Astronomy

Can I derive the position of my house's shadow from sun altitude?

Can I derive the position of my house's shadow from sun altitude?

I'd like to pull in my awning if my house's shadow has reached a point where the awning has no use any more. The house is almost perfectly aligned in a North-South direction, the garden with the awning is in the east.

My home automation (fhem) offers a module that gives me a variety of astronomic parameters, based on my location and altitude:

"SunAlt": -3.3, "SunAz": 309.5, "SunDec": 22.3, "SunDiameter": 31.5, "SunDistance": 151752013, "SunDistanceObserver": 151752409, "SunHrsInvisible": "08:10", "SunHrsVisible": "15:49", "SunLon": 72.7, "SunRa": "04:47", "SunRise": "05:16", "SunSet": "21:05", "SunSign": "Zwillinge", "SunSignN": 2, "SunTransit": "13:10",

Is it enough to target sun's altitude above the horizon? I would think so, but I'm not sure… Currently I'd withdraw the awning when sun's altitude goes below 54⁰.

Edit: Sorry, I seem to have written my question in a very unclear way. Here's more information:

I know my location, at least with GPS precision. Given that location, fhem's astro module gives me all kind of information about sun, moon,…

I have a patio that's to the east of my N-S aligned house. The house is a row house, so for my purpose it's long enough that only the roof is interesting for the shadow.

Sun shines onto the patio in the morning until (currently) something like 15:00. I tend to make shadow with the awning in the morning. After 15:00, the patio is in the shadow of the house and I don't need the awning any more and I would like to remove the awning automatically.

I looked at fhem's astro module exactly at the time when the shadow was far enough on the patio that I could remove the awning. I took the "Sun altitude" value (54⁰) and now the awning is removed when the sun reaches an altitude of 54⁰

This was some days ago and I think this might not be good enough: it seems as if the shadow is extending more and more until the awning is removed. Or the other way round: It seems that I have to adjust the 54⁰ to, maybe, 50⁰ now to get the right timing.


Control the Sun with Sunshades

The primary purpose of a sunshade is to control the amount of direct sunlight through your building's windows. The benefits can be found in so many articles that we will not go into them here. The intent of this page is to show you how it works and give you insight into designing a louvered sunshade system that is right for your building, whether it is to be located in Houston, TX or Minneapolis, MN. The explanation can be as simple or as complicated as we want to make it. We opted for simple, yet effective. We will cover these topics:

Location, Location, Location

Start with the project location and gather these key pieces of information:

  1. Solar altitude at hourly intervals during peak heating season. *Jan 16 (30°) (click to view)
  2. Solar altitude at hourly intervals when the heating & cooling seasons swap. *Apr 15 (60°) and *Sept 1 (59°)
  3. The orientation of your building relative to due South (if you are located in the Northern Hemisphere).
  4. Option: generate solar azimuth angles throughout the day at the times in steps 1 and 2.

*Example: Cincinnati, OH (of course!). Cooling seasons for locations further South will likely be longer and Northern climates shorter. Click the dates above to view the hourly solar altitudes.

Solar altitude is the angle of the sun to the Earth's surface. An angle perpendicular to the Earth's surface is 90° (which only happens near the equator). Locations futher North will have lower solar altitudes than Southern locations. Solar altitude and azimuth for specific locations, by date, are available at www.sundesign.com. You can also find your own favorite websites by doing a search for "Sun Position Tools". To find the latitude and longitude for your project location, go to Google Earth. Keep in mind that West longitude and South latitude must be entered as negative values in most programs.

Solar azimuth is the angle of the sun in relation to due South at any given time. During the day the sun azimuth angle changes from a negative angle (sunrise or East of due South) to a positive angle (sunset or West of due South). These angles change with the seasons based on the solar altitude. Theoretically, the solar azimuth at sunrise at the equator is -90°, 0° at solar noon and 90° at sunset.

Southern, Eastern, and Western exposures of your building will derive benefits from solar shading. The Southern exposure is the easiest to shade and provides the greatest energy savings. Occupants, however, will appreciate any reduction in morning sun glare (Eastern exposure) and afternoon sun glare (Western exposure). In some climates these exposures can generate large energy savings as well. Northern exposures do not require solar shading. The only reason to shade a Northern exposure is to create uniformity in the building appearance. Otherwise, virtually no energy benefit can be gained from shading the North side of a building (again, we are referring to a location in the Northern Hemisphere).

How to Shade Southern Exposures

Based on the solar altitude and azimuth and orientation of your building, shading methods will vary. A shelf system is best utilized on Southern exposures and will allow the best configuration for energy savings. Variations in the shelf location, projection, and blade spacings will optimize the energy benefits. The objective is to maximize shading during peak cooling season while allowing direct sunlight and heat gain during the heating season. In most of the southern climates, the need for shading throughout the cooling season generates the greatest energy savings, so we will optimize the shading for this period (April 15 through September 1). This altitude is 60° in our example.

  • Draw the height of the window to be shaded (in section view).
  • Step 1: Draw the "peak heating season" altitude angle with the starting point at the top of the window.
  • Step 2: Draw the "heating and cooling swap" altitude with the starting point at the bottom of the window.

These lines represent the shadow lines at solar noon on the given dates. The intersection of the lines is the optimal point for the outermost tip of the sunshade. This configuration will allow full sun to enter the window during January (the coldest month) and allow little or no sun to enter the window from April 15 through Sept 1 (the warmest months).

  • Step 3: Draw a line from the intersection of the altitude lines to the building exterior. This line will represent the bottommost portion of the sunshade in section view.

The sunshade location is 30" above the window with a projection of 52". Adjustments can be made to these dimensions as desired to create more or less shading, but the energy benefit will likely suffer.

Also drawn are the maximum and minimum solar noon altitudes for the example location. These give an idea of the shading throughout the year. Notice that the solar altitude stays in the fully shaded region from April 15th through September 1st. The angle change is only 14° during this time of year. Yet the angle changes a remarkable 32° during the remainder of the year. This difference is less dramatic closer, and more dramatic further, from the Tropic of Cancer (the latitude where the sun is directly overhead during June Solstice).

To finish our example, the window width is 116". Width of the sunshade is 4" greater than the window width (120" centered). The sunshade model is H6A36 with a tube trim perimeter frame. This model has airfoil shaped blades at a 35° angle, spaced 6" apart. See below for the resulting shadow maps.

Results: Southern exposure shadow map on January 16 (no shade during 30° altitude peak sun at window). Sunrise to sunset are shown.

Results: Southern exposure shadow map on April 15 (full shade during 60° altitude peak sun at window). Sunrise to sunset are shown.

Results: Southern exposure shadow map on June 21 (full shade during 74° altitude peak sun at window). On this date, the sun rises North of East and sets North of West. Therefore, the diagrams below are only showing 9:00 am through 4:00 pm because the Southern exposure gets no sun at the remaining times of day.

Keep in mind that the sun changes azimuth and altitude during the day. Additional considerations are: how far the sunshade overhangs the ends of the window and whether low altitude sun angles can be blocked with baffles or by recessing the windows. The optimal shading will only occur at solar noon for a given day. When the sun is lower in the sky (and to the East at sunrise and West at sunset), the sunshade will be less effective blocking glare and heat gain (though the heat gain will be minimal). Additional sunshades can be applied if necessary for occupant comfort (see below - Southeast and Southwest).

How to Shade Southeastern and Southwestern Exposures

Consider these as South-facing for calculations and sunshade projection from the building, but apply a factor based on the equation:

  • A = angle from south
  • SP = projection from South-facing calculation
  • SEP = SP * cos(A)

Example: calculated projection for direct South was 52" (SP = 52) in our original example. Direct Southeast or Southwest will be 45° from South, so A = 45. SEP = 52 * cos(45) = 36.75". The optimal shelf-type sunshade projection for a Southeast or Southwest exposure is 36.75". A sunshade with these dimensions and the 2" overhang is shown below left. Notice that the sun will enter the Southern portion of the window during peak exposure times. Consider extending the sunshade overhang to about 36.75" (shown below right). If you have a number of contiguous or closely spaced windows, consider making the sunshade continuous over the entire span.

Mornings (for Southeast exposures) and late afternoons (for Southwest exposures) will have significant glare. The sun azimuth at these times will be more perpendicular to the windows than a South exposure, admitting more direct sunlight into the building.

Interior of the building at SE exposure, no auxillary shade

More sunshades can be utilized to minimize direct sunlight and glare at either end of the day. Options are baffles or vertical blade louvers over the windows. Baffles require larger projections than vertical blade louvers, which can be flush or surface mounted. Below is the application of flush mounted louvered sunshades, model H6A48 blades vertical.

Since the blades are 8" apart, occupants will still enjoy a view of the outdoors, but the glare from morning sun is minimized. During the cooling season, the shelf sunshade will block the sunshine starting at about 10:00. The combination of the vertical blade sunshades and the shelf sunshades work in tandem throughout the day. In the heating season, the vertical blade and the shelf sunshade will allow sun to enter from about 10:00 on, capturing most of the heat gain benefits. Option: if your wall is thick enough for the window and the louvered sunshade combined, the sunshade can be recessed into the wall instead of flush mounted.

How to Shade Eastern and Western Exposures

The principles are the same for Eastern and Western exposures, so we will address the Eastern Exposure only. Use the same concepts to shade the Western exposure, but account for late-day sun instead of early morning sun.

The sun angles early in the morning start at 0° (sunrise). Obviously we will be unable to block all sunshine from entering the building without blocking the view for occupants. The best compromise is to block the sun from about 10:00 am - noon in the cooling season, while admitting this sun during the heating season. Use interior blinds or shades to block glare for occupants. This will allow the heat gain to enter the interior space during the heating season, gaining the energy benefits.

We are going to evaluate one shading method, though others can be used. The steps for finding the right sunshade position and projection are similar to those of the Southern exposures, but with a few variations:

  • Draw the height of the window to be shaded (in section view).
  • Step 1: Draw the "peak heating season" altitude angle for 10:00 a.m. with the starting point at the top of the window.
  • Step 2: Draw the "heating and cooling swap" altitude angle for 11:00 or 12:00 a.m. with the starting point at the bottom of the window. We are using 11:00-12:00 am altitude during the cooling season because we may have to sacrifice a bit of heat gain for practicality of shade design. For our example, I used 11:00 am to demonstrate that the difference in sun exposure will be minimal.
  • Step 3: Draw a line horizontally from the top of the window, intersecting both azimuth lines.

  • Step 4: Draw a vertical line from the intersection of the "top of window" line and the Step 2 "bottom of window" altitude line upward until it intersects the Step 1 "top of window" altitude line.
  • Step 5: Draw a line from the intersection of these lines back to the building.

Draw the shelf sunshade (any model can be used). Draw an extension at the front dropping vertially based on the line from Step 4. The extension will effectively block the sun while providing an uninhibited view for occupants of the building. The objective of the extension is to allow the low angle sun (25°) to pass, while prohibiting the high angle sun (45°). For our example we have chosen sunshade model H6A24. This model has blades angled at 25° and spaced at 4". To evaluate the capabilities of any sunshade model, draw 2 blades in section, including the appropriate solar altitude angles.

.(Alternate method)

It is evident that we will allow about 75% of the 25° sun to pass, while blocking about 85% of the 45° sun. These calculations can be more carefully evaluated if you wish, but for our example the diagram and an estimate are sufficient. Also included above is an alternate sunshade configuration (vertical mount) that will provide the proper shading, but will partially obstruct the view for occupants.

Results: Eastern exposure shadow map on January 16 (minimal shade during 25° altitude 10:00 sun at window). Sunrise to noon are shown. The sun will not shine on the Eastern exposure during the remainder of the day.

Results: Eastern exposure shadow map on April 15 (full shade during 45° altitude 10:00 sun at window). Sunrise to noon are shown. The sun will not shine on the Eastern exposure during the remainder of the day.

In conclusion, shading methods can vary for the various building exposures. The methods shown are for demonstration, and can be utilized on most building projects. Keep in mind they are merely one method, with numerous other methods available. Feel free to take liberties and utilize your own sun shading techniques.

© 2021 Harray, LLC
dba Architectural Louvers,
all rights reserved


Solar Info

Solar Info is a app that it provides information on Sun´s diurnal motion and Sun´s position during the year, which facilitates the understanding of some phenomena which, despite being familiar to us, we sometimes do not fully understand.
It is a useful tool for installation and setting of sundials because it provides an accurate solar time, calculated using astronomical algorithms.
Besides, there are a widget that can be placed anywhere in the home and shows the solar time at all times, sunrise and sunset times and the Sun´s relative position in the sky (when the Sun is visible).
The solar time in widget is updated both automatically and manually when touching anywhere on the widget area. When pushing on the icon on the top right corner of the widget, you can access the app menu.
The start screen now shows the solar time continuously, which is updated every second, as well as the sun Azimuth and Altitude, Equation of Time and UTC.
The Ephemeris section features the following information:
Latitude
Longitude
Sun altitude
Sun azimuth
Right Ascension
Declination
Distance
Morning Astronomical Twilight
Morning Nautical Twilight
Morning Civil Twilight
Sun rise
Transit
Sun set
Evening Civil Twilight
Evening Nautical Twilight
Evening Astronomical Twilight
Day lenght
Julian Day
Equation of Time
Local sideral Time
GMST
Logitude correction
UTC
Solar Time
Cast shadow
Spring Equinox
Summer Solstice
Autumn Equinox
Winter Solstice

In the Location section, the location coordinates can either be obtained featuring several options :
• Favourites list (offline).
• Using the integrated GPS (it is required that the location is activated).
• From the map (mobile data is required).
• Manual (offline).
• From an internal database containing 20.000 cities (offline).

It is now possible to change the location in the ephemeris module, which allows you to know the ephemeris of the Sun anywhere and at any time.

The ‘Equation of Time’ section shows a plot of the Equation of Time values. By moving the cursor, it is posible to see graphically the relationship between True Sun and Mean Sun as well as the value of Equation of Time for a specific date.
Graph of Analema and its components, displaying its value for each day.
Graph of daily Sun Path and hourly analemma. Possibility to add a horizon mask and the illumination limits for a horizontal or vertical declining dial.
It is posible to change the year for which the Equation of Time is calculated.
It is posible to export the data from the Equation of Time to an Excel file for subsequent processing in a PC.
The location of the widget is automatically updated every hour.
If the device is set to adjust the Time Zone automatically, the obtained precision may be in the order of ±5 seconds.
If you want to help translate the application into other languages, contact the support email.

Bibliography:
- "Astronomical algorithms". Jean Meeus
-" La gnomonique". Denis Savoie
-"Formule e metodi per lo studio degli orologi solari piani". Gianni Ferrari


Sun Surveyor Lite 4+

Sun Surveyor Lite takes the mystery out of the sunrise, sunset and magic hours, helping photographers and filmmakers scout the best locations, plan effectively, and get the perfect shot. Solar Industry (PV) Professionals, architects, real estate agents, and gardeners will also find a wealth of empowering, interactive features.

The 3D Compass and detailed Ephemeris provide a wealth of information about the largest natural light source in the galaxy:

- Predict and plan for the golden hour, blue hour and every sunrise & sunset
- Visualize the sun's path throughout the day or through the year

- Visual time machine - take a quick glance at the light for a day, or dial in desired compositions easily
- Twilight times - civil, nautical, astronomical
- Solstice and Equinox visualization
- Sun shadow information - calculate the length of shadows cast by objects
- Magnetic declination compensation

Check out the Full Version of Sun Surveyor for more:

- Live Camera View - augmented reality projections of the sun and moon paths, pinpoint the time the sun or moon will be at a particular location in the sky
- Interactive Map View - plan a remote shot or PV array placement, interact with a top-down perspective of sun and moon paths and events
- Street View Panoramas - 360 degree spherical panoramas with selected sun, moon and milky way events overlaid, where available
- Moon Information: moon position, moonrise, moonset, moon phases, apogee, perigee, distance and a Super Moon finder
- Show clients the quality and quantity of seasonal sunlight at a remote location
- Understand potential shade of surroundings and discover any obstructions
- Create images of the summer and winter Solstice & Equinox paths for a site
- Prepare night photography shots with the Milky Way & star trail features
- Offline usage (excludes Map View, Street View) - enter coordinates, save & load locations with no data connection or GPS available
- Measure distance, and difference between elevations, and vertical angle differentials with the Map view
- Import and export Google Earth .kmz/.kml locations


Navigation

(2) The time of year when navigation is possible in terms of local climatic conditions.

(3) The main branch of ship handling, in which the theoretical grounds and practical procedures of ship operation are developed.

The origin of maritime navigation dates to remote antiquity. The simplest procedures of navigation were known not only to the ancient Egyptians and Phoenicians but also to peoples who were at a lower stage of development. The principles of modern navigation were established by use of a magnetic pointer to determine the ship&rsquos course (11th century), the compilation of charts in a direct orthogonal cylindrical projection (G. Mercator, 1569), and the invention of the deck log (19th century). At the turn of the 20th century, advances in physics were the basis for the development of electrical and electronic navigation instruments. In Russia the first training aid for navigation was compiled in 1703 by L. F. Magnitskii, an instructor at the School of Mathematical and Navigational Sciences, which was founded by Peter I in 1701. Russian seamen and scholars such as S. I. Mordvinov, L. Euler, and M. V. Lomonosov made a major contribution to work on navigational problems. Round-the-world voyages and scientific expeditions conducted by Russian seamen contributed to the further development of navigational science. Textbooks were written in which the methods of navigation were given a treatment close to that of the present day. P. Ia. Gamaleia&rsquos textbook Theory and Practice of Navigation, which was published in several editions and served as a main guide to navigation in the first half of the 19th century, first came out in 1806. A new stage in the development of navigation was opened by the invention of radio by A. S. Popov. Major contributions to the establishment and development of the Soviet school of navigation were made by such scientists as N. N. Matusevich, N. A. Sakellari, A. P. Iushchenko, and K. S. Ukhov.

The tasks of modern navigation are the selection of the safest and most convenient route for a ship, the use of navigational instruments and devices to determine the direction of travel and the distance covered by a ship at sea (including determination of corrections for the readings of such instruments), the study and selection of the cartographic projections that are most convenient for navigation and their use to solve problems of navigation by analytical and graphic methods, the consideration of the effect of external factors that cause deviation of the ship from the selected route, the determination of the ship&rsquos location on the basis of land reference points and navigation satellites, and the assessment of the accuracy of such determinations. A number of problems of navigation are solved using methods of geodesy, cartography, hydrography, oceanography, and meteorology.

A ship&rsquos voyage between specific points requires the calculation and plotting of its route on maritime navigation charts, and also determination of a course that will ensure that the ship travels along the planned route with consideration for the effect of external disturbances (wind and currents). The nautical mile has been adopted as the fundamental unit for measuring distance at sea, and the degree as the fundamental unit for measuring direction.

The shortest distance between two given points on the surface of the earth, which is assumed to be spherical, is the shorter arc of the great circle that passes through the points. Except in cases when a ship travels along a meridian or the equator, the great circle intersects the meridians at various angles. Therefore, a ship traveling along such a curve must change course continuously. In practice it is more convenient to travel a course that is a constant angle to the meridians and that can be represented in a Mercator projection on a chart by a straight line&mdasha rhumb line. At great distances, however, the difference between the length of the great circle and that of the rhumb line becomes significant. Therefore, in such cases the great circle is computed and intermediate points are plotted, between which the ship sails along the rhumb line.

The graphic representation of a ship&rsquos route on a chart is called a plot. During the voyage the navigator keeps a continuous record of the ship&rsquos position, according to its direction and the distance traveled, on the basis of readings of the ship&rsquos compass and log and data on the current and drift. The method of computing a ship&rsquos position on the basis of the elements of its motion is called deal reckoning, and the ship&rsquos position on a chart as obtained by this method is called the dead-reckoning position of the ship. However, no matter how carefully the dead reckoning is performed, the position thus determined always deviates from the actual position of the ship because of errors in the corrections of compass readings and the log, inaccuracies in incorporating the elements of the current and drift, and deviations of the ship from course caused by various factors. Therefore, to eliminate errors, the dead reckoning is continuously corrected during a voyage by means of periodic determinations of the ship&rsquos position (observations) according to land reference points (that is, by navigational methods) or according to heavenly bodies by using methods of nautical astronomy. The navigational methods are based on measurement of the distance and direction (or combinations thereof) to objects whose coordinates are known, or of the angles between the objects. Each measurement gives one position line. The intersection of two position lines determines the ship&rsquos observed position. With three or more lines it is possible not only to determine the ship&rsquos position but also to find the probable values of the errors of observation. Reference points for navigational determinations near the coast include natural landmarks or artificial structures (mainly navigational aids, such as lighthouses, signs, and channel markers), which are entered on the chart and can be observed visually or by radar or the signals of circular or course radio beacons sound signals and deeps. Pulsed, pulsed-phase, and phase radio navigation systems or quadrant radio beacons are used at great distances from shore.

The increase in the traffic density on sea routes and in the dimensions and speeds of oceangoing ships requires improvements in equipment and methods of navigation. Use of the Doppler effect in sonar logs, which makes it possible to measure the speed of a ship with respect to the bottom, is one way of increasing the accuracy of dead reckoning. During approaches to ports and when sailing in crowded channels, the required accuracy of guidance is ensured by the use of precision short-range radio navigation systems or coastal radar stations. Global radio navigation systems that make possible determination of a ship&rsquos position at any point are being developed for navigation on the open ocean. The system of navigation satellites is extremely promising in this regard.

The development of navigational equipment is making possible automation of the acquisition and processing of navigational information and direct input of data into the control system to solve the problem of stabilization of the ship on a prescribed path. The development and use of autonomous inertial navigation systems on transport vessels is promising.

REFERENCES


Jaipur’s Jantar Mantar: Legacy of an Astronomer-King

Culturally vibrant and terribly atmospheric, Rajasthan’s capital city, Jaipur, is a heady mix of past and present. Among the city’s many palaces, architectural wonders, and chaotic and colourful bazaars is the Jaipur Observatory or Jantar Mantar.

Located near the City Palace and Hawa Mahal in the Old City, the observatory is a sprawling property where discs, dials, arcs, arches, orbs, pillars and tablets are a testament to the astronomer-king who charted the heavens to indulge his passion for astronomy and to enhance his diplomatic and political career as well.

The Jaipur Observatory or ‘Jantar Mantar’, built by Maharaja Sawai Jai Singh II (r. 1686 – 1743) between 1724 and 1727, is a collection of 20 large instruments that calculate the position and movement of celestial bodies with the naked eye. These instruments are not only impressive for their scale and size but also because they are made of stone and masonry. Amazingly, these monumental instruments were state-of-the-art and were even more accurate than their contemporary, compact brass counterparts being used in other parts of the world.

Why did Jai Singh II send his men far and wide to gather knowledge about the frontiers of astronomy? And why did he build, not just the observatory in Jaipur, but four other observatories, one each in Delhi, Varanasi, Mathura and Ujjain?

Who was this Astronomer-King?

Jai Singh was born on 3rd November 1688, in Amber, capital of the Kachwaha Rajputs located on the outskirts of the city of Jaipur. He was born into a royal Rajput family that ruled a regional kingdom with diminishing power under Mughal rule. The era in which he was born and was educated was instrumental in his keen interest in astronomy.

His father, Bishan Singh, the regional ruler between 1689 and 1700, carried forward the royal legacy of education for his two sons. He enrolled them at a Sanskrit college in Varanasi, which is where Jai Singh mastered Hindi, Sanskrit, Persian, Mathematics and Martial Arts.

Jai Singh was inclined towards mathematics and astronomy from a very young age. Apparently, he had made copies of two astronomy manuscripts at the age of 13 and these are still preserved in the City Palace museum in Jaipur.

Although he ascended to the throne at the age of 11 years, after his father’s untimely death in 1699, the young royal never gave up his academic pursuits. He had inherited great diplomacy skills and wit, which had impressed Aurangzeb so much that the Emperor bestowed on him the title ‘Sawai’, which literally meant ‘one and a quarter times greater than one’ (implying he was superior to his predecessors and contemporaries). Later, he was bestowed the titles of Saramad-i-Rajaha-i-Hind, Raj Rajeshwar, Shri Shantanu ji and Maharaja Sawai by Emperor Muhammed Shah.

Jai Singh’s rule coincided with the decline of Mughal power after the death of Aurangzeb. Despite the turmoil and conflict of these times, he managed to expand and consolidate his kingdom and gained much respect. As the boundaries of his kingdom expanded, Jai Singh decided to build a new, planned, fortified city and he named it after himself – ‘Jaipur’. While construction of the new city began in 1725, Jaipur replaced Amber as the capital in 1733.

This was a grand city, planned to the very last detail. It was built to incorporate aspects of the ancient architectural treatise Shilpa Shastra, the best of European town planning and Jai Singh’s own ideas. This plan was entrusted to ace architects from different eras – Vidyadhar Bhattacharya of Bengal and later Sir Samuel Winston Jacob, British Army Officer and an architect-engineer.

The biographical account of Jai Singh II on the British Museum website states: “Jaipur, which was built on the grid system with nine rectangular zones corresponding to the nine divisions of the universe and had different zones allotted to different professions, boasted 119-feet-wide main streets that were perpendicularly intersected by 60-feet-wide auxiliary streets, which were further honeycombed by 30-feet-wide lanes and 15-feet-wide by-lanes. Beautiful, harmonized buildings and shady trees lined the streets, and the city was well-provided with water conduits and wells. The European travellers of the time, like the Frenchman Louis Rousselet, and the English bishop, Heber, were greatly impressed by Jai Singh’s unparalleled excellence in city-planning.”

The Maharaja meets his Mentor

During his travels to the Deccan to meet Aurangzeb, Jai Singh II befriended Jagannatha, who had a keen mastery over astronomy and mathematics. He soon became the king’s mentor and chief advisor in matters concerning astronomy. Jagannatha also served in the royal court and significantly influenced the design of the Jaipur Observatory.

Both men often discussed traditional Indian astronomy treatises and Islamic astronomy treatises, which were the main guiding principles for the calendars that decided auspicious times for any rituals or for embarking on new conquests.

In due course, Jai Sigh discovered many discrepancies in the tables and the measurement of time and position of the planets, which led him to realise the need for accurate astronomical instruments. The Indian astronomical treatises, right from the Vedic era, siddhantas by Aryabhata and Brahmagupta mentioned observational instruments but they never disclosed their exact design. Meanwhile, Islamic astronomy mentioned the astrolabe.

While Hindu astronomers mainly mentioned instruments to measure time rather than the coordinated systems of stars and planets, like water clocks and sundials, Islamic astronomy had compiled numerical astronomical tables called ‘Zijes’, which included latitudes, longitudes, trigonometric functions and elements of spherical astronomy. All these were derived from the Ptolemic model of the solar system.

Islamic astronomers had compiled more than 200 different types of Zijes between the 8th and 15th century CE. The most famous Zijes were compiled in India – Zij-i-Muhammad Shahi – based on observations made at Jantar Mantar observatories (it is possible that Jai Singh had honoured Emperor Muhammad Shah for his support and repeal of unjust taxes). The last known Zij, known as Zij-i-Bahadurkhani, was compiled by Indian astronomer Ghulam Hussain Jaunpuri and it incorporated the heliocentric system.

These constant modifications and corrections indicate that there were significant discrepancies in the observed and mathematical tables, and attempts were constantly being made to correct them. Hence, positional astronomical instruments played a key role in the continued study of astronomy across the globe and the Jantar Mantar Observatories of Jai Singh are a testament to that era.

Cutting-Edge Innovations

The most interesting aspect of the instruments at Jai Singh’s Jantar Mantar Observatories is that they are calibrated for multiple coordinate systems. With Jai Prakash (an instrument that is supposed to mirror the heavens), for a single celestial object, one can indicate its position with respect to the azimuthal and equatorial coordinate system. The same is true of the instruments that measure time. The smallest division of the giant Samrat Yantra – the giant sundial – corresponds to two seconds, so one can experience the motion of the earth as the shadow shifts. The various large instruments meant to measure the spatial coordinates of celestial objects with respect to the horizon at a given time also enhance this experiential learning!

This makes these observatories relevant even today to study the basic principles of Positional Astronomy. Dr Nandivada Ratnashree, director of the Nehru Planetarium in Delhi, uses them to teach basic astronomy lessons. Often students are encouraged to visit these observatories and make measurements or observe the path of the sun and planets across the sky.

Some historians believe that the giant instruments at the five observatories be built were meant as a show of power and wealth by Sawai Jai Singh II. Even if that were true, the fact that he invested space, money and manpower to build these architectural wonders to study basic astronomy cannot be refuted. Also, the intellectual and mathematical pursuit of astronomy has never been glorified by any other king in Indian history.

Most importantly, these huge instruments made of stone as opposed to small brass instruments (vulnerable to shaking, temperature changes and inaccuracies), combined the principles of Indian, Islamic and western astronomy to attain their unprecedented accuracy. Portuguese Jesuits who had arrived in India by then and were based in Jaipur helped Jai Singh plan an expedition of his court astronomers to Portugal to understand the observation techniques and tabulations that were being used in Europe.

Jai Singh was intrigued by the discrepancies and errors in the astronomical tables of La Hire (Layyer), which they had brought back. He corresponded with and invited French Jesuit astronomer Claude Boudier, who was based in Chandernagore (in Bengal), for consultation. Although Jai Singh did not use these tables, as they were based strictly on the Copernican system, Boudier went on to assist the Maharaja in setting up telescopes in Jaipur.

Thus, Jai Singh can be counted as one of the most pioneering pre-colonial astronomers who made serious attempts to understand European science and astronomy, which later thrived in India. India has gone on to contribute greatly to the world of science thanks to this legacy of the open-minded pursuit of knowledge.

The Instruments

Following are the basic instruments at Jaipur’s Jantar Mantar:

Samrat Yantra: This is the largest sundial in the world. Shaped in the form of a right-angle triangle with a hypotenuse (also called a ‘gnomon’), it rises 73 feet above the ground. Its primary objective is to indicate solar time. The gnomon is pointed towards the celestial pole and is supported by an arc that rises 45 feet. The shadow of the gnomon throughout the day sweeps through the calibrated quadrant from one end to the other. The time of day is indicated by the edge of the shadow on the quadrant scale.

The instrument has a sighting device, which is designed to be versatile enough to study stars at night as well. One can also study the sun’s declination and the right ascension of any celestial object. A secondary instrument, called Shasthansa Yantra, which uses a pinhole camera mechanism, has been built within the towers that support the quadrant scales. It measures the zenith distance, declination and diameter of the sun.

Jai Prakash: This is the most intriguing instrument, whose working concept dates to the Greco-Babylonian era (early 300 BCE) when first the hemispherical sun dial was made by astronomer Berosus. It is one of the most versatile and complex instruments that give the coordinates of the celestial objects in multiple systems – the Azimuthal-altitude system and the Equatorial coordinate system. This enables easy conversion and perception of the popular celestial coordinate system.

The instrument itself is a big bowl that partially rises above and below the ground. The Jaipur Jai Prakash instrument’s diameter of the rim is 17.5 feet, whereas it is bigger – 27 feet – in Delhi. The bowls are inverted celestial spheres – one for the day and the other aided with a sighting device for night observations. They have the respective coordinates inscribed on them to enable observing any celestial object and measuring their coordinates in any of the systems. The multimedia website in collaboration with an outreach program of Cornell University in the United States is enabling a better understanding of these instruments through virtual simulation.

Ram Yantra: This is a cylindrical structure instrument, built in pairs, to measure the altitude and azimuth of celestial objects. It was a first of its kind instrument in the history of Indian and Islamic schools of astronomy for measuring the altitude and azimuth with accuracy.

Kapala Yantras: They were built before the construction of the Jai Prakash on the same principle but these are more demonstrative instruments to indicate the transformation of one coordinate system to another. They are not for active celestial observations. These could have been prototypes for the Jai Prakash.

Rasivalya Yantras: There are 12 of these – each one referring to the Zodiacal constellations. They measure the latitude and longitude of a celestial object at the exact moment when that constellation crosses the meridian.

Legacy & Scope

As the design and scope of the instruments indicate, Jai Singh did not build these observatories as architectural marvels to merely enhance his reputation. He was serious about accurate and precise celestial observations in order to correct the discrepancies in the existing astronomical observation tables. The astronomical charts and tables that came out of these projects have led to almanacs that are still in use in Rajasthan.

Apart from the astronomical charts, Jai Singh has created an entire open-field classroom to learn physics, astronomy and mathematics. His observatories are mathematical spaces with huge instruments that have inscribed scales in multiple coordinate systems and these are great spaces for learning time measurement, coordinate geometry, coordinate transformation, astronomical observations and much more.

As mentioned earlier, Dr Nandivada Rathnashree, director of the Nehru Planetarium in Delhi, often conducts classes and observations of celestial events at Jai Singh’s Delhi Observatory. These can be replicated at the other observatories by science teachers and amateur astronomy enthusiasts so that instruments are well maintained and are in use.

Of the five observatories built by the Maharaja, only four exist today. While the one at Mathura was dismantled in the 19th century, the observatories at Jaipur and Ujjain have been considerably restored.

India should be proud to own a scientific and mathematical heritage like this, built in stone and mortar by a regional king who had a passion for Positional Astronomy based purely on scientific observations, mathematical calculations and evidence. Unfortunately, not much has been done to showcase and promote this legacy. Although these observatories are under the Archaeological Survey of India, there are no scientifically trained guides to explain the working and scope of these instruments and bring them to life for the public. Until such an attempt is made, visitors will have to figure out this monumental legacy of a Rajput king for themselves.

Madhuri Katti is a Kolkata based physics teacher, heritage enthusiast and an aspiring writer.


Eclipse Circumstances

When you click on the map a red marker is added and a popup window opens giving the Eclipse Circumstances calculated for that location. The predictions in the popup window can be divided into two sections.

In the top part of the window, the decimal Latitude and Longitude of the marker are given. The Eclipse Type (either total, annular or partial) seen from that position is given. The Duration of Totality (or Duration of Annularity) lists the length of the total (or annular) phase in minutes and seconds. The Eclipse Magnitude is the fraction of the Sun's diameter eclipsed. The Eclipse Obscuration is the fraction of the Sun's area eclipsed.

The bottom part of the window consists of a table listing the times for important stages of the eclipse. The Event column lists eclipse phase, followed by the date and time (both in Universal Time). Finally, the Altitude and Azimuth of the Sun is given for each event. The altitude is measured from the horizon (0°) to the zenith (90°). The azimuth is measured from due North and rotating eastward (North = 0°, East = 90°, South = 180°, and West = 270°).

Footnotes

1. An excellent source for weather prospects for upcoming eclipses is meteorologist Jay Anderson's Eclipse Weather Page. ↩

2. This web page approximates the curved eclipse path by using a series or straight line segments. To maintain the validity of this approximation, the maximum zoom level is limited to ӭ mile/inch (Ӭ.7 kilometers/centimeter). This should prevent over-interpretation of the eclipse path accuracy. You can disable the zoom limit using the link Full Zoom to reload the map. ↩


Are you ready for the Great American Eclipse? These local people are.

SOUTH BEND — Linda Marks has always had a fascination with the sky.

It began as she was growing up on the east coast. Her mother was a small airplane pilot in a time before airplanes had complex navigational systems. Pilots used the position of celestial objects — constellations, planets and individual stars — to navigate from origin to destination.

"I looked up in the sky a lot," said Marks, of North Liberty. "My mom would take me out and show me different things in the sky. When I was old enough, I joined Girl Scouts and they had a star badge. As you can guess, I dived right into that."

Marks will draw upon her life-long interest in gazing skyward in two weeks as she and millions of others across the nation look to the heavens to catch a glimpse of one of the rarest natural phenomenon — a total solar eclipse.

It happens Aug. 21 when the moon's shadow will travel around 10,000 miles across the Earth's surface, from the middle of the Pacific Ocean across the continental United States to the Atlantic Ocean off the coast of Africa.

Weather-permitting, all of North America will have a view of a partial eclipse, when the moon blocks a portion of the sun. In South Bend, the moon is expected to block approximately 86 percent of the sun with the maximum eclipse coming at 2:22 p.m., according to NASA.

Marks, vice president of the Michiana Astronomical Society, said she and a number of other club members will be traveling, to be under the path of totality, the area that will experience the total eclipse.

"We're spread out," she said. "We're pretty much everywhere."

It's a calculated strategy. The group doesn't want everyone bunched together in case their chosen location has less than ideal weather conditions.

A long time coming

Unlike a lunar eclipse, in which the earth casts a shadow across the surface of the moon that is visible to a wide swath along on Earth, a total solar eclipse is very focused.

"You have to be in exactly the right spot," said Peter Garnavich, professor and department chair of Astrophysics and Cosmology Physics at the University of Notre Dame. "It leads to a bit of excitement."

The relative rarity of a total solar eclipse also helps build excitement. There hasn't been one in the United States since Feb. 26, 1979.

This year's event is being billed as the Great American Eclipse because it will occur exclusively in the United States. When it last happened, Woodrow Wilson was president of the United States.

Starting off the coast of Oregon at 9:05 a.m. PDT, the moon's inner shadow, known as the umbra, will cast a 70-mile-wide shadow that will turn day into night across 14 states before exiting off the coast of South Carolina at 4:09 p.m. EDT.

While everyone in Indiana will be able to view a partial eclipse this go-around, there is no spot in the state that will be in the path of the total solar eclipse. For eclipse enthusiasts, there will be an opportunity a little closer to home. On April 8, 2024, the center line of a total solar eclipse will pass just south of Indianapolis. Another total solar eclipse, on Sept. 14, 2099, will place all of the South Bend region in the path of totality.

Eclipses as events

Garnavich's interest in astronomy and physics began as a boy. He witnessed a partial solar eclipse in the 1970s and received a telescope when he was in the fifth grade.

"The eclipse is what pushed me over the edge and I decided this is what I wanted to do for the rest of my life," he said.

Eclipses used to provide the greatest opportunity for scientists to study the sun and learn more about it and its impacts on the Earth.

"The scientific yield is not as great as it used to be," Garnavich said. "Nowadays, there are really specialized satellites where we can continually monitor the sun and take measurements."

Jerry Hinnefeld, a professor of physics at Indiana University South Bend, said the appeal of solar eclipses now is the ability to garner interest in science and mathematics.

"It is very exciting. It's an opportunity to generate interest and enthusiasm in astronomy," Hinnefeld said. "It piques people's curiosity and gets people thinking about things they may not ordinarily think about."

Students will just be returning to the IU South Bend campus for the first day of classes when the eclipse happens, Hinnefeld said. There will be a number of activities on campus as part of welcome week festivities tied into the eclipse, including eclipse viewing from the green mall.

Though Notre Dame students don't start classes until the day after the eclipse, there will be activities there as well. Garnavich said the university will have viewers set up outside the Jordan Hall of Science for people to safely view the eclipse. The university's Digital Visualization Theater will host a simulation of the eclipse on Aug. 9 and Aug. 12.

A unique partnership

One area organization has a unique connection that is paying dividends for the upcoming eclipse.

The Elkhart Public Library is one of 75 public libraries nationwide to partner with NASA as part of the [email protected] My Library program, a partnership between NASA, the libraries, the Ameircan Library Association and the Space Science Institute. The program offers materials and training to help the libraries lead fun, educational science, technology, engineering and mathematics-based programming.

"We were thrilled to be chosen for this program," said Allison McLean, head of young people's services at the library and the project director for the NASA grant. "The timing couldn't have been better. The eclipse will be our first big event with the program."

McLean said the library has already held one eclipse-related event for adults back in July. On Monday at 4:30 p.m., the library will host an Eclipse 101 program for kids ages 5 and up. The library is also hosting a viewing party on Aug. 21 at Central Park in downtown Elkhart, complete with eclipse glasses.

"We can see the excitement building everywhere," McLean said. "We've definitely seen an uptick in people looking for eclipse-related materials."

Another perspective

While most people will have to be content to view the eclipse from the ground, or view images from organizations like NASA, Dave Bohlmann, an engineer who teaches part-time at Ivy Tech Community College's South Bend campus, will have another perspective.

Bohlmann has spent the last several years sending balloons to the very edge of space. He's had four practice runs preparing for a launch the day of the eclipse from Perryville, Mo., inside the path of totality. Bohlmann's mission is simple, he's sending the balloons up to a height of 100,000 feet or more — where the curvature of the earth is visible — in an effort to capture images and video of the moon's shadow as it traverses the earth.

"Right now, we're just doing some final preparations," Bohlmann said. "We're almost ready."

Bohlmann's group is one of several planning to do launches from the Perryville area. In addition to amateur high altitude balloon enthusiasts like Bohlmann, there are also more than 50 NASA-funded balloons and numerous ground-based observations planned to gather a host of images and data.

After four test flights, Bohlmann knows his balloons take about two hours to get up to altitude. He's planning to launch about an hour and 40 minutes before totality in Perryville in order to make sure his balloon is in position.

"It's going to be exciting," Bohlmann said.

[email protected]

@TheBobBlake

While a portion of the country will experience a total solar eclipse on Aug. 21, in the South Bend area the sun will be about 86 percent covered. Here are some tips for safely viewing:

• Never look directly at the sun.

• When looking at the eclipsed sun, use a device with a solar filter or wear eclipse glasses.

• Do not look at the eclipse through the viewfinder of a camera.

• Use a pinhole projector, a home-made device that projects an image of the eclipsed sun on another surface.


Step 7: Spreadsheet Calculations

As described in Steps 2 to 6, the equations needed for this exercise are:

δ = -23.45 x cos (360 * (N+10)/365)

A = arcsin (sin ø sin δ + cos ø cos δ cos h)

L is the (projecting) length of the gnomon

H is the net height of the chart (= height of y-axis)

δ is the angle of declination

N is the day number, counting from 1st January

T is the time using a 24 hour clock

y is the y co-ordinate of the hour lines, which are plotted against the chosen dates

Another equation you’ll probably need is:

because all the trigonometrical functions in Excel (and probably other spreadsheets too) require an argument in radians not degrees.

You will have to build a spreadsheet that contains the above equations. If you need some help to do that, have a look at the PDF attached to this step which shows my spreadsheet. The formulae within some of the key cells are as follows:

You'll need to change the latitude in cell C2 and the net height of the chart in cell J2 to suit your needs. (The reason why the net height is 5 - 9mm shorter than the actual height of the cylinder, as described in Step 2, is to allow the month letters to be placed below the x-axis where they can be seen clearly.)

If you want to check a few random figures in the spreadsheet to reassure yourself that they’re right, the NOAA Solar Calculator will provide a sense check. But bear in mind that you will need to adjust the local time to the solar time (eg if on any given date solar noon is given in the calculator as say 12h:16m:06s and you want to check the declination angle and altitude/elevation angle at 2pm, you’ll need enter 02h:16m:06s pm as the local time). Even then, there will be small discrepancies because the NOAA calculator builds in additional factors such as the equation of time and the refraction of the earth’s atmosphere.

Attachments


Astrology Asteroids [interest in astrology/career in astrology]

Urania [80]

In Greek Mythology Urania was one of the nine Muses, the eldest daughter of Zeus and Mnemosyne. She was the Muse of astronomy, astrology, philosophy and cosmology. She is also associated with Universal Love and the Holy Spirit. Back then, Astrology and Astronomy were considered one in the same. They went together and were not separate studies.
Astrologically, Urania represents interest in Astrology or Astronomy, or at least the capacity to understand it. She represents logic and rational thought, astronomy the ability to conceptualize and incorporate theoretical or abstract knowledge. She represents a gift for looking past small detail to a larger concept or theme.
“While Urania shows involvement with astronomy, astrology, mathematics or any kind of theoretical, abstract or symbolic knowledge, it is also the ability to extrapolate principles and relevant data from a mass of facts”. [Mechanics of the Future – Asteroids, Martha Lang-Wescott, 1988]
Look for conjunctions to Planets or the Ascendant. This will represent your ability to naturally analyze data. It will also show your interest or ability to understand Astrology. If conjunct Saturn it could indicate a career in Astronomy, Astrology or data analytics.

Astrowizard [24626]

Dave Rodrigues (a.k.a. the AstroWizard) is a lecturer at Morrison Planetarium and at the California Academy of Sciences in San Francisco. He is also the program director of the East Bay Astronomical Society at Chabot Space and Science Center in Oakland. He is often interviewed on astronomical topics in the Oakland Tribune, San Francisco Chronicle, KCBS news radio, and local TV. He has been a guest on the “KidTalk with Dr. Mary” show on Radio Disney. He assisted in the rescue of Apollo 13 at Chabot Observatory in 1970. Asteroid 24626 “Astrowizard” was named after him for his contributions to Astronomy education.
He would dress up as a wizard to talk to kids about Astronomy. He was very passionate about his work. This asteroid represents the pure fixation and dedication to Astrology or Astronomy. It would be prominent in the charts of those who are die hard commited astrological learners and teachers.

Stargazer 8958 -
This represents those who nobely pursue Astronomy and Astrology knowledge.


Watch the video: Sun-Earth angles. Declination,Altitude, Longitude,Amizuth Angle,Hour Angle,Zenith Angle REE GTU (September 2021).