Apparent Motions of the Sun and Stars
Like many people of his time Nicole Oresme (c.1320/5-1382), a prominent philosopher of the late Middle Ages, observed that just as sailors on passing ships find it difficult to identify which of the ships is moving, so Earth rotating under a stationary Sun would give the same appearance as the Sun orbiting a stationary Earth. He also noted how much simpler things would be if the former were true rather than the latter.
The whole of the Universe is in motion: the galaxies are receding from each other; the stars, including our star, the Sun, orbit the centre of the Galaxy (ours); Earth orbits the Sun; the Moon orbits Earth; and Earth rotates on its axis. With respect to Earth, however, the Sun (due to its relative position to Earth) and the stars (because of their distance from Earth) can be regarded as being (almost) fixed in space.
In the northern hemisphere to see the Sun we look southwards and east is to our left. It is Earth rotating anticlockwise (eastwards) that makes the Sun appear to be moving left to right westwards (clockwise) across the face of the planet.
Earth spins at 360/24=15°/hour, which makes the Sun appear to be moving westwards at approximately one angular diameter every two minutes (60×0.5/15) – the Sun and Moon each have an angular diameter of approximately half a degree.
Earth’s axis points northwards to a position close to Polaris, the North Star or Pole Star, which seems to remain almost motionless while the other stars rotate anticlockwise around it ‘above’ Polaris other stars appear to be moving westwards, and ‘below’ Polaris they seem to be moving eastwards) and complete one revolution in about twenty-four hours. But at this distance the movement of the stars is almost undetectable; it is Earth’s own anticlockwise rotation that gives the appearance of the other stars rotating around Polaris.
Ecliptic
If we could see the stars during the day (the glare of the Sun blots them out) then as Earth moves along its anticlockwise path around the Sun, our line-of-sight with the Sun would move westwards among the stars in a great arc encircling Earth. This arc is known as the ecliptic, so-named because lunar (Moon) and solar (Sun) eclipses can only occur when the Moon crosses it. Its plane is coplanar with Earth’s orbit.
At night as the hours pass, the stars retain their relative positions to each other in patterns we call constellations. The Sun can take weeks to ‘pass through’ a constellation so each revolution of Earth about its axis can provide a snapshot of the Sun’s apparent journey. On a clear night just after sunset (the horizon fixes the Sun’s position and blocks out the Sun’s direct light) a constellation visible just above the western horizon will a few weeks later be replaced by the next constellation when our line-of-sight with the Sun moves on to it.For each complete revolution about its own axis Earth travels 360/365≈1° of its orbit around the Sun. From day-to-day the Sun therefore appears to move approximately two angular diameters (2×0.5) westwards against the background of the fixed and normally invisible stars.
Solar System
| Body | Solar Distance (106 km) | Equatorial Diameter (km) | Orbital Period (years) | Orbital Inclination (degrees) |
| Sun | – | 1,391,400 | – | 0 |
| Mercury | 57.91 | 4,879 | 0.24 | 7.0° |
| Venus | 108.2 | 12,104 | 0.615 | 3.39° |
| Earth | 149.6 | 12,742 | 1.000 | 0 |
| (Moon) | – | 3,474 | 1.000 | 5.15° |
| Mars | 227.9 | 6,779 | 1.882 | 1.85° |
| asteroid belt | 329-478 | – | 3.0-6.0 | – |
| Jupiter | 778.5 | 139,822 | 11.956 | 1.31° |
| Saturn | 1429 | 116,464 | 29.457 | 2.49° |
| Uranus | 2871 | 50,724 | 84.02 | 0.77° |
| Neptune | 4498 | 49,244 | 164.793 | 1.77° |
| Pluto | 5909 | 2,274 | 248.4 | 17.1° |
The Solar System consists of the Sun and all the bodies held to orbits around it by the force of its magnetic field. These bodies include the nine planets and their sixty-one natural satellites (moons) plus countless asteroids, meteoroids and comets. Pluto’s orbit marks the outer boundary of the planetary system but many objects lie well beyond this with some of the comets travelling perhaps halfway to the nearest star.
The terrestrial (relating to Earth) planets Mercury, Venus, Earth and Mars are relatively small, similar in composition and density, and because they lie between the Sun and the asteroid belt they are known as the inner planets. The gas giants Jupiter, Saturn, Uranus and Neptune are called the great or Jovian planets, and because they lie beyond the asteroid belt they are known, together with Pluto, as the outer planets. Pluto itself is more like an asteroid.
Motions of the Planets
The ecliptic plane is coplanar with Earth’s orbit around the Sun, and the orbital planes of the Moon and the planets lie within a few degrees of it. Viewed from above (looking south), the planets orbit the Sun in an anticlockwise direction and this is called prograde or direct motion. Most of the planets rotate about their axis in the same sense, but the spin axes of Venus, Uranus and Pluto are tilted at more than 90º and therefore rotate in the opposite, retrograde sense.
Orbital inclination is the angle between a planet’s orbital plane and the ecliptic plane; axial tilt is that between a planet’s axis and the normal to its orbital plane; obliquity of the ecliptic (≈23.45°) is that between Earth’s orbital plane (coplanar with ecliptic) and Earth’s equator (=Earth’s axial tilt)
Conjunction and Opposition
When two Solar System bodies straddle Earth they are said to be in opposition, and when they are in line with Earth they are said to be in conjunction. The Sun and Earth always lie on the ecliptic plane. During Earth’s orbit, the Moon sometimes comes close to the ecliptic plane. When it is between the Sun and Earth (conjunction) there will be an eclipse of the Sun, and when it is on the side of Earth remote from the Sun (opposition) there will be an eclipse of the Moon; hence the name ‘ecliptic’. A heliacal setting is the last visible sighting of a celestial object in the evening sky before its conjunction with the Sun, and a heliacal rising is the first visible sighting of a celestial object in the morning sky after the conjunction.
Equinoxes and Solstices
Earth behaves like a gyroscope in that throughout its journey around the Sun the direction of its spin axis remains constant relative to the plane of the ecliptic. The direction of Earth’s spin axis relative to the Sun is therefore continuously changing during this time. At any instant in time, one half of Earth is in sunlight and the other half is in darkness. The edge dividing daylight from night is called the circle of illumination.
On c.21 December in the northern hemisphere, the winter solstice, the shortest day; the North Pole is pointing directly away from the Sun, the Arctic Circle has twenty-four hours of darkness, and at noon the Sun is vertically over latitude ≈23.45° South, the Tropic of Capricorn.
Six months later Earth reaches the opposite side of the Sun. On c.21 June in the northern hemisphere, the summer solstice, the longest day; Earth’s North Pole points directly towards the Sun, the Arctic Circle has twenty-four hours of sunshine, and at noon the Sun is vertically over latitude ≈23.45° North, the Tropic of Cancer.
Three months either side of these two extremes Earth’s spin axis is tilted neither towards nor away from the Sun but is tangential to the path of Earth’s orbit around the Sun; the circle of illumination passes through the North and South poles, and at all locations Earth’s day and night are of equal length. In the northern hemisphere on the c.21 March, the vernal equinox, and on the c.21 September, the autumnal equinox, the Sun is directly over the equator.
Earth’s axial tilt thus causes the seasons – different latitudes receive varying amounts of sunlight during the year as Earth journeys around the Sun. In the tropics the Sun travels almost directly overhead. In the northern hemisphere the setting position of the Sun oscillates between the northwest (midsummer) and the southwest (midwinter). In midsummer the days are long, but thereafter the Sun’s rising and setting points move steadily further south and the days get shorter and colder.
Precession and Nutation
Due to its rotation Earth is flattened at its poles. The gravitational attractions of the Sun, Moon and the other planets attempt to pull Earth’s equatorial bulge into the plane of the ecliptic. The main effect of this action is that Earth’s axis is forced to undergo a precession – a cone-shaped rotation, both north and south, the movement of which is similar to the motion of a spinning top. This wobbling motion does not affect the tilt angle of Earth but simply varies the direction in which Earth’s axis is pointing. Superimposed on precession is the much smaller oscillation nutation; analogous to the nodding of a spinning top, which causes the tilt of Earth’s axis to rock back and forth and has a period of ≈18.6 years.
Each end of Earth’s axis thus traces out a loop in the sky at an angular radius of ≈23.45°, moving at ≈50.3″ per year along each loop and completing a circuit in ≈25,700 years (≈1° or ≈1 day every 71 years).
The changing position of Earth’s axis makes the stars’ apparent centre of rotation appear to be moving anticlockwise around the loop. At present, Earth’s axis points north to ≈1° of Polaris, the Pole Star; and south to ≈1° of Sigma Octantis. Because precession and nutation cause celestial coordinates to change with time, the coordinates of celestial objects must be referred to a given date or epoch. The epoch in common use is 12 noon 1 January 2000 (written as J2000.0).
Zodiac
| Constellation | Description | Dates | Brightest Star |
| Aries | Ram | 21.03-19.04 | Hamal |
| Taurus | Bull | 20.04-20.05 | Aldebaran |
| Gemini | Twins | 21.05-21.06 | Castor & Pollux |
| Cancer | Crab | 22.06-22.07 | Al Tarf |
| Leo | Lion | 23.07-22.08 | Regulus |
| Virgo | Virgin | 23.08-22.09 | Spica |
| Libra | Scales | 23.09-22.10 | Zubeneschamali |
| Scorpius | Scorpion | 23.10-21.11 | Antares |
| Sagittarius | Archer | 22.11-21.12 | Kaus Australis |
| (Ophiuchus) | Serpent-bearer | 29.11-17.12 | Rasalhague |
| Capricornus | Sea-goat | 22.12-19.01 | Deneb Algedi |
| Aquarius | Water-bearer | 20.01-18.02 | Sadalmelik |
| Pisces | Fishes | 19.02-20.03 | Alpherg |
From day to day the Sun, Moon and all the other planets except Pluto (inclination ≈17.1º) appear to move anticlockwise across the sky within the zodiac, a strip ≈8º either side of the ecliptic. The Moon overtakes the Sun about once a month.
The Greeks divided the zodiac into twelve areas and named them after the constellations that occupied the positions at the time. Due to precession the constellations are now 30º east of the constellations for which they were named. The astrological dates are therefore about a month out from those of the constellations, the astronomy dates advancing by approximately one day every seventy-one years.
Claudius Ptolemaeus (c.100-c.170) listed forty-eight constellations, all of them, of course, visible from the northern hemisphere. More were added in the sixteenth, seventeenth and eighteenth centuries, especially when explorers began to visit the southern hemisphere.
In 1930 the sky was divided up into eighty-eight areas. This was primarily to help make the work of the astronomers more efficient, and so the revised boundaries of the constellations do not therefore in any meaningful sense equate to those of the zodiac signs. Along fwith the twelve original constellations a thirteenth constellation, Ophiuchus, was included within the bounds of the zodiac. The direction of any celestial object can be indicated by saying that it ‘lies in’ a certain constellation.
Calendars
Earth’s period of orbital revolution around the Sun with reference to the fixed stars is called the sidereal year: 356.25636 days. However, the positions of the stars are gradually changing because of precession. The solar or tropical year is measured between successive passages through the mean equinox, which takes account of precession and is equal to 365.24219 days. This is the most commonly adopted definition of the year as it is the one that relates directly to seasonal changes.
The Moon keeps the same face towards Earth because its sidereal period of axial rotation of 27.322 days is the same as its orbital period. The lunar or synodic month, i.e. the mean period between complete successive occurrences of identical lunar phases, is 29.53059 days.
Calendars of the world have usually been set by the Sun and Moon, measuring the day, month and year. As the year (≈365¼ days) and the month (≈29½ days) are not commensurate, early astronomers found it necessary to assign different numbers of days to successive months or years to make their calendar year correspond with the solar year.
In ancient times people thought that celestial phenomena, especially the planetary motions, were related to their own destinies. This belief, astrology, encouraged the development of mathematical schemes for predicting planetary motions and this helped to advance the science of astronomy.
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