AstroSpeedrun
O3.1

Reading the dome

Builds on
Sections O1.1, 1.2 and 1.4
Reading time
30 min
Exercises
3
Olympiad problems
0

In the observation round of IOAA 2019 in Keszthely, three skies were projected in turn on the dome of a planetarium. The first was the sky above Keszthely at midnight on an unnamed date. The second came from an unnamed place on Earth, and the third was seen from the surface of the Moon. Between them the three skies asked for a latitude, a time, the stars that never set and objects marked on the dome, and most parts needed nothing beyond Chapters 1 and 2. They needed the habit of reading a whole sky quickly, which this chapter trains.

O3.1.1What the dome shows

Before you readMake a guess first

A chart shows the whole sky overhead, with north at the top. On which side of the chart is east?

A planetarium is a room with a hemispherical dome for a ceiling and a projector that shows the stars on it as they would be seen from any place at any moment. The top of the dome stands for the , and its rim for the horizon. The projector can run time forwards or backwards, move the observer to another latitude or another world, and add or remove lines such as the celestial equator, the ecliptic and the figures of the constellations. In a question it usually shows a sky without saying where or when, and the place and time are part of what we are asked to find.

On a worksheet the dome is printed as a flat circle, with the zenith at the centre and the horizon round the edge. North is at the top, south at the bottom, and east on the left. The reason is that we look up at the sky. Lying on our back with our head to the north, we have east on our left hand and west on our right, and a chart of what we see keeps them there. A map of the ground, seen from above, has them the other way round.

Figure O3.1The sky on a planetarium domeinteractive
View
Draw
StarTap a star on the dome.
Altitude and azimuth
Declination
The figure shows the whole sky as a planetarium dome shows it, drawn from a star catalogue, with the zenith Z at the centre and the horizon as the outer circle. N, E, S and W are the north, east, south and west points of the horizon, with east on the left. The sliders set the latitude of the observer and the local sidereal time, and the buttons draw the celestial pole P, the meridian, the celestial equator and the ecliptic. Tapping a star gives its altitude, azimuth and declination. The view switch shows the same sky as it looks from under the dome, facing one way, with the ground hatched below the horizon, and dragging the picture turns the view. The sky starts above , with Orion high in the south. Orion has just set in the west and Leo is high in the south-west. From Orion stands upside down in the north and Polaris is gone below the horizon. Standing , we find P 40° up, with Polaris beside it and east on our right.

The of a star is measured along the horizon from the north point through the east point, as Section 1.2 explained, so on the chart it runs anticlockwise, from N at the top through E on the left. Its altitude is its angle above the horizon, 90° at Z and 0° at the edge.

Quick checkA star towards the west

On the chart of the dome, a star lies on the straight line from the zenith to the west point. What is its azimuth?

degrees

O3.1.2Angles on the dome and on the chart

Seen from the centre of the dome, angles are true. A star halfway up the dome, from the horizon to the zenith, is at an altitude of 45°, and the angle between two stars can be judged with a hand held at arm's length, as Section O1.1 described. A flat chart of the dome cannot keep every angle true. The charts in this course use a projection that keeps the shapes of the constellations, and in it the sky is stretched towards the horizon. A star halfway from the centre to the edge of such a chart is lower than 45°, as the example below shows. Printed worksheets in the exam may use other projections, so altitudes are best judged on the dome, or from any grid of altitude printed on the sheet.

Example O3.1Halfway to the edgefinish it

On the charts of this course a star at zenith distance z lies at a distance proportional to tan⁡(z/2) from the centre. How high is a star drawn halfway from the centre to the edge?

The start

The horizon, at z=90°, lies at a distance proportional to tan⁡45°=1. Halfway out, tan⁡(z/2)=0.5.

Your stepNow find z, and then the altitude.
degrees

O3.1.3A plan for the round

The time in the dome is short and the room is dark. In 2014 in Suceava the round inside the dome took 30 minutes for three questions, and each object was pointed out with a small red arrow for two minutes only. A fixed order of work saves that time.

  1. We first find the four points of the horizon, which the projector usually marks, and then the brightest stars and the patterns we know from Chapter O1.
  2. Next we find the celestial pole and the meridian, since almost every question about the place or the time starts from one of them. Section O3.2 shows how.
  3. Then we read all the questions before answering any, so that we know what to look for while each part of the sky is shown.
  4. We write answers in large, clear letters, using a red torch if one is allowed. A small error in the dark is easy to make and costly, since some questions take a point away for each wrong mark, such as each extra circle on a chart.
Common errorsSection O3.1
  1. On a chart of the sky overhead, east is on the left when north is at the top. A chart read like a map of the ground puts every east and west the wrong way round.
  2. Distances on a flat chart of the dome are not true all over. On the charts of this course the sky near the horizon is stretched, so a star near the edge is lower than it looks.
  3. The dome may show the sky from any place on Earth or beyond it. The latitude has to be read from the sky itself, and should never be taken from the city where the exam is held.
ExercisesSection O3.13 questions
  1. O3.1.1

    A star lies on the horizon of the dome, exactly halfway between the north point and the east point. What is its azimuth?

    degrees
  2. O3.1.2

    On a chart of the dome with north at the top, where is the west point?

  3. O3.1.3

    On one of the charts of this course, a star is drawn three quarters of the way from the centre to the edge. Using the rule of the finish-it example above, what is its altitude?

    degrees