Kepler derived his laws from observational data alone, without knowing the underlying physics. Whose data did he use?

Galileo's telescope observations of Jupiter's moons Tycho Brahe's precisely recorded naked-eye observations of planetary positions over many years Isaac Newton's mathematical predictions derived from gravity Ancient Babylonian records of eclipses dating back 1,000 years

Kepler's First Law says planets travel in ellipses with the Sun at one focus. What is the difference between the Sun being at one focus versus at the center?

There is no difference — a focus and a center are the same point in an ellipse At one focus means the Sun is off-center, so the planet is sometimes closer and sometimes farther from the Sun — if it were at the center, the distance would never change Having the Sun at the focus means the orbit is always circular The focus position determines whether the orbit is clockwise or counterclockwise

Kepler's Second Law states that a planet sweeps equal areas in equal times. What does this mean for a planet's orbital speed?

The planet moves at constant speed throughout its orbit The planet moves fastest when closest to the Sun (perihelion) and slowest when farthest away (aphelion) The planet moves fastest at aphelion because it has the most potential energy The planet slows down whenever it crosses the plane of the solar system

Kepler's Third Law states P^2 = a^3 for planets orbiting the Sun (with period in years and distance in AU). Earth has P = 1 year and a = 1 AU. What is the orbital period of a planet at 4 AU?

4 years 8 years 16 years 64 years

Mars has a semi-major axis of about 1.52 AU. Using Kepler's Third Law (P^2 = a^3), approximately what is Mars's orbital period?

About 1.00 year — Mars has the same period as Earth because it orbits the same Sun About 1.52 years — the period equals the distance in AU About 1.88 years About 3.51 years

Kepler's Third Law also applies to moons orbiting planets. If a moon orbits at twice the distance of another moon around the same planet, how do their orbital periods compare?

The outer moon's period is exactly twice as long The outer moon's period is 4 times longer The outer moon's period is about 2.83 times longer — the square root of 8, because P^2 = a^3 means doubling a multiplies P by sqrt(8) The periods are the same — all moons of one planet orbit at the same rate

What is orbital eccentricity, and what does an eccentricity of zero mean?

Eccentricity is the planet's distance from the Sun in AU; zero means the planet is at the Sun's surface Eccentricity measures how stretched an ellipse is; zero eccentricity means a perfectly circular orbit with no variation in distance from the Sun Eccentricity measures how fast a planet orbits; zero means it is stationary Eccentricity describes the tilt of the orbit; zero means the orbit is in the plane of the solar system

Kepler did not know why his laws worked — he had no physics to explain them. What did Newton's work add?

Newton corrected Kepler's laws because they were found to be slightly wrong Newton showed that Kepler's three laws are mathematical consequences of his law of universal gravitation combined with his second law of motion Newton showed that Kepler's laws only apply to the six planets known in Kepler's time Newton used Kepler's laws to invent calculus as a new mathematical tool

Kepler's laws apply beyond the solar system. An exoplanet orbits its star with a period of 8 years. Using the same P^2 = a^3 relationship (assuming the star has the same mass as the Sun), how far is it from its star?

2 AU 4 AU 8 AU 64 AU

Halley's Comet has an orbital period of about 75 years. What is the semi-major axis of its orbit around the Sun?

About 5 AU — roughly Jupiter's distance About 17.8 AU About 75 AU — the period in years equals the distance in AU About 5,625 AU