Information on where to look for the stars and planets can be found in the monthly articles published in some newspapers. There are also annually published books containing data on the daily positions of stars and planets.

Star charts

• Patrick Moore (ed.) The Yearbook of Astronomy, Macmillan
• Whitaker's Almanack, A & C Black

Astronomical Ephemeris, such as:

• The Astrolabe World Ephemeris, Whitford Press, U.S, ISBN 0924608226
• Raphael's Astronomical Ephemeris, Foulsham, ISBN 0572031823 (also contains daily planetary and stellar data, though they emphasise the astrological connections)

The Yoursky website gives the position of the planets in the sky at any defined time and date. Yoursky also provides a variety of displays that can be set for major cities all over the world. Yoursky includes an interactive star map that can be set for major cities all over the world for any specified date and time. The map permits you to view in different directions. A downloadable (commercial) version is also available from the website:

Yoursky website

Model planetariums

Models of the solar system (orreries) are available at a very wide range of sophistication and price. A very inexpensive model to make, costing a few pounds, is the Kidz Labs Solar System Model:

Amazon website

A sophisticated motorized orrery costing several hundred pounds is the Helios Planetarium, obtainable from many suppliers including Cochranes of Oxford:

Cochranes of Oxford website

The National Schools Ovservatory also provides a virtual orrery which provides animated models of the planets rotating around the Sun, so that the epicyclic motion can be seen:

National Schools Ovservatory (NSO) website

An animation demonstrating epicyclic motion is available from the University of Nebraska:

University of Nebraska website

A simple but clear animation of the retrograde motion of Mars is shown on the NASA website:

NASA website

Planetariums are located all over the world, offering visits to school parties. An alternative is provided by the Starlab portable planetarium, which is available in many countries. It offers an inflatable planetarium accommodating 30 to 35 students:

Starlab website

At noon the Sun is always due south in the northern hemisphere and due north in the southern hemisphere. It appears to make one revolution from noon to noon (except for some minor deviations which are connected with the changing speeds of the Earth’s orbital motion round the Sun).

The stars appear to make about 1° more than one revolution (360°), so the Sun does not move quite so fast. Like the Moon, the Sun lags behind the movement of the star pattern. But you cannot see it doing this because the stars are not visible during the daytime.

The lagging motion of the Moon carries it right round the ecliptic circle through the star pattern in a month. But the lagging motion of the Sun is slower: 1° in a day, all the way round in a year.

The Zodiac is a belt of the celestial path tilted 23½° from the Equator. The Sun’s yearly path (the ecliptic) runs along the middle line of this belt. The paths of the Moon and planets lie within this belt, which is only 15° wide.

The observations of early astronomers enabled them to determine the following:

• There is an unchanging pattern of stars, revolving daily round an axis through the Pole Star.
• Sun, Moon and planets share that daily motion, except they drift slowly backward through the star pattern.
• The paths of the Sun, Moon and planets fall in a narrow band of the star pattern called the Zodiac.
• ‘Freezing out’ the daily rotation, we find the Sun travels round the ecliptic, the central line of the Zodiac, in a year.
• The Moon travels round an orbit in the Zodiac, tilted at some 5° to the ecliptic, in a month.
• Mars, Jupiter, and Saturn travel round orbits in the Zodiac, making reverse loops, one for each Earth year, as they do so.
• Mercury and Venus are only visible shortly after sunset and before sunrise – they remain close to the Sun.
• Jupiter completes an orbit of the Sun in 12 years, Saturn in 30 years, Venus in a fraction of an Earth year

Early astronomers, in different civilizations, used the observed motion of the stars, the Sun, Moon and planets as the basis for clocks, calendars and a navigational compass. The Greeks developed models to account for these celestial motions.

Copernicus, in the 16th century, was the first to explain the observed looping (retrograde) motion of planets, by replacing a geocentric heliocentric model of the Universe with a heliocentric model. Modern planetary astronomy really began in the 17th century with Kepler, who used Tycho Brahe’s very accurate measurements of the planetary positions to develop his three laws.

Galileo contributed to the development of astronomy by teaching the Copernican view, and by devising a telescope which he used to show Jupiter’s moons as a model for the solar system, among other things.

Newton built on earlier insights with his universal law of gravitation and its fruits: predictions or explanations of Kepler’s laws, the motion of comets, the shape of the Earth, tides, precession of the equinoxes and perturbations in the motion of planets which led to the discovery of Neptune. He also had to invent the mathematics to do this: calculus.

A round Earth

Pythagoras' pupils, if not the great man himself, knew that the Earth is round. Traveller's tales of ships disappearing over the horizon and noticing bright stars, such as Polaris, shifting to a higher position in the sky as one journeyed north suggested a curved Earth.

Aristotle (about 340 BC), two centuries later, supported the idea of a spherical Earth, Moon and planets because:

• the sphere is a perfect solid and the heavens are a region of perfection
• the Earth's component pieces, falling naturally towards the centre, would press into a round form
• in an eclipse of the Moon, the Earth's shadow is always circular: a flat disc would cast an oval shadow
• even in short travels northwards certain stars, such as Polaris, appear higher in the sky.

This mixture of dogmatic reasons and experimental common sense was typical of him and he did much to set science on its feet.

A spinning Earth

When Tycho Brahe was 17, he observed the conjunction of Jupiter and Saturn and was dismayed to find that the astronomical tables of the time were inaccurate in predicting the event by as much as a month. He decided to devote his life to making better tables, for which purpose he constructed better and better instruments.

The birth of modern planetary astronomy, with the three planetary laws discovered by Kepler, was based on the precise observations resulting from Tycho Brahe’s passion for accuracy.

Kepler: Law-giver of the heavens

In the course of his lifetime, Kepler extracted the three great planetary laws which we now call by his name.

• The orbit of each planet is an ellipse with the Sun at one focus.
• The arm from the Sun to a planet sweeps out equal areas in equal periods of time. If you mark the position of a planet once a month on its elliptical orbit, and draw radii from the Sun to those points, the areas of sectors between those radii are all equal.
• If for each planet you take an average radius, R , and the time, T , the planet takes to go once round its orbit (its year) then the ratio R³T² is the same for all planets

The third law, which binds the movements of the planets together mathematically, Kepler discovered, with tremendous delight, quite late in life.

Mapping the Earth’s orbit in space and time

To map the Earth’s orbit around the Sun on a scale diagram you need many sets of measurements, each set giving the Earth’s bearings from two fixed points. Kepler took the fixed Sun for one of these and for the other he took Mars at a series of times when it was in the same position in its orbit.

Kepler proceeded thus: he marked the ‘position’ of Mars in the star pattern at one position (opposite the Sun, overhead at midnight). That gave him the direction of a base line, Sun – Earth – Mars, SE₁M. Then he turned the pages of Tycho’s records to a time exactly one Martian year later. (The time of Mars’ motion around its orbit was known accurately from records over many centuries).

Keplers Scheme to plot the Earths orbit.

Then Kepler knew that Mars was in the same position, M, so that SM had the same direction. By now, the Earth had moved on to E₂ in its orbit. Tycho’s record of the position of Mars in the star pattern gave him the new apparent direction of Mars E₂ M and the Sun’s position gave him E₂ S. Then he could calculate the angles of the triangle SE₂M from the record thus: since he knew the directions E₁ M and E₂ M (marked on the celestial sphere of stars) he could calculate angle A between them. Since he knew the directions E₁ S and E₂ S he could calculate angle B. Then on a scale diagram he could choose two points to represent S and M and locate the Earth’s position,E₂ as follows.

At the ends of the fixed base line SM, draw lines making angles A and B and mark their intersection E₂ . One Martian year later he could find the directions E₃ M and E₃ S from the records and mark E₃ on his diagram. Thus Kepler could start with the points S and M and locate E₂ ,E₃ ,E₄ ..... enough points to show the orbit’s shape.

Knowing the Earth’s true orbit he could invert the investigation and plot the shape of Mars’ orbit. He found that he could treat the Earth’s orbit either as an eccentric circle or as slightly oval but Mars’ orbit was far from circular: it was definitely oval. It was an ellipse with the Sun at one focus – Kepler’s First Law of planetary motion.

Planetary data and Kepler’s Third Law

Kepler continued to brood on one of his early questions: what connection is there between the size of the planet’s orbit and the times of its year?

Students can try and investigate the relationship between the planetary orbit radius, R , and the orbital time, T, using modern data. These are more accurate than the data available to Kepler. It will become obvious, fairly quickly, that simple proportion will not do. For example as R almost doubles in going from Mercury to Venus, T, almost triples; as R grows almost 10 times from Earth to Saturn, T , grows about 30 times.

Kepler wrestled with this for a very long time, trying different combinations, until he found that R³T² was a constant. Kepler was overjoyed!

His three laws were clear, simple and powerful and they fitted the facts very accurately. He earned the title law-giver of the heavens.

Copernicus did not only offer an alternative model that looked simpler than the heliocentric model. He also extracted new information from his heliocentric scheme: the order and relative sizes of the planetary orbits.

But he did not know the real values of planets' orbit radii. For that he needed an accurate measurement of one of the distances. All he had was a Greek measurement of the distance of the Earth from the Sun.

Estimating the size of the planets themselves would have to wait until telescopes had been invented. A rough model of the solar system known to Copernicus would then be:

• Sun - beach ball
• Mercury - a grain of sand, 16m from the Sun
• Venus - a pea, 29m from the Sun
• Earth - a pea, 40m from the Sun
• Mars - an apple pip, 61m from the Sun
• Jupiter - a ping pong ball, 210m from the Sun
• Saturn - a ping pong ball, 380m from the Sun

By the 17th century, people like Descartes and Newton were questioning the Greek view that the circular motions of celestial objects were natural.

For Aristotle, the answer to the question "why does an object go on moving?" had been "Because a force continues to push it along". Galileo suggested that no force is needed to keep an object moving with constant velocity. Newton took this as his first law of motion.

Newton's answer to "What force pushes a planet along?" was "No force is necessary, the motion simply continues". At the time, this was a revolutionary idea. Newton's explanation: an inward force is needed for a curved orbit, continually pulling the planet away from simple straight line motion. Any satellite must fall inward from the tangent to its circular orbit, again and again and again. That falling constitutes an inward acceleration.

Gravity, Newton argued, provides the inward pull acting on every satellite. The acceleration due to gravity is v²R, where v is the satellite’s orbital speed and R is the radius of its circular orbit.