Solution to Exercise 1

1. The semi-major axis ( average distance from the Sun ) is the average of its perihelion and aphelion distances or a = 0.723.

For Kepler's 3rd Law,

P2= a3
 = (0.723)3
 = 0.378
P= (0.378)1/2
 = 0.62 yr

2. Mars' orbit is more elliptical because there is a greater difference in aphelion-perihelion distances.

a = (1.38+1.66 AU) / 2 = 1.52 AU
P2= a3
 = (1.52 AU)3
 = 3.46
P= (3.46)1/2
 = 1.88 yr

3. Use Kepler's Third Law in its shortes form P2 = a3, which is valid as long as the orbital period is expressed in Earth years and the average distance is in Astronomical Units.

P2 = a3 = (2.8)3 = 22 ;       P = 4.7 years

4. The average distance from the Sun is the semi-major axis of its ellipse. This is the average of its perihelion and aphelion distances; a = 26 AU.

P2 = a3 = (26)3 = 17,546       P = 132.5 years

5. Neptune's orbital period is 165 years.

a3 = P2 = (165)2 = 27,225       a = (27,225)1/3 = 30 AU (approx)