Figuring for Yourself
By what factor would a person’s weight be increased if Earth had 10 times its present mass, but the same volume?
Suppose astronomers find an earthlike planet that is twice the size of Earth (that is, its radius is twice that of Earth’s). What must be the mass of this planet such that the gravitational force (Fgravity) at the surface would be identical to Earth’s?
What is the semimajor axis of a circle of diameter 24 cm? What is its eccentricity?
If 24 g of material fills a cube 2 cm on a side, what is the density of the material?
If 128 g of material is in the shape of a brick 2 cm wide, 4 cm high, and 8 cm long, what is the density of the material?
If the major axis of an ellipse is 16 cm, what is the semimajor axis? If the eccentricity is 0.8, would this ellipse be best described as mostly circular or very elongated?
What is the average distance from the Sun (in astronomical units) of an asteroid with an orbital period of 8 years?
What is the average distance from the Sun (in astronomical units) of a planet with an orbital period of 45.66 years?
In 1996, astronomers discovered an icy object beyond Pluto that was given the designation 1996 TL 66. It has a semimajor axis of 84 AU. What is its orbital period according to Kepler’s third law?