, and it shows time exactly like the sites do.

This API seems to work for me:

The accepted answer for this was a JavaScript implementation, which didn't suit my application because I needed to do the calculation in C#.

If I round seconds to the nearest minute, the C# implementation's sunrise and sunset times match the corresponding values displayed on timeanddate.com, including cases of daylight savings. The code is a bit overwhelming though (unless you'd like moon phase data also), so I'll be refactoring it to do specifically what I require now the numbers are correct.

I have tested this nuget package in UWP.

The documentation is a bit sketchy, and is here:

You can use this to get the sunrise, given

la = latitude and lo = longitude for your area:

You can install it in Visual Studio using the PM manager

or by looking up SolarCalculator in the "Manage NuGet Packages" Visual Studio library.

VB.Net version of dotsa's answer, which can also determine time-zones automatically.

Output (checked by watching the sunset this evening):

I'm using this to wright a ruby script that is still in the making. I'm having trouble understanding the multi-part julian dates.

One thing that is clear is that you should go for exact solar transit time. Then subtract and add the semi_diurnal_arc = acos(cos_omega) which is based upon your latitude and the solar declination. Oh! And be sure to include solar center and earth refraction. It seems this earth is quite the magician.

Another good JS implementation is suncalc.

The number of code lines is manageable, so porting to other languages (C#) is certainly possible.

I've made a quick Python script to do that : SunriseSunsetCalculator

I have yet to wrap it inside a class but it may be useful for others.

Edit : Open source is awesome, since committing the basic script, someone wrapped it in a module and another one added a cli interface! Thanks to mbideau and nfischer for their contributions!

You need a formula which includes the equation of time to allow for the eccentric orbit of the Earth moon system around the sun. You need to use coordinates with proper datum points such as WGS84 or NAD27 or something like that. You need to use the JULIAN calendar and not the one we use on a daily basis to get5 these times right. It is not an easy thing to guess within a second of time. Id like to have the time at my location where the shadow length is equal to the whatever height. this should happen twice per day when the sun is elevated 60 degrees above the horizon before and after high noon. Also, as far as I understand, you just need to add exactly one day per year to get sidereal time so if you like increase your clock frequency X 366.25/365.25 you might now have a sidereal clock instead of a civil clock . "MATH is the LANGUAGE in which someone powerful has written the universe"

If you prefer an external service you could use this nice and free sunrise and sunset times API: http://sunrise-sunset.org/api

I have been using it for several projects and it works very well, data seems to be very accurate. Just do an HTTP GET request to http://api.sunrise-sunset.org/json

Accepted Parameters:

  • lat: Latitude in decimal degrees. Required.
  • lng: Longitude in decimal degrees. Required.
  • date: Date in YYYY-MM-DD format. Also accepts other date formats and even relative date formats. If not present, date defaults to current date. Optional.
  • callback: Callback function name for JSONP response. Optional.
  • formatted: 0 or 1 (1 is default). Time values in response will be expressed following ISO 8601 and day_length will be expressed in seconds. Optional.

The response includes sunrise and sunset times as well as twilight times.

and this was a project that I did for Planet Source Code long ago but luckily I saved it elsewhere because that site lost data.

Now for a brief explanation of the technique to do that.

First for any day you need true solar noon or transit for your location.

That takes into account your local longitude. It may be converted to a time just by dividing it by 15.

That is how much time later you are from Zulu zone time or zero longitude.

That starts at 12:00 PM or Noon.

And on your time calculated from the longitude.

Now the hard part. You need a way to calculate the Equation of Time.

That is a time difference caused by Earth tilt and orbit around the Sun.

This guy has some books that a lot of people go by or buy. :-D https://en.wikipedia.org/wiki/Jean_Meeus

Use your first calculation for your mean solar transit and calculate a JDN. https://en.wikipedia.org/wiki/Julian_day

This gets used by all the angle formulas as a time in Julian century https://en.wikipedia.org/wiki/Julian_year_(astronomy)

It's basically your JDN minus the epoch such as J2000 or 2451545.0 all divided by 36525.0 to give you the Julian century or t which gets used for most formula that have t as a parameter. Sometimes Julian millennia is used. In that case it's 3652500.0

The trick is to find those angle formulas that help you solve the Equation of Time.

Then you get your true solar transit and subtract the half day or add the half day of sunlight for your location. You'll find those around in the answers and the software.

Once you get something going you can check it against a search for the times or online calculators.


Geodetic Astronomy

a branch of practical astronomy, closely related to geodesy and cartography. It studies the theory and methods of determining the latitude &Phi and the longitude &lambda of a place as well as the azimuth a of the direction to a terrestrial object and the local sidereal time s from astronomical observations made during geodetic and cartographic work. Since these observations are made in the field, geodetic astronomy is often called field astronomy. The point on the earth&rsquos surface for which the latitude, longitude, and azimuth are determined by astronomical observation is called the astronomical point. Geodetic astronomy consists in the study of (1) portable astronomical instruments, (2) the theory of observation of celestial bodies and methods of determining &Phi, &lambda, a, and s, and (3) the methods of processing the data obtained from astronomical observations. Small, portable astronomical instruments are used in geodetic astronomy they make it possible to measure the zenith distance and the directions toward celestial bodies and also the horizontal angles between the different directions. The primary instruments used are a theodolite, a field chronometer, and a radio receiver for receiving time signals.

A number of methods of astronomical observation have been developed. The method to use depends on what is being determined (time, latitude, longitude, or azimuth), what celestial body is being observed (stars or the sun), and how and what kind of values are being directly measured through observations of the celestial bodies (zenith distance z, altitude h, azimuth a * , and time T of the star&rsquos transit across a given plane). The choice of any of these methods is determined by the particular problem, the accuracy of its solution, the availability of instruments, and other factors. For these calculations, the celestial coordinates of the observed celestial body, that is, its right ascension &alpha and declination &delta, are considered known they are found in astronomical annuals and catalogs of stars.

By connecting the pole PN, the zenith of point Z, and the observed celestial object &sigma on a celestial sphere (see Figure 1) by arcs of great circles, we get the so-called parallactic triangle PNZ&sigma, where the angle of vertex Z is the supplement of the azimuth a * of the celestial object and the angle of vertex PN is equal to the time angle t of the celestial object.

All methods of astronomical determination are based on the solution of the parallactic triangle after measuring its elements. Therefore, by measuring the zenith distance z of the celestial object at time T according to the chronometer and knowing the latitude &phi of a place, the time angle t of the celestial object can be determined from the expression

cos z = sin &Phi sin &delta + cos &Phi cos &delta cos t

The equation t = s - &alpha = T + u - &alpha is used to obtain the correction u to the chronometer reading and the local sidereal time s. By knowing the chronometer correction u and by measuring the zenith distance z of the celestial object, the latitude &phi of a place can be determined. The chronometer correction can be most easily determined by observing the star in the first vertical and the latitude, by observing the star in the meridian&mdashthat is, at the culmination of the celestial object. If the zenith distance of two stars located at the meridian to the north or south of the zenith of the place is measured, then,

Methods based on the measurement of small differences in the zenith distances of northern and southern stars at the meridian by eyepiece micrometers are especially convenient (Talcott&rsquos method). In the methods of corresponding heights, the points T1, and T2 of the passage of two stars across the same almucantar are noted. If &Phi is known, then u can be found (Tsinger&rsquos method), and if u is known, then &Phi can be determined (Pevtsov&rsquos method). From observations of a series of stars uniformly distributed by azimuth at a fixed altitude of 45° or 30°, &Phi and &lambda can be determined (Mazaev&rsquos method).

The azimuth a * of a celestial body is determined by measuring its time angle or zenith distance and finding the latitude &Phi of the point of observation. The azimuth a of a terrestrial object is obtained by adding the horizontal angle Q between the star and the terrestrial object to the azimuth of the observed star (usually the North Star).

The difference of the longitudes of two points is equal to the difference of the local sidereal times of these points or the difference of the chronometer corrections, referred to one physical moment by a known functioning of clocks, so that &lambda1- &lambda2, = s2 - S1 = (T + u2 - (T + u1) = u2 - u1+ T2 - T1. The longitude &lambda is calculated from the Greenwich meridian. Therefore, &lambda = s - S = u - U. The chronometer correction u with respect to the local sidereal time s is determined from stellar observation, and U with respect to Greenwich sidereal time S is determined from the reception of rhythmic radio time signals. In modern high-accuracy operations, errors in determining latitude, longitude, and azimuth do not exceed ±0.5&rdquo.


How can I polar align in the daytime?

By: The Editors of Sky & Telescope July 17, 2006 1

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I want to see a planetary transit. How can I polar align my telescope in the daytime?

Mercury transits the Sun on May 7, 2003.
Enrico Perissinotto

One good way is to use the Sun. Carefully level your mount with a bubble level and set the polar axis to the latitude of your site. Hang a weighted string from the mount (between the tripod legs) and lay a protractor on the ground,centered under the string. Rotate the protractor until the string’s shadow points to the Sun’s known azimuth (measured from north through east) plus 180°. Finally, swivel the mount until the polar axis stands directly above 0° on the protractor. You are now polar-aligned.

To obtain the Sun’s azimuth, enter the date, time, latitude, and longitude of your site into a planetarium program. Even better, make your own “protractor” using our Interactive Sky Chart. You’ll need several of these all-sky charts, preprinted for your planned viewing site. Make them for convenient times 10 minutes apart. Each sheet will show the Sun, and you can draw the north-south line (from the middle of the label “north” through the middle of the label “south”). A line from the Sun through the exact center of the north-south line gives you the direction of the shadow it will cast. Since these sky charts were designed for looking up at the sky, they have to be placed face down to make north, south, east, and west correspond to directions on the ground. So transfer the north-south line, center point,and direction of the shadow to the back of the sheet for use as a scope-aligning aid. (Put the sheet up against a windowpane and trace.)

This alignment method works any time of day, unless the Sun is very high overhead.


Snapshots


Details and Options

    SunPosition [ ] makes use of $GeoLocation and $TimeZone to determine your location and time zone. The default form of the results is in the form < azimuth , altitude >. Locations can be specified as Entity objects, assuming they represent objects with geographic coordinates, GeoGraphics primitives, or they can be latitude/longitude pairs, assuming degrees as units. Dates can be specified as a DateObject or as a string that resolves to a date. locationspec and datespec can be either individual items or lists of individual items. If datespec is a list of dates, then the results will contain TimeSeries objects. datespec can be specified as < start , end , increment >for compatibility with DateRange specifications. SunPosition [ … , func ] is used to specify the format of output when locations are specified. Possible settings for func include:
  • Automaticreturns intervals for extended locations only
    Intervalreturns intervals for all specified locations
    Meanreturns mean value for extended locations
    Minreturns minimum values for extended locations
    Maxreturns maximum values for extended locations
    StandardDeviationreturns standard deviation for extended locations
    SunPosition [ CelestialSystem->"Equatorial" ] gives the right ascension and declination of the Sun. SunPosition can accept the following options:
  • CelestialSystem"Horizon"whether to return azimuth/altitude or right ascension/declination
    AltitudeMethod"TrueAltitude"whether to take atmospheric refraction into account when computing altitude
    Possible settings for CelestialSystem include:
  • "Horizon"returns results as a pair of azimuth/altitude ( az/alt ) values
    "Equatorial"returns results as a pair of right ascension/declination ( / ) values
    Possible settings for AltitudeMethod include:
  • "TrueAltitude"assume no atmospheric refraction for altitude computations
    "ApparentAltitude"take atmospheric refraction into account for altitude computations

Given a date obtain latitude and longitude where is the sun zenith - Astronomy

SunCalc is a tiny BSD-licensed JavaScript library for calculating sun position, sunlight phases (times for sunrise, sunset, dusk, etc.), moon position and lunar phase for the given location and time, created by Vladimir Agafonkin (@mourner) as a part of the SunCalc.net project.

Most calculations are based on the formulas given in the excellent Astronomy Answers articles about position of the sun and the planets. You can read about different twilight phases calculated by SunCalc in the Twilight article on Wikipedia.

SunCalc is also available as an NPM package:

Returns an object with the following properties (each is a Date object):

Property Description
sunrise sunrise (top edge of the sun appears on the horizon)
sunriseEnd sunrise ends (bottom edge of the sun touches the horizon)
goldenHourEnd morning golden hour (soft light, best time for photography) ends
solarNoon solar noon (sun is in the highest position)
goldenHour evening golden hour starts
sunsetStart sunset starts (bottom edge of the sun touches the horizon)
sunset sunset (sun disappears below the horizon, evening civil twilight starts)
dusk dusk (evening nautical twilight starts)
nauticalDusk nautical dusk (evening astronomical twilight starts)
night night starts (dark enough for astronomical observations)
nadir nadir (darkest moment of the night, sun is in the lowest position)
nightEnd night ends (morning astronomical twilight starts)
nauticalDawn nautical dawn (morning nautical twilight starts)
dawn dawn (morning nautical twilight ends, morning civil twilight starts)

Adds a custom time when the sun reaches the given angle to results returned by SunCalc.getTimes .

SunCalc.times property contains all currently defined times.

Returns an object with the following properties:

  • altitude : sun altitude above the horizon in radians, e.g. 0 at the horizon and PI/2 at the zenith (straight over your head)
  • azimuth : sun azimuth in radians (direction along the horizon, measured from south to west), e.g. 0 is south and Math.PI * 3/4 is northwest

Returns an object with the following properties:

  • altitude : moon altitude above the horizon in radians
  • azimuth : moon azimuth in radians
  • distance : distance to moon in kilometers
  • parallacticAngle : parallactic angle of the moon in radians

Returns an object with the following properties:

  • fraction : illuminated fraction of the moon varies from 0.0 (new moon) to 1.0 (full moon)
  • phase : moon phase varies from 0.0 to 1.0 , described below
  • angle : midpoint angle in radians of the illuminated limb of the moon reckoned eastward from the north point of the disk the moon is waxing if the angle is negative, and waning if positive

Moon phase value should be interpreted like this:

Phase Name
0 New Moon
Waxing Crescent
0.25 First Quarter
Waxing Gibbous
0.5 Full Moon
Waning Gibbous
0.75 Last Quarter
Waning Crescent

By subtracting the parallacticAngle from the angle one can get the zenith angle of the moons bright limb (anticlockwise). The zenith angle can be used do draw the moon shape from the observers perspective (e.g. moon lying on its back).

Returns an object with the following properties:

  • rise : moonrise time as Date
  • set : moonset time as Date
  • alwaysUp : true if the moon never rises/sets and is always above the horizon during the day
  • alwaysDown : true if the moon is always below the horizon

By default, it will search for moon rise and set during local user's day (frou 0 to 24 hours). If inUTC is set to true, it will instead search the specified date from 0 to 24 UTC hours.


Step 3. Determine the Sun's Solstice Altitudes

Starting on the vernal equinox in the northern hemisphere on March 22 or 23, the first day of spring, the amount of time the Earth spends in light continues to increase, and the sun climbs to a progressively higher point each day. After three months, on June 22 or so, the summer solstice, the first day of summer and the so-called "longest day of the year," arrives. Because of the 23.5-degree tilt mentioned above, the sun at noon in Boston is now:

71.14 degrees above the horizon. This is about 80 percent of the way from the horizon to the zenith.

Six months later, on December 22 or 23, the autumnal equinox has come and gone and the winter solstice arrives. On this day, the first day of winter and the so-called "shortest day of the year," the situation from summer is reversed, and the sun only reaches an altitude of:

24.1 degrees. This is just over one-fourth of the distance from the horizon to the zenith.


Introduction

Captain James Cook is famous and rightly admired for the accuracy of his charts of New Zealand and the east coast of Australia made on his first Pacific voyage on the Endeavour (1768–1771). It is less well appreciated that he achieved this using methods of determining longitude that did not use accurate sea clocks reading Greenwich Mean Time. Here I describe his methods and reassess his results in the light of today's astronomical knowledge and the inherent limitations of his methods. Specifically I reassess his observation of the transit of Mercury to determine the longitude and argue that it was not as definitive as is often assumed. Cook's own records show that he did just as well with his regular methods. I also argue that the absence of a longitude value that is attributed specifically to the Mercury transit observation raises doubts about the common view of this iconic event.


3. Method 3

Kuppanna Sastry has described the third method as follows:

We can also calculate the time directly by comparing the position of Śraviṣṭhā (β Delphini) at the time when the winter solstice was 270°, with its position in 1940 A.D. (Rt. as. 20h 36m 51s = 309° 13′, and declination 15° 42′ N). In the figure: The obliquity is about 23° 40′, γ is the vernal equinox, S is Śraviṣṭhā and R its Rt. As. position. Rγ = 360° — Rt. as. = 50° 47′. RS is the declination = 15° 42′. RS′ is the continuation of SR up to the ecliptic. Now:

(i) From the rt. angled spherical triangle RγS′, it can be calculated that RS′ = 18° 46′ S′γ = 53°13′ and angle S′ = 75° 17′.

(ii) From the rt. angled spherical triangle SS′S′′, S′S′′ = 9° 53′3′′, S′′ being the celestial longitude of S in A.D. 1940. It was at 270° at the time required. Therefore, the precession is 360° — 53° 13′ — 270° + 9° 53′ = 46° 40′. Multiplying by 72, the time is 3360 years before A.D. 1940, i.e. c. 1400 B.C. If the beginning of the segment is meant and Śraviṣṭhā is about 3° inside, it is c. 1180 B.C. Since all these is subject to small errors of observation, it would be noted that we have got from all almost the same date for VJ. [1]

The date of Vedāṅga Jyotiṣa in this method is calculated by the difference in the position of the yogātarā of Śraviṣṭhā during the time of the composition of the Vedāṅga Jyotiṣa and 1940 CE. There is no need to get into the details of the mathematical calculation performed by Kuppanna Sastry, as the aim was simply to estimate the date when β Delphini was at winter solstice. Nowadays the date can be accurately determined using astronomical software.

To obtain the date when β Delphini was at winter solstice using Stellarium, it is important to note that the ecliptic longitude of the winter solstice is 270° as shown in Figure 3. The date obtained by Stellarium is circa 1350 BCE as shown in Figure 4. Kuppanna Sastry estimates that β Delphini was at winter solstice circa 1400 BCE. This matches reasonably with the date obtained by Stellarium. Kuppanna Sastry next says that the currently accepted yogatara of Śraviṣṭhā, β Delphini, was 3° inside the Śraviṣṭhā nakṣatra and based on that the winter solstice was at the beginning of Śraviṣṭhā nakṣatra in circa 1180 BCE. Kuppanna Sastry then notes that all three methods yield reasonably matching dates between 1150 BCE to 1400 BCE, the difference being attributable to observational errors.

It all seems fine until it is realized that the information given in Sūrya Siddhānta has been fudged by the interpretation of the given coordinates as polar coordinates. With the assumption of given coordinates as polar coordinates, the ecliptic longitude of the yogatārā of Śraviṣṭhā has been converted to 296⁰ 15′ from 290⁰ given in the text. This makes the yogatārā of Śraviṣṭhā nearly 3° inside the Śraviṣṭhā nakṣatra, while the evidence is clearly the opposite. Sūrya Siddhānta explicitly mentions that the yogatārā of Śraviṣṭhā nakṣatra was outside the Śraviṣṭhā nakṣatra. According to Sūrya Siddhānta (8.1–9), the yogatārā of Śraviṣṭhā nakṣatra was at the junction of 3rd and 4th quarter of Śravaṇa nakṣatra. The span of Śraviṣṭhā nakṣatra was between 293° 20′ to 306° 40′, while its yogatārā had the longitude of 290° 0′ [4]. Thus when the beginning of Śraviṣṭhā nakṣatra had a longitude of 270°, its yogatārā had the longitude of 266° 40′. Figure 5 shows that the assumed yogatārā of Śraviṣṭhā, Rotanev (β Delphini), had a longitude of 266° 40′ in circa 1590 BCE. This is clearly outside the accepted dates of the composition of Vedāṅga Jyotiṣa. However the date of the composition of Vedāṅga Jyotiṣa was even earlier as discussed below.

Śraviṣṭhā nakṣatra has four stars as shown in Figure 6. The details of these stars are given in Table 1. Currently, Rotanev (β Del) is the accepted yogatārā of Śraviṣṭhā nakṣatra. However, the yogatārā of Śraviṣṭhā nakṣatra should be Al Salib (γ2 Del). The star Al Salib (γ2 Del) has relative longitude of 289° 57′ in the Aświnī-beginning Rohiṇī system, which is an excellent match with the 290° 0′ longitude given in Sūrya Siddhānta [5, 6]. Thus, Al Salib (γ2 Del) has a better claim of being the yogatārā of Dhaniṣṭhā than Rotanev (β Del).

The star Al Salib (γ2 Del) was at winter solstice in circa 1585 BCE as shown in Figure 7. The star Al Salib had ecliptic longitude of 266° 40′ in circa 1830 BCE as shown in Figure 8. As discussed earlier, when winter solstice was at the beginning of Śraviṣṭhā nakṣatra, its yogatārā had an ecliptic longitude of 266° 40′. Based on the identification of Al Salib (γ2 Del) as the yogatārā of Śraviṣṭhā nakṣatra, the winter solstice was at the beginning of Śraviṣṭhā nakṣatra in circa 1830 BCE. The date of the composition of the Vedāṅga Jyotiṣa is thus determined as circa 1830 BCE.

A date closer to this date for composition of the Vedāṅga Jyotiṣa has also been proposed by Narahari Achar, who has calculated the date of circa 1800 BCE based on the identification of Deneb Algedi (δ Cap) as the yogatārā of Śraviṣṭhā Nakṣatra [7]. Deneb Algedi has J2000.0 ecliptic longitude of 323° 33′ and ecliptic latitude of -2° 36′. The yogatārā of Śraviṣṭhā Nakṣatra has the latitude of 36° according to Sūrya Siddhānta (8.1–9). Deneb Algedi is close to the ecliptic and south of the ecliptic, while the yogatārā of Śraviṣṭhā Nakṣatra is far north from the ecliptic according to Sūrya Siddhānta. Thus the identification of Deneb Algedi as the yogatārā of Śraviṣṭhā Nakṣatra is without merit.

The reason Narahari Achar has obtained a date close to 1800 BCE is due to the ecliptic longitude of Deneb Algedi being approximately 4° greater than the ecliptic longitude of Al Salib, the proposed yogatārā of Śraviṣṭhā nakṣatra. As discussed above, the ecliptic longitude of the beginning of Śraviṣṭhā nakṣatra is 3° 20′ greater than the ecliptic longitude of its yogatārā. This makes the ecliptic longitude of Deneb Algedi very close to the ecliptic longitude of the beginning of Śraviṣṭhā nakṣatra as specified in Sūrya Siddhānta (8.1–9). Thus the close matching of the date of composition of the Vedāṅga Jyotiṣa derived by Narahari Achar with my work is fortuitous and not based on in-depth analysis of the textual data.

To put things in perspective, the date of the composition of the Vedāṅga Jyotiṣa has been brought forward by up to 650 years based on two factors. First, the longitude of the yogatārā of Śraviṣṭhā nakṣatra has been increased from 290° to 296° 15′ by asserting that the coordinates given in the Sūrya Siddhānta are polar coordinates. Thus the yogatārā of Śraviṣṭhā nakṣatra has been artificially positioned inside the Śraviṣṭhā nakṣatra by 2° 55′. The actual position given in the Sūrya Siddhānta (8.1–9) is 3° 20′ outside the Śraviṣṭhā nakṣatra. This results in pushing forward the beginning of Śraviṣṭhā nakṣatra by 6° 15′. Second, Rotanev (β Del) has been selected as the yogatārā instead of Al Salib (γ2 Del). The difference in their ecliptic longitudes is approximately 3°. In effect, the beginning of Śraviṣṭhā nakṣatra has been pushed forward by 9° 15′. Each degree amounts to pushing forward the Indian history by 72 years. Thus 9° 15′ is equivalent to pushing Indian history forward by approximately 666 years. This is roughly the time difference between the beginnings of Mauryan era and Gupta era. This is also roughly the time difference between Cyrus Śaka era (550 BCE) and Śālivāhana Śaka era (78 CE). Thus we see that both historical information and astronomical information have been misinterpreted to give the impression that they corroborate each other.


Watch the video: Sun-Earth angles. Declination,Altitude, Longitude,Amizuth Angle,Hour Angle,Zenith Angle REE GTU (August 2022).