The general plan is straightforward.
With WebGL, this can be done on a web page that anybody can access. With the three.js library, the 3-D part of the programming is relatively easy.
We derive star colors from the B – V color index of the star using a rough, but probably satisfactory, method, derived from the table in a Cornell Ask an Astronomer answer.
I see methods given on Stack Exchange that may be better. They involve converting B – V to the star‘s temperature and then a large-ish table to convert temperature to color.
I read that, viewed from space, the Sun looks white. Going by the RBG color that the Planetarium computes from its B – V value, that would mean that about half of the Sun’s blue light is scattered by Earth’s atmosphere (making the sky blue). Therefore, when the viewer is off the Earth’s surface, I have doubled the blue component of a star’s RGB color to approximate what its color would be when it has not been filtered by Earth‘s atmosphere.
All this is rather rough. But we can compare how the Big Dipper looks (from space) in the Planetarium, with NASA photo ISS006-E-40544, taken from the International Space Station. The Planetarium view comes off pretty well.
If we simply place double stars onscreen in the positions given by the catalog, they don’t look as bright as they ought, because they overlap, one blocking out part of the other.
We address this problem by enlarging the star that is behind so that its visible area, not overlapped by the star in front, is about the same as its unenlarged area was. As zoom increases, the planetarium increases apparent star radius more slowly than apparent distance between stars. That makes stars overlap less, and creates less need to enlarge one of them, until they no longer overlap at all.
Most common names of stars come from the Wikipedia Proper Names of Stars article.
For proper planets (not the Sun, which is at the origin, or moons of various planets), positions are computed from their Keplerian elements as given in Keplerian Elements for Approximate Positions of the Major Planets by E. M. Standish.
We only need to compute the heliocentric positions of the planets. The WebGL engine does the work of converting those to positions in the sky relative to the observer, wherever that observer may be.
We need an especially good approximation of the orbit of the Moon around the Earth because its position is easily observed and also documented in historical observations of eclipses.
To do this, I have borrowed Javascript code this from Martin Vézina’s Planet Positions project, which was itself translated from Matlab code by David Eagle. But this code is a straightforward implementation of the “Tables for Osculating Orbital Elements” section in the ELP book, Lunar Tables and Programs From 4000 B.C. TO A.D. 8000 by Michelle Chapront-Touzé and Jean Chapront.
Using the osculating orbital elements seems to be slightly more accurate than using the abbreviated form of ELP given by Meeus in chapter 47 of his Astronomical Algorithms. Implementing full ELP is beyond our scope for now.
We take the orbital elements of other moons from Planetary Satellite Mean Orbital Parameters at JPL. These do not represent all the moons’ orbits very accurately, but for many are fairly good. They cannot be very accurate because a planet’s moons perturb each other’s orbits, something that the Keplerian orbital elements cannot represent. We have done some extensive, though not exhaustive testing on accuracy, discussed below under Accuracy.
Starting in 3.5.0, precession of the Equinoxes is modeled for Earth only. For Earth, we must model precession to get both an accurate position for the Earth and accurate times for the equinoxes.
Data on radii, oblateness, and rotation rates of planets are taken from NASA planetary fact sheets. Information on radii and rotation of their moons is taken from the satellite fact sheets linked to each planet fact sheet.
For planets that have visible features with known longitude – Mercury, Earth, and Mars – I have made the line of longitude zero correspond to the proper place on the planet’s image. That has always been either the left edge or the middle. I also found a map of Jupiter that gave longitudes and latitudes and followed that for longitude, though I don’t know how useful that really is on a planet covered by clouds driven by high winds. For the other planets – Venus, Saturn, Uranus, Neptune – longitude is arbitrary.
For synchronously rotating moons (currently, that is all of them), the Planetarium always makes the line of longitude zero point toward the moon’s parent planet. (I understand this is not quite right and may adjust it, eventually.)
Except for Earth, I don’t have any information giving the rotation of a planet at any given epoch. The rotation rates I have are also not especially accurate, so how planets are rotated in the planetarium will not correspond to how they are actually rotated.
Almost all the moons represented in the Planetarium rotate (or are thought to rotate) synchronously, once for each orbit around its planet. The Planetarium represents a few moons for which I don’t have rotation information (such as Uranus’s moons Ophelia, Cordelia, and Margaret). For want of anything better, the Planetarium treats their rotation as synchronous, too.
When the home planet is a proper planet, a purple line indicates the plane of its orbit around the Sun. Declination corresponds to latitude on the planet. The line of right ascension 0 is the line orthogonal to the equator that passes through the standard (ICRF) spring equinox point, approximately the point where the Sun crossed Earth’s equator from south to north in March, 2000. (This is a change in 3.5.0, in order to use the standard definition of the prime meridian.)
For moons, the purple line represents the parent planet’s orbital plane, since that is still the approximate plane of the moon’s orbit around the Sun and that is where other planets will be found. Other than Earth’s Moon, most moons have equatorial orbits and little obliquity, so other moons of the same parent will be found along the equator.
Many of the moons represented in the Planetarium are not very round. For Phobos and Deimos, Thebe, Amalthea, Larissa, and Proteus there are old, not very detailed 3-D models by Philip Stooke, pioneer of the “geography” of small bodies in the Solar System. (I found them on the Small Bodies Data Ferret.) I used these models rather than newer, more detailed ones because they are simple, small, and computationally cheap. When there is a good image of a moon to go with the model (Phobos!), they seem pretty adequate. Even when there is no image, they are definitely more realistic than prolate ellipsoids.
The Planetarium represents non-spherical moons that have no 3-D model as ellipsoids with axes as given in the "Bulk parameters" section of their parent planet’s "Satellite Fact Sheet" under the NASA Planetary Fact Sheets page. For example, for Jupiter, the satellite fact sheet page is Jovian Satellite Fact Sheet Page.
Planet images (cylinder maps) come from various sources.
As of version 3.3, the Planetarium models the speed of light as finite (at 1 AU per 499 seconds).
The main effect is unobtrusive – planets and moons will appear to be where they were when the light left them, a few minutes or hours ago. One may also be able to see a planet turn or its moons move during a "slow" (non-instantaneous) jaunt. One can definitely see those two effects when backing away from a planet using the Altitude control, because it works exponentially.
The Planetarium does not try to model the red/blue shift of light color when moving at high velocity. During a “slow” jaunt, we may be moving at 500 or 1000 times the speed of light, so the shift does not really make sense.
Here are some things the Planetarium is not doing right.
There are several reasons why positions calculated for moons are less accurate than those for planets.
That would mean that the Planetarium orbit is at least qualitatively right, and that at least I haven’t miscopied the orbital elements.
We see this for almost all moons. The obvious exceptions are Janus, Mimas, Tethys, and maybe the inner moons of Jupiter. It would be interesting to have a model where we could watch them being jostled around by their neighboring moons.
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