PART 2 - MOTIONS IN THE SKY - ASTRONOMY BY EYE

What we see in the sky

• What astronomical objects do we see in the sky? Where are they in the general context of the overview of the Universe?
  • All of the stars we see are in the Milky Way galaxy, most of them relatively close to the Sun.

  • The stars we see in the sky come in a range of brightnesses, partly because stars come in different intrinsic brightnesses, and partly because some are closer than others.

  • When we look at an astronomical object ``by eye'', we can't tell just by looking how far away it is (because not all objects have the same intrinsic brightness). All we can see is what direction it is in.

  • As a result, the positions of stars on the sky is described by their direction only; you can imagine that the sky is a big sphere with astronomical objects located at different positions on it. This is called the celestial sphere
    • The positions of the stars can be described with a sort of astronomical longitude and latitude, called right ascension and declination.

  • Constellations are patterns of stars seen in the sky. However, although the stars in any constellation are all in the same general direction in the sky, the different stars in a constellation may be at very different distances from Earth, hence constellations may not be real associations of stars in space, just stars in the same general direction as seen from Earth.

  • Only the nearest galaxies are visible to the naked eye, as relatively faint smudges of light, although two of the very nearest galaxies, the Magellanic Clouds, are visible are moderately large clouds from the Southern hemisphere.

Motions in the sky

• Observing and understanding motions in the sky is what led people to understand the layout of the Solar System, and to understand how the Earth moves in space.

• Do objects in the sky appear to move? Group exercise

• Objects can appear to move in the sky either because they are actually moving, or because they reflect our motion through space
  • For stars, almost all apparent motion comes from reflex motion, because they are so far away that their intrinsic motion appears very small.

  • For planets, apparent motion in the sky comes from a combination of their intrinsic motion (around the Sun) and their reflex motion.

• The rotation of the Earth on its axis causes all objects to appear to move around the sky once each day. The apparent motion of a star to an observer which arises from the Earth's rotation depends on the location of the observer on Earth, and the location of the star relative to Earth's rotation axis.
  • A diagram shows the idea

  • Stars appear to travel in circles around the celestial sphere. Objects near the poles travel in small circles; far from the poles, they travel in large circles.

  • The orientation of the circles as seen by observers depends on their latitude on Earth. Depending on your location, some stars are visible all of the time, others rise and set, and some are never visible. (Note that when I say visible all of the time, I mean they could be seen in the sky all the time if sunlight didn't overwhelm them during daylight!).
    • Example: view from the North Pole
    • Example: view from the equator
    • Example: view from northern hemisphere, e.g. Las Cruces

    • Example: a real picture of stars (question: how long did it take to make this picture?) in the direction of the North pole (time lapse movie)

• Day and night occur because of the same rotation of the Earth, which makes the Sun appear to move around the sky once each day.

• The motion of the stars and the Sun can be used to tell time. We define a day to be the length of time it takes for the Sun to come back to the same position in the sky.
  • It takes about 24 hours for the stars to return back to the same position in the sky. Consequently, one can measure time by the fractional distance a star has gone in its full circle around the sky. This is best done for stars which never set, i.e., stars near the north celestial pole. It is made easier because there happens to be a star located almost at the location of the pole, called the North Star. This movie shows the idea.

Earth's revolution and the seasons

• In addition to the Earth's rotation, the Earth also revolves around the Sun, once every 365.25 days.
  • Consequently, the Sun appears to move with respect to the stars. Each day the motion of the Sun is like the motion of a star, but not always the same star throughout the year.

  • Because of the Earth's revolution, we see different stars during the night over the course of a year.

• The Earth's rotation axis is tilted by 23.5 deg with respect to the plane of its revolution around the Sun.
  • Because of this tilt, the latitude (or declination) of the Sun changes throughout the year. As a result, the path of the Sun through the sky changes throughout the year. During our summer, the Sun is further north than it is during our winter.

  • The tilt of the Earth's rotation axis defines several special locations in the Earth's orbit: solstices occur when the rotation axis is pointing towards or away from the Sun, and equinoxes occur halfway between the solstices.

• Different seasons occur at different points in the Earth's orbit
  • Group exercise: why do we have seasons?

  • The tilt is the main thing that is responsible for the difference between our seasons. In summer, the Sun's rays hit the earth with more energy being concentrated in each location, as a result of the Sun being higher in the sky. This is the main reason that it is warmer in the summer.
    • The same argument about the angle with which the Sun's rays hit the Earth also explains why it is colder at higher latitudes, and also why it is hottest in the middle of the day.

    • The different paths that the Sun takes across the sky as a result of the tilt of the rotation axis also causes the length of the time the Sun is above the horizon to change over the course of the year. Days are longer in the summer than in the winter, and this also contributes to making it warmer during the summer.

  • Seasons are NOT produced by the varying distance to the Sun as the Earth makes its elliptical orbit about the Sun (Earth's orbit is very close to circular).

  • All planets rotate and revolve around the Sun, but different planets have different tilts of their rotation axes relative to their axis of revolution. The tilt of Mars' axis is similar to that of Earth. The rotation axis of Jupiter, however, is perpendicular to its plane of rotation. The rotation axis of Uranus lies almost totally in its plane of rotation! Consider the implications for the existence of seasons on other planets. For some planets (but not Earth!), like Mars, the non-circularity of their orbits also plays a role.

• The nearest stars appear to move slightly over the course of the year because of the reflex motion from the Earth's revolution; this motion is called parallax. Most stars, however, are so far away that this motion is unobservable. It is very small even for the closest stars - so small that it requires good equipment on a telescope to even detect it.

Moon's orbit and phases

• The Moon moves around the Earth, once every 28 days or so. Hence the apparent motion of the Moon is a combination of the reflex motion from Earth moving, as well as the intrinsic motion of the Moon around its orbit.
  • The plane of the Moon's orbit is close, but not identical, to the plane of the Earth's orbit around the Sun. Because of this, its motion in the sky over the course of a day (from the reflex motion of the Earth's rotation) is similar to that of the Sun. However, the motion of the Moon on any given day will not in general be the same as the Sun on that day.

    From day to day, the position of the Moon will change due to its intrinsic motion in its orbit, causing the Moon to appear to move through the background stars. The daily motion is more substantial than that of the Sun, because it only takes 28 days to complete an orbit, as opposed to the 365 days it takes for the Earth to go around the Sun.

  • The Moon also differs from the stars and Sun in that we are seeing reflected light (from the Sun) when we look at it. The appearance (phase) of the Moon is determined by the relative locations of the Sun, Earth, and Moon. One hemisphere of the Moon is always illuminated by the Sun, but from Earth, we may only see a part of this hemisphere, depending on the location of the Moon.
    • The time of day we can see the Moon depends on where the Moon is in its orbit relative to where the Sun is
    • Since the apparent phase of the moon is also related to the Moon's location, it is directly related to the time at which the Moon rises and sets.

  • Although the orbit of the Moon is tilted with respect to the plane of the Earth's rotation, at certain times of year the Moon can be in the same plane as the Earth and the Sun around new or full moon, and when this happens, we can get eclipses. Eclipses occur when one astronomical body moves into the shadow cast by a second astronomical body.
    • A lunar eclipse can occur at full moon when the Moon moves through the shadow of the Earth, if all three objects (Sun, Earth, Moon) are in the same plane.

    • A solar eclipse can occur at new moon when the Moon's shadow falls upon the Earth, if all three objects (Sun, Moon, Earth) are in the same plane.

    • We don't see an eclipse every month because the plane of the Moon's orbit is slightly tilted with respect to the plane of the Earth's orbit around the Sun.

    • Since the Earth is larger than the Moon, during a lunar eclipse the moon fits entirely in the Earth's shadow, and an eclipse can be seen from all over the Earth. However, during a solar eclipse, the Moon's shadow only falls on a portion of the Earth, so each solar eclipse can be seen only from some portion of the Earth.

• For solar system objects (Sun, Moon, planets), the appearance in the sky can qualitatively be described by considering:
  • What path do they appear to travel in over the course of a day?
  • What time of day can we see the object? Alternatively, if we look at the same time of day, day after day, how does the object move across the sky?
  • Do they have phases? How do the phases change?
  • For example, consider the Sun and the Moon

Apparent motion of the planets

• Now consider the planets. We consider the apparent motion and appearance of planets because they provide a good exercise in visualization, and also because observations of planetary motions were very important historically in helping us to come to understand how objects move in the Solar System, as we'll discuss shortly. The planets also move around the Sun. Because of this and also because of the reflex motion from the Earth's revolution, the planets also appear to move with respect to the stars.
  • The qualitative motions of the planets can be understood if one recognizes that:
    • All of the planets move around the Sun in roughly the same plane

    • All of the planets move around the Sun in the same direction

    • The planets which are nearer to the Sun move faster than those which are farther away

  • Consider Mercury, Venus, Mars, and Jupiter for a group exercise

  • The motion can be complex, exhibiting retrograde motion, which occurs when the planet appears to move backwards in its normal path. Retrograde motion occurs because the apparent motion of planets arises from a combination of their intrinsic motion and the reflex motion which appears because Earth is moving.
    • The inner planets (Mercury and Venus) show retrograde motion because they are moving around the Sun, and we are viewing this motion from outside of their orbits. For half of their years, they appear to move in one direction as seen from Earth; for the other half, they appear to move in the other direction.

    • The outer planets show retrograde motion because the Earth moves around the Sun faster than the outer planets, and thus it will periodically pass the outer planets in their orbits. When this happens, the planets will appear to reverse direction when seen from Earth.

  • Because we see planets in reflected light, they have phases; not all of the sunlit half can be seen from Earth at all times. Different planets have different phases in which they can be seen, depending on whether the planet is closer or further from the Sun than the Earth.

Historical development of ideas about the Solar System

• The historical development of ideas about motions in the Solar System provides a good example of the process of science. (presentation format)

• The history of astronomy demonstrates that progress in scientific models often results from either a change in world view (or preconceptions about how people expect the universe is organized) or the availability of new, more accurate measurements, which often result from the development of new technology.
  • The current picture we have of motions in the Solar System was figured out by making careful observations of motions of objects in the sky.

  • Basic observations:
    • Sun appears to go around in the sky
    • Stars appear to go around in the sky, but a slightly different rate
    • Moon appears to go around in the sky, at a different rate
    • Planets are objects with more irregular motion in the sky; they occasionally exhibit retrograde motion. Some are visible only at certain times of day (in particular, Venus).

  • The Greeks, led by Aristotle & Ptolemy, envisioned an idealized universe with the Earth at the center and all planets, the Sun, & the Moon revolving around us in grand circles. No reason except ``natural motion'' was given for these orbits. Circles were preferred for reasons of simplicity.

  • The Greek astronomers preferred an Earth-centered or geocentric universe because of the apparent lack of observed parallax of the stars. At that time, measurements were not sufficiently accurate to detect parallax.

  • Since the planets were observed to undergo retrograde motion, the Greeks developed a theory of epicycles. A detailed geocentric model was developed by Ptolemy. This model was quite complex motions, but did a reasonable job of predicting future positions of planets, given the large uncertainties in making such measurements. However, the predicted positions of the model were not confirmed by more precise measurements.

  • The problems & complexities of the geocentric model, as well as a general philosophical shift, caused Nicholas Copernicus (1473-1543) to examine an alternative sun-centered or heliocentric model of the solar system. His model proposed that:
    • The Sun is at the center of the Universe.

    • The distance between the Earth and the stars is much greater than the Earth-Sun distance. This would explain the lack of observed stellar parallax.

    • The east to west daily motions of stars, planets, the Moon, and the Sun are caused by the rotation of the Earth on its axis.

    • The Earth and all the planets revolve around the Sun on circular orbits. This produces the change in constellations observed from one time of year to the next.

    • Retrograde motion is an effect caused by the fact that we are observing other planets on the planet Earth which itself is moving around the Sun.

    • Although Copernicus' idea of a heliocentric solar system is correct, his assumption of circular orbits made his model no more accurate than that of Ptolemy. But, it had the beauty of simplicity.

  • There was active debate in the 16-17th century about the relative merits of the geocentric (Earth-centered) and heliocentric (Sun-centered) models.

  • Galileo Galilei's (1564-1642) contribution to astronomy & physics was immense as a result of his careful observations & experiments, and several of his observations provided critical evidence for the heliocentric model:
    • With his simple telescope, he was the first to observe that Venus has phases. This proved that Venus must revolve around the Sun & thus supports the heliocentric solar system.

    • Galileo discovered the 4 brightest moons of Jupiter which move around the planet like a mini solar system. This showed that it was possible for objects to orbit things different from the Earth, and thus contradicted the philosophy that the Earth was at the center of everything.

    • Galileo discovered sunspots which violated Aristotle's view that the Universe was perfect & unchanging.

  • Copernicus' model with circular orbits still did not do a very good job of predicting the position of planets accurately. Refinements to the heliocentric theory were made possible by Tycho Brahe's (1546-1601) precise observations of Mars and the other planets. These accurate observations set the stage for Johannes Kepler (1571-1630) to make major modifications and improvements on the heliocentric model. Tycho's measurements provided the improvement in accuracy necessary to distinguish between competing models.

Kepler's laws

• Kepler devised three Laws of Planetary Motion. These provide the correct description of planetary motion.
  1. Planets orbit the Sun in elliptical orbits with the Sun located at one of the focii of the ellipse. An ellipse is characterized by a size and an eccentricity (or "squashedness"). A circle is an ellipse with zero eccentricity. The size of an ellipse is usually described by the length of its semimajor axis, i.e. half the length of the long axis of the ellipse. Planets orbit in elliptical orbits, although these orbits are of very low eccentricity and hence are almost circular. In fact, Kepler's laws apply to all objects orbiting in the Solar System; for example, comets travel on very eccentric elliptical orbits.

  2. In their elliptical orbits, planets travel faster when they are closer to the Sun. This statement can be made more quantitative with the Law of Equal Areas, which states that a hypothetical line drawn between a planet and the Sun sweeps out equal areas in equal intervals of time.

  3. The time it takes for a planet to make one full revolution around the Sun is related to the size of its orbit. If P is a planet's orbital period around the Sun (measured in Earth years) and A is the semimajor axis of the planet's orbit distance (measured in astronomical units), then
     P² = A³.
     The astronomical unit is a unit which measures distance, and one astronomical unit is, by definition, the size of the semimajor axis of the Earth's orbit. For example, if a planet had an orbital period of 8 yrs, then P² = 64 = A³ ; so A = 4 AU. So, by measuring the orbital period of a planet through careful observations of the planet with respect to the stars, one can determine its distance from the Sun.

• Kepler's laws are a correct description of all solar system motions. However, Kepler's laws do not provide any explanation as to why solar system objects move in this fashion.