assignment 1

Astronomy Assignment 1

Visualising the Motion of the Stars

Introduction

This exercise can be done with your eyes closed, perhaps while trying to get to sleep; it can be done by drawing diagrams on a sheet of paper; it can be done by going outside on a starry night and waving your arms around. Perhaps you will try all three methods. It isn’t an exercise to try in a few minutes but one to come back to several times until you really have a good picture in your head of the apparent motion of the stars. When you succeed, you will also be able to visualise how the Sun moves across the sky in all seasons.

Revision Before reading the exercise, here is a reminder of some terms introduced in the lecture course.

Position of the North Celestial Pole Take a line on the ground due North and look from it up into the sky at an angle equal to the latitude of your location on Earth, namely 57° for Aberdeen. You are looking in the direction of the North Celestial Pole. The Pole Star is very close by.

The ZenithThe point in the sky vertically above you.

A Great Circle A circle on a sphere (e.g. the Earth or the sky) whose plane cuts the centre of the sphere. For example the equator is a great circle.

A Small CircleA circle on a sphere whose plane does not contain the centre of the sphere. For example, all points on the Earth that have a latitude of 57° N lie on a small circle.

If these ideas are new to you, take any ball and mark on it an equator and lines of latitude and longitude. Longitude lines are all great circles; latitude lines are small circles, except for the equator.

The Exercise

Take your location as Aberdeen, latitude 57° N. Each question is very short. If you haven’t thought about the motion of the stars before, take the questions slowly and think about each one. The answers are given in [ ]. If you can’t deduce the answer unseen, at least try to figure out why the given answer is correct.

Look up towards the North Celestial Pole (in reality, on paper or in your imagination). How do the stars near the pole seem to move? [in anticlockwise circles centred on the Pole]

Are these stars above the horizon all the time, night and day? [yes]

What is the angle between the North Celestial Pole and the Zenith? [90° -57° = 33° ]

Are stars that pass through the Zenith always above the horizon? [yes]

How big an angle must you look away from the North Celestial Pole before you see a star that just touches the Northern horizon at the bottom of its motion? [57° ]

Does such a star pass South of the Zenith? [yes, because 57° > 33° ]

Stars that are 90° from the North Celestial Pole lie on the Celestial Equator. (e.g. Orion’s belt is close to the Celestial Equator). All stars on the Celestial Equator rise due East and set due West.

Where do stars that lie North of the Celestial Equator rise and set? [Those with Celestial latitudes (called declination) up to 33° rise somewhere between East and North and set between West and North. Stars with a declination of 22.6° rise NE and set NW at Aberdeen. All stars rise and set symmetrically about the North-South line. As you have seen, stars with declination above 33° are circumpolar at Aberdeen and never set.]

Where do stars in the Southern Celestial hemisphere rise and set ? [They rise South of due East and set South of due West]

Do any stars travel along a great circle over the sky? [Yes, the stars on the Celestial Equator. All other stars appear to move around small circles.]

If you have a very clear picture of the motion of the stars, you now have a clear picture of the motion of the Sun in the sky. The sun moves in front of different stars at different times of the year. At the Spring Equinox, it lies on the Celestial Equator (near the star q -Pisces).

Where does the Sun rise and set at the Spring Equinox? [It rises due East and sets due West, as for any star on the Celestial Equator].

What is the Sun’s path at the Spring Equinox? [A great circle. You see a semicircle above the horizon.]

How high in the Southern sky does the Sun get at the Spring Equinox? [90° from the North Celestial Pole; 90° -33° = 57° from the Zenith or 33° from the Southern horizon].

At Summer Solstice, the Sun’s declination is 23°½° (vertically overhead at the Tropic of Cancer).

How high in the Southern Sky does the Sun get at Summer Solstice? [33° + 23½° = 56½° from the Southern horizon.]

Where does the Sun rise and set at Summer Solstice? [ It rises just North of North East and it sets just North of North West, because 23½° > 22.6° , see above.]

How far below the horizon is the sun at midnight on midsummer’s day? [ 9½°, because the Sun is 66½° from the North Celestial Pole and a body at 57° from the North Celestial Pole just touches the Northern Horizon, as you saw earlier.]

Postscript

All the answers to the questions have been given in square brackets. You can be pretty pleased if you got them all right. The point of this exercise is to visualise what is going on. Some find it easier than others. Stars have pretty constant declinations throughout the year. The Sun, on the other hand, changes it’s declination from +23½° at midsummer to – 23½° at midwinter, and back again. In any day, though, you won’t notice the change of declination so it, too, goes around the sky in small circles except for two days of the year (the equinoxes).

If you are thinking about what shape the earth might be and observe how the stars rise, travel and set, not only from "home" but from other places too, then all the facts are explained only by the earth being round (i.e. spherical). If the earth were flat, or cubic or shaped like a tortoise, the facts would be different. It seems to me likely that the brightest of our ancestors would have worked this out, long before written records that constitute the history of civilisation appeared.

Finally, can you visualise how different the motion of the stars will look for a latitude very different from 57° N? Try it for an Arctic explorer or from the plains of Kenya on the equator. When you visit the planetarium you will see if you are right.

JSR