Many ancient cultures constructed elaborate structures that served as calendars and astronomical observatories. The study of the universe on the very largest scales is called cosmology.
Unlike the Sun and the Moon, planets sometimes appear to temporarily reverse their direction of motion (from night to night) relative to the stars and then resume their normal "forward" course. This phenomenon is called retrograde motion.
Geocentric models of the universe were based on the assumption that the Sun, the Moon, and the planets all orbit Earth. The most successful and long-lived of these was the Ptolemaic model. To account for retrograde motion within the geocentric picture, it was necessary to suppose that planets moved on small circles called epicycles, whose centers orbited Earth on larger circles called deferents. The heliocentric view of the solar system holds that Earth, like all the planets, orbits the Sun. This model accounts for retrograde motion and the observed size and brightness variations of the planets in a much more natural way than the geocentric model. The widespread realization during the Renaissance that the solar system is Sun centered, and not Earth centered, is known as the Copernican revolution, in honor of Nicholas Copernicus, who laid the foundations of the modern heliocentric model.
Johannes Kepler improved on Copernicus's model with his three laws of planetary motion: (1) Planetary orbits are ellipses, with the Sun at one focus. (2) A planet moves faster as its orbit takes it closer to the Sun. (3) The semi-major axis of the orbit is related in a simple way to the planet's orbit period. Most planets move on orbits whose eccentricities are quite small, so their paths differ only slightly from perfect circles.
Galileo Galilei is often regarded as the father of experimental science. His telescopic observations of the Moon, the Sun, Venus, and Jupiter played a crucial role in supporting and strengthening the Copernican picture of the solar system.
The distance from Earth to the Sun is called the astronomical unit. Nowadays, the astronomical unit is determined by bouncing radar signals off the planet Venus and measuring the time taken for the signal to return.
Isaac Newton succeeded in explaining Kepler's laws in terms of a few general physical principles, now known as Newtonian mechanics. The tendency of a body to keep moving at constant velocity is called inertia. The greater the body's mass, the greater its inertia. To change the velocity, a force must be applied. The rate of change of velocity, called acceleration, is equal to the applied force divided by the body's mass. To explain planetary orbits, Newton postulated that gravity attracts the planets to the Sun. Every object with any mass is surrounded by a gravitational field, whose strength decreases with distance according to an inverse-square law. This field determines the gravitational force exerted by the object on any other body in the universe.
Newton's laws imply that a planet does not orbit the precise center of the Sun but instead that both the planet and the Sun orbit the common center of mass of the two bodies.
For an object to escape from the gravitational pull of another, its speed must exceed the escape speed of the second body. In this case, the motion is said to be unbound, and the orbital path is no longer an ellipse, although it is still described by Newton's laws.
1. Historical records show that it was Aristotle who first proposed that all planets revolve around the Sun. HINT
2. The teachings of Aristotle remained unchallenged until the eighteenth century a.d. HINT
3. Ptolemy was responsible for a geocentric model that was successful at predicting the positions of the planets, Moon, and the Sun. HINT
4. The heliocentric model of the universe held that Earth was at the center, and everything else moved around it. HINT
5. Kepler's discoveries regarding the orbital motion of the planets were based on his own observations. HINT
6. The Sun's location in a planet's orbit is at the center. HINT
7. The semi-major axis of an orbit is half the major axis. HINT
8. A circle has an eccentricity of zero. HINT
9. The astronomical unit is a distance equal to the semi-major axis of Earth's orbit around the Sun. HINT
10. The speed of a planet orbiting the Sun is independent of the planet's position in its orbit. HINT
11. Kepler's laws work for only the six planets known in his time. HINT
12. Kepler never knew the true distances between the planets and the Sun, only their relative distances. HINT
13. Galileo's observations of the sky were made with the naked eye. HINT
14. Using his laws of motion and gravity, Newton was able to prove Kepler's laws. HINT
15. You throw a baseball to someone. Before the ball is caught, it is temporarily in orbit around Earth's center.
1. Stonehenge was used as a _____ by people in the Stone Age. HINT
2. Accurate records of comets and "guest" stars were kept over many centuries by _____ astrologers. HINT
3. The astronomical knowledge of ancient Greece was kept alive and augmented by _____ astronomers. HINT
4. The apparent "backward" (westward motion) of the planets Mars, Jupiter, or Saturn in the sky relative to the stars is known as _____ motion. HINT
5. Observation, theory, and testing are the cornerstones of the _____. HINT
6. The heliocentric model was reinvented by _____. HINT
7. Central to the heliocentric model is the assertion that the observed motions of the planets and the Sun are the result of _____ motion around the Sun. HINT
8. Kepler's laws were based on observational data obtained by _____. HINT
9. Kepler discovered that the shape of an orbit is an _____, not a _____, as had previously been believed. HINT
10. Kepler's third law relates the _____ of the orbital period to the _____ of the semi-major axis. HINT
11. Galileo discovered _____ orbiting Jupiter, the _____ of Venus, and the Sun's rotation from observations of _____. HINT
12. The modern method of measuring the astronomical unit uses _____ measurements of a planet or asteroid. HINT
13. Newton's first law states that a moving object will continue to move in a straight line with constant speed unless acted upon by a _____. HINT
14. Newton's law of gravity states that the gravitational force between two objects depends on the _____ of their masses and inversely on the _____ of their separation.
15. Newton discovered that, in Kepler's third law, the orbital period depends on the semi-major axis and on the sum of the _____ of the two objects involved. HINT
1. What contributions to modern astronomy were made by Chinese and Islamic astronomers during the Dark Ages of medieval Europe? HINT
2. Briefly describe the geocentric model of the universe. HINT
3. The benefit of our current knowledge lets us see flaws in the Ptolemaic model of the universe. What is its basic flaw? HINT
4. What was the great contribution of Copernicus to our knowledge of the solar system? What was still a flaw in the Copernican model? HINT
5. When were Copernicus's ideas finally accepted? HINT
6. What is the Copernican principle? HINT
7. What discoveries of Galileo helped confirm the views of Copernicus? HINT
8. Briefly describe Kepler's three laws of orbital motion. HINT
9. If radio waves cannot be reflected from the Sun, how can radar be used to find the distance from Earth to the Sun? HINT
10. What is meant by the statement that Kepler's laws are empirical in nature? HINT
11. List the two modifications made by Newton to Kepler's laws. HINT
12. Why does a baseball fall toward Earth and not Earth toward the baseball? HINT
13. Why would a baseball go higher if it were thrown up from the surface of the Moon than if it were thrown with the same velocity from the surface of Earth? HINT
14. What is the meaning of the term escape speed? HINT
15. What would happen to Earth if the Sun's gravity were suddenly "turned off?" HINT
1. Tycho Brahe's observations of the stars and planets were accurate to about 1 arc minute (1'). To what distance does this angle correspond (a) at the distance of the Moon, (b) of the Sun, (c) of Saturn (at closest approach)?
2. Assume for simplicity that Earth and Mars move on circular orbits of radii 1.0 A.U. and 1.5 A.U., respectively, in exactly the same plane. To an observer on Earth, through what angle will Mars appear to move relative to the stars over the course of 24 hours, when the two planets are at closest approach? Will the apparent motion be prograde or retrograde? HINT
3. Using the data in Table 2.1 show that Pluto is closer to the Sun at perihelion (the point of closest approach to the Sun in its orbit) than Neptune is at any point in its orbit. For simplicity, you may assume that Neptune has a circular orbit, which is not far from the truth.
4. An asteroid has a perihelion distance of 2.0 A.U. and an aphelion distance of 4.0 A.U. Calculate its orbital semi-major axis, eccentricity, and period.
5. Halley's comet has a perihelion distance of 0.6 A.U. and an orbital period of 76 years. What is its aphelion distance from the Sun?
6. How long will a radar signal take to complete a round trip between Earth and Mars when the two planets are 0.7 A.U. apart? HINT
7. Jupiter's moon Callisto orbits the planet at a distance of 1.88 million km. Callisto's orbital period about Jupiter is 16.7 days. What is the mass of Jupiter? [Assume that Callisto's mass is negligible compared with that of Jupiter, and use the modified version of Kepler's third law (Section 2.7).] HINT
8. The acceleration due to gravity at Earth's surface is 9.80 m/s2. What is the acceleration at altitudes of (a) 100 km? (b) 1000 km? (c) 10,000 km? HINT
9. Use Newton's law of gravity to calculate the force of gravity between you and Earth. Convert your answer, which will be in newtons, to pounds using the conversion 4.45 N equals 1 pound. What do you normally call this force? HINT
10. The Moon's mass is 5.97 1024 kg and its radius is 1700 km. What is the speed of a spacecraft moving in a circular orbit just above the lunar surface? What is the escape speed from the Moon? HINT
1. Look in an almanac for the date of opposition of one or all of these bright planets: Mars, Jupiter, and Saturn. At opposition, these planets are at their closest points to Earth and are at their largest and brightest in the night sky. Observe these planets. How long before opposition does each planet's retrograde motion begin? How long afterward does it end?
2. Draw an ellipse. (See Figure 2.11) You'll need two pins, a piece of string, and a pencil. Tie the string in a loop and place it around the pins. Place the pencil inside the loop and run it around the inside of the string, holding the loop taut. The two pins will be at the foci of the ellipse. What is the eccentricity of the ellipse you have drawn?
3. Use a small telescope to replicate Galileo's observations of Jupiter's four largest moons. Note the moons' brightnesses and their locations with respect to Jupiter. If you watch over a period of several nights, draw what you see; you'll notice that these moons change their positions as they orbit the giant planet. Check the charts given monthly in Astronomy or Sky & Telescope magazines to identify each moon you see.