Solar Coaster provides accurate position, time, motion and eclipse information for Earth's nearest star, Sol, our Sun, and nearest celestial body, Luna, our Moon. Information includes 3D movement graphs, upcoming eclipses and their circumstances, rise and set times, positions, distances and velocities, moon phase, illumination and crescent rotation.

Solar Coaster automatically updates its state every minute, or you can examine minutes randomly. The simulation uses a local horizontal coordinate system when displaying information, which essentially means that your current position is the center of the Universe and all calculated values are relative to you. Sun and Moon positions are also available in equatorial coordinates.

Solar Coaster stores enough onboard astronomical data to keep it running through the year 2100 AD, which means that all calculations can be performed locally without the need of a network connection — useful while in the wild chasing an eclipse. Algorithms are accurate at all longitudes, and latitudes between -61° south and +60° north (roughly speaking, locations outside the Polar regions). Of course, you must have Location Services enabled and allow Solar Coaster to access your position for accurate simulation results, and to properly detect eclipses visible at your location. You can also allow Notification Center to keep you informed when those eclipses will occur.

When Solar Coaster first runs, iOS and macOS ask for permission to access your current location with this note: "Your location is required for solar and lunar orbital calculations, and eclipse predictions". If you decline this request a default location of the Royal Observatory, Greenwich, England is used. To subsequently enable Location Services:

• For iOS touch Settings / Privacy & Security / Location Services, ensure the service is on, then scroll down to Solar Coaster and enable While Using the App.
• For macOS click System Settings / Privacy & Security / Location Services, ensure the service is on, then check all of Solar Coaster and legacyScreenSaver.

Solar Coaster comes in various flavors: for iOS a native App; and for macOS a native App, Screen Saver and Web App.

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The Solar Coaster window is simplest when it first opens, you'll see something like this:

• A sinusoidal curve, with its highest point representing Solar Noon
• A horizontal horizon line
• The Sun and its rise and set times
• The Moon, assuming it's up, in its proper phase and the crescent (not the Moon) rotated exactly as it appears in your sky

The horizon line is drawn such that it intersects the curve at precisely two points, Sunrise and Sunset. This means that all points on the curve above the horizon line are Day, and those below are Night. As the lengths of Day and Night change this horizon line shifts up and down the curve, and a trend direction triangle indicates how the shift is moving.

Solar Coaster has many active elements that you may touch/click - the horizon line trend triangle is one, touching it displays the number of daylight hours. In Image 1 there are four other active elements:

• The disclosure boomerang at the top-left
• The ellipsis menu at the top-right
• The Sun
• The Moon

Image 2

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Sometimes the Basic screen is all you want and need, but for deep diving touch the disclosure boomerang and transition to Solar Coaster's Details screen where you can:

• Probe for imminent eclipses and discover their circumstances.
• Randomly inspect instantaneous metrics for every minute of an eclipse day.
• Generate a 3D position vs time plot comparing Sun and Moon tracks.

You can manipulate simulation time by sliding the yellow circle along its vertical track, selecting any of the day's 1,440 minutes - and that's the state depicted in Image 3a, where sim time is 08:27, 6 hours and 6 minutes before the sim time in Image 3b. This time delta, δt, relative to Now, whether positive or negative, is shown above the horizon line.

In a left-right comparison, visually the Sun has gained Altitude as time increases, which the Altitude metric confirms numerically. Visually the Moon has fallen in Altitude, also confirmed numerically. Numerical metrics for Distance and Velocity and their trend arrows are also consistent. (The decrease in the Moon's crescent is tougher to verify visually, although we'll try, shortly ...)

Other items of interest are:

• The date and GPS coordinates (just beneath the Sun's rise and set times) are the same.
• A green Start button that runs the simulator at Express speed to rapidly animate sim time through the entire day.
• A "diff" comparison button that creates the 3D position plot (discussed in the next section).
• There's a change in background color - refer to section Custom Backgrounds and the Palette Editor for the explanation.
• The circular markers of various colors that dot the curve. The yellow marker is Now, where the Sun sits. The silver markers indicate Moonrise and Moonset, assuming there is a rise and/or set for Today. White markers represent the cardinal times of the day Solar Midnight, Dawn, Sunrise, Solar Noon, Sunset and Dusk. There are two physically separated Solar Midnight markers, but they are logically the same, they are dual in time. Touching a marker displays its time of day (unavailable for the Screen Saver).

And finally, you judge if the Moon's crescent has actually decreased by 2.5%. Checkout this short movie compressing almost 10 hours of clock time (-8:30 ≤ δt ≤ +1:10) and watch simulation time and δt flow, and the crescent (not the Moon) roll over - zoom in and pay close attention to the landmarks on the Lunar surface. Touching the Start button created the actual animation, the movie simply cropped the result:

Touch the disclosure boomerang once again and resume the real time simulation. Don't be surprised if you notice the visualization catch up for lost time. And depending on what the time differential is and whether the simulation time is before or after Now, the tweening may be fast or slow or forward or reverse.

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From Details touch compare tracks .   A 3D plot appears, graphing Sun and Moon altitude vs azimuth vs simulation minute 0 - 1439.

The two discontinuities marked by straight lines exist because time is modulus 1440. Perhaps they hint that a coordinate transformation can logically join the ends of each track by projecting azimuth onto a 2D viewing plane. Watch Movie 2 and see, while also convincing yourself that neither track intersects the other.

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From Details touch an Eclipse Probe to initiate a search for upcoming Solar or Lunar eclipses. If one is visible from your location the eclipse circumstances are displayed and the simulator is temporarily reset to the eclipse date, allowing you to view metrics and do a tracks plot.

Close Details to restore the simulation date to Today.

The next section highlights these eclipses using interactive 3D plots of the daily tracks the Sun and Moon traverse in altitude-azimuth-time space. Eclipse times are in 24 hour format HH:MM (ignore seconds); in contrast, 3D plot times are in simulation minutes, so this conversion formula will prove useful:

Thus, the middle of the Lunar eclipse at 04:59 is sim minute ( 4 * 60 ) + 59 = 299, and Solar eclipse maximum 12:59:29 is sim minute ( 12 * 60 ) + 59 = 779.

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The examples in this section are based on the total eclipses detailed in Image 4a and Image 4b. The corresponding metrics, proximate to each maximum eclipse, are shown in Image 5a and Image 5b.

A total Lunar eclipse occurs when the Moon's phase is Full and Illumination 100%, where Earth is between and precisely in-line with the Sun and Moon. Becauase the diameter of Earth's shadow upon the Moon is much larger than the Moon, this event is visible from the entire hemisphere of Earth facing the Moon. And the physical configuration of the three bodies requires that Sun-Moon azimuths differ by 180 °, as Interactive Plot 1 confirms.

A total Solar eclipse occurs when the Moon's phase is New and Illumination 0%, where the Moon is between and precisely in-line with the Sun and Earth. Because the diameter of the Moon's shadow upon Earth is relatively tiny, this event is visible only inside a narrow path of totality. The 2017 eclipse path width varied from ~= 55km to 115km. And the physical configuration of the three bodies requires that Sun-Moon azimuths and altitudes coincide, as Interactive Plot 2 confirms.

Separation distance between the bodies is also critically important, encoded in the metric angular diameter. Ideally the Moon should appear slightly larger than the Sun - if not the total eclipse is called an annular eclipse.

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Access to Settings hides inside the ellipsis menu.

Solar Coaster's background is actually a gradient of colors keyed by time of day. To create a custom gradient see the next section Custom Backgrounds and the Palette Editor.

Typically, the host operating system automatically determines your position - the notable exception is the Screen Saver which is denied location services. To set a location all three fields must be valid numbers:

•  -61 <= Latitude  <=    60
• -180 <= Longitude <=   180
•    0 <= Altitude  <= 26000 (if unknown use 0)

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Solar Coaster's background is patterned after a continuously varying color gradient. In reality the background changes discretely throughout the day, minute-by-minute. A custom background behaves identically and once created is useable on iOS, macOS and Screen Saver.

Custom backgrounds are generated using the Palette Editor bundled with Solar Coaster for macOS. The editor uses a palette of colors you choose and associate with cardinal times of the day (Sunrise, etc.), builds a special text data structure of the background palette, and saves it to the Mac's filesystem. Selecting Custom in Settings on macOS opens a file chooser, while on iOS you Share the background palette from Files, or some other App such as Mail.

Edit / Palette Editor ⌘ P opens the palette currently in use and displays it, as in Image 7.

• The top row reflects any palette edits.
• The bottom row shows the unedited palette.
• There are four action buttons, Open / Save work as expected, while Reset clears any edits and reverts the top row to look just like the bottom row. Test is described below.
• The green triangle points to the current simulation minute.
• The small circular Time Markers represent cardinal times (notice the cursor hovering over Sunrise, sim minute 353) and break the day into various sections. Touch a marker then select a color from the chooser to blend that color with the neighboring sections.
  Realize that a time marker does not represent an actual numeric minute like 353, instead it represents a symbolic time of day like Sunrise, whose actual value will vary day by day over the course of a year.
• The two shorter gray sentinel circles represent sim minute 0 - they are dual in time - and mark where the background wraps upon itself.
• The color of text painted onto the background is given by Foreground Color. The special color opposite means use the background color complement.

Movie 2 demonstrates that creating a custom background is as simple as selecting a palette of colors and distributing them in the desired pattern. The background is assigned its name when saved, fancifully called RGB here.

Test whenever and as many times as required. The candidate background palette is pushed to Solar Coaster and the simulator is kicked to Express speed. While testing, the lower Palette Editor panel is usurped and used to display the changing background - Movie 3.

(Although highly un-recommended, peruse JS-Obj-C-Entanglement.pdf for internal specifications.)

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The Solar Coaster Apps for iOS and macOS are available from their respective App Store and install in the standard manner. Be sure to enable Location Services as described in the Introduction.

Once installed, the macOS App is responsible for exporting the Screen Saver and Web App.

• To install the Screen Saver, which has been digitally signed by BigCatOS and notarized by Apple for your security:
  • Use the File / Export Screen Saver ⌘ E menu item to save the zipped Screen Saver.
  • Or download SolarCoasterSS.zip from BigCatOS.
  In either case double-click the resulting zipped Screen Saver package to unzip it, which creates the module Solar Coaster.saver. Double click the saver module to finish the install and select it from System Settings / Screen Saver.
• To create a Web App for development and experimentation:
  • Use the File / Export Web App ⌥ ⌘ E menu item to save the zipped Web App.
  Double-click the zip file, create the folder named SolarCoasterWeb and open SolarCoasterWeb/SolarCoaster.html. The Web App is also trivially embeddable:

  <embed id='solarcoaster' src='SolarCoasterWeb/SolarCoaster.html?SolarCoasterEmbed'/>

And that's Solar Coaster. Enjoy. Any similarity to the Apple Watch Face Solar Graph is, indeed, intentional.

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OS Compatibilty

iOS	14.0 - 18.5
iPadOS	14.0 - 18.5
macOS	11.0 - 15.5
visionOS	1.0   - 2.5

5.0 - 2025.06.16

• Available as Apps for iOS, macOS, Web, and Screen Saver for macOS.
• 3D visualization that compares the Sun and Moon position tracks in altitude-azimuth-time space.
• New Sun and Moon metrics: maximum altitude, right ascension and declination.
• Dynamic backgrounds that vary lighting as a function of the time of day.
• Improved UI.
• Unified Settings.
• For Mac, a Palette Editor that creates custom dynamic background palettes, useable by iOS, macOS and Screen Saver.
• Bug fixes, miscellaneous improvements and internal modernization.
• Remove Today Extension.
• Refresh documentation.
• Update for iOS 18.5, iPadOS 18.5, macOS 15.5.

4.0 - 2023.01.06

• Add instantaneous orbital velocity based on current distance.
• Add current moon phase name and illumination percentage.
• User interface and documentation improvements.
• Miscellanenous bug fixes.
• Minimum iOS version is 11.0 and minimum macOS version is 10.15.
• Update for iOS 16.2 and macOS 13.1.

1.0 - 2017.01.02

• Initial release.

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