Planetarium and Star Chart, Explained

After reading this you will know how a flat chart can hold the whole dome of the sky, how to convert a star's fixed coordinates into an altitude and azimuth for your backyard, and why a satellite pass can be predicted to the second yet still fail if your data is a week old.

What the tool shows and one example

The planetarium draws the sky as you would see it if you lay on your back and looked straight up. The point directly overhead is the zenith, plotted at the centre. The horizon is the outer ring. Between them sit about 5,000 stars down to sixth magnitude (the faintest a good dark-sky eye can catch), the Sun, the Moon, the seven other planets, and the paths of satellites like the ISS.

Here is the hook. Stand in London (latitude 51.5°N) at 22:00 UTC on 21 June. Vega, the bright star of Lyra, stands high in the east: its altitude is about 60°. Six months later, at the same clock time, Vega skims the north-north-western horizon at about 6°. Nothing moved on the star. The Earth carried you to the far side of its orbit and turned your local midnight to face a different slice of the celestial sphere. The chart makes that swing visible in seconds when you play time forward.

When to use it, and when not

Reach for the planetarium when you want to know what is up right now, where to point a telescope, when the Moon rises, or whether the ISS will cross your sky before bed. It answers "what will I see from here at this time" better than any table.

Do not use it as a precision ephemeris for professional astrometry: the plot cannot show detail finer than a pixel, roughly a tenth of a degree, while the underlying positions are good to a few arc-seconds. Do not use it for deep-space satellites. Objects with orbital periods over 225 minutes, including GPS and geostationary craft, are outside the SGP4 model here and are not drawn.

The coordinate math and the intuition

Every star has a fixed address on the celestial sphere: right ascension \alpha (like longitude, measured in hours) and declination \delta (like latitude, in degrees). Your sky, on the other hand, is described by altitude (angle above the horizon) and azimuth (compass bearing). The bridge between them is the local hour angle and your latitude.

First, the hour angle. It measures how far the star has swung west of your meridian:

Here H is the local hour angle, \theta_L is your local sidereal time (the right ascension currently crossing your meridian), and \alpha is the star's right ascension. When H = 0 the star is due south at its highest.

Then altitude comes from spherical trigonometry:

a is altitude, \phi is your latitude, \delta is the star's declination, and H is the hour angle from above. The intuition: a star's greatest possible altitude is 90^\circ - |\phi - \delta|. From London a star on the celestial equator (\delta = 0) tops out at 90 - 51.5 = 38.5^\circ.

Azimuth uses the companion formula:

A is azimuth measured from north through east. Watch the signs and quadrants: a naive arctangent lands in the wrong half of the sky half the time, so the tool uses the two-argument form.

A worked example reproducing the demo

Reading and interpreting the chart

North is up and east is on the left in the default sky view, because you are looking up, not down at a map. If that feels reversed, switch to map view to put east on the right.

The dashed orange arc sweeping across the dome is the ecliptic, the Sun's yearly path. Planets and the Moon are always found within a few degrees of it, so if a bright "star" sits far from the ecliptic it is a star, not a planet. Magnitude sets dot size: a first-magnitude star like Vega (magnitude 0.03) is drawn much larger than a sixth-magnitude one, and the scale is logarithmic, so each step of 1 magnitude is a brightness ratio of about 2.512.

For satellites, the pass table tells you three things that matter: the peak altitude, whether the pass is sunlit, and whether your sky is dark. A pass is visible only when the satellite is in sunlight while you are in darkness, which is why the best ISS passes come in the couple of hours after dusk or before dawn.

Common mistakes

The first trap is time zones. The tool reads and shows your browser's clock, but the physically meaningful instant is the UTC value printed under the chart. If you enter 22:00 while your computer is set to a different zone than the place you are studying, you are looking at a different moment of the sky than you think. Always check the UTC line.

The second trap is stale satellite elements. SGP4 propagation is precise, but a two-line element set drifts. Errors of a few kilometres per day accumulate, so a set that is a week old can put the ISS in the wrong part of your sky by a minute or more of pass time. Fetch fresh elements for passes tonight.

Related tools

If your interest is the Sun rather than the stars, two neighbours help. The Day and Night World Map shows the sunlight terminator sweeping the globe, which tells you at a glance whether a place is in the darkness a satellite pass needs. The Solar Time vs Clock Time tool explains why your clock noon is rarely the Sun's noon, the same offset that shifts a star's meridian crossing away from a round clock hour.

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Solar Time vs Clock Time

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