Galileo's drawings of the phases of the Moon. With his telescope Galileo made these drawings in about 1610, and they were published in his book The Starry Messenger.
Johannes Kepler (1571-1630), German astronomer, who is the author of three empirical laws known as Kepler's laws of planetary motion.
Galileo Galilei (1564-1642), Italian physicist-astronomer, who work on motion laid the foundation for Newton's mechanics and who's first use of the telescope launched astronomy into the telescopic era.
Kepler's three laws of planetary motion. Kepler found that the planets move in elliptical orbits with Sun at one foci. (To draw an ellipse, loop a string taut around two tacks--the foci--and a pencil as shown.) The mean distance of the planet is equal to one-half the length of the major axis, or the semimajor axis, whose end points are 1 and 7. Because the areas of all sectors, gray and colored, are equal, the planet passes through the number positions in equal intervals of time. The planet moves fastest when near the Sun and slowest when farthest away. Kepler's third law is illustrated by the numbers in the fourth and fifth columns of the table. If the sidereal period is measured in years (the Earth's sidereal period) and the mean distance in astronomical units (AU, the Earth's mean distance from the Sun), the two columns are approximately, but not precisely, equal. The slight discrepancy is removed by Newton's modification of this law.
Mass, weight, and density. Mass is a measure of the inertia of a body or the amount of matter it contains, whereas weight is the force exerted on a body by the gravitational field of a massive body, such as the Earth or the Moon. In the lower part of the figure a mass hung on a spring extends the spring fully on the Earth, but it is only partially extended on the Moon since the Moon's gravitational attraction is one-sixth that of the Earth. The illustration at the top left shows two bodies of the same mass but different densities on a balance. They are the same mass because they balance, and they must have different densities because one is much smaller (that is, it has a smaller volume) than the other. At the top right the two bodies have the same densities, with the one on the left proportionately larger, but that makes it more massive, so they do not balance.
Frame of reference for measuring planetary distances. Shown is a very simple reference frame, with the Sun as the origin and the reference direction as the direction toward the bright star Regulus (Alpha Leonis), which is almost in the plane of the ecliptic. Two directions at right angles to the reference direction, one in the plane of the ecliptic, complete the three axes of the three-dimensional reference frame. Units of distance, in this case arbitrary ones, are used to locate the planets at any one moment relative to the three axes. Thus the Earth is located by going 6 units along the reference direction, 5 units perpendicular to it and 0 units perpendicular to the orbital plane of the planets. This frame of reference is only for illustration and is not one actually used by astronomers.
Space-time diagram. Shown is a space-time diagram of a trip by airplane between Washington, D.C. and Boston with a stop in New York. The horizontal axis is the distance between the three cities; the vertical axis is the time elapsed since leaving Washington. We fly first to New York, stop over, and then continue to Boston. In Boston we realize that our appointment is not until next week, so we board another plane and fly nonstop back to Washington. Our spatial position goes forward and backward while time moves only forward. The vertical axis and the two other vertical lines represent what happens to the three cities: Time advances, but the cities do not change position. The three lines are called world lines. The speed (actually, the average speed) can be found for each leg of the trip by dividing the distance traversed by the elapsed time, as shown.
Momentum or quantity of motion. The two bodies whose momenta are being compared are a cannonball and a musket ball. Both are given velocities of 100 m/s, but the cannonball has 1000 times the mass of the musket ball (10 kg and 0.01 kg, respectively). Upon striking the stone wall, the cannonball, having greater momentum, or quantity of motion, can transfer some to the stones of the wall, so that they move in the original direction of the cannonball. However, the musket ball has insufficient momentum to transfer any of it to the stones.