Kepler's Laws in Numbers: Practice Problem Solutions

1. T = 8 years.

2. T = square root of 21.3 = about 4.6 years.

3. 16 AU.

4. Perihelion = 1.52 x (1 - 0.093) = about 1.38 AU. Aphelion = 1.52 x (1 + 0.093) = about 1.66 AU.

5. At perihelion, when it is closest to the Sun; Kepler's second law (equal areas in equal times) means it must move faster there.

6. 1.017 / 0.983 = about 1.03, so about 3% faster.

7. Measure the moon's orbital period and distance; Newton's version of Kepler's third law then gives the mass of Jupiter.