Name: _______________________________________
Kepler Practice Quiz
Date: ______________________
Directions: Show all work and write out all equations with units. You will lose credit if work is not included.
Reference Equations:
P = orbital period
a = semi-major axis
e = eccentricity
P2 = a3
Distance at perihelion: a(1 – e)
Distance at aphelion: a(1 + e)
1 AU = 1.5 x 108 km
1. What is the importance of Kepler’s 2nd Law for Earth in particular? (2 points)
Kepler’s 2nd Law indicates that planets change speed in their orbits. For Earth, that means
that our seasons remain approximately equal in length, but not exactly.
2. How long will it take Saturn to go around the Sun (orbital period, P) if its semi-major axis (a) is
9.54 au? (2 points)
P2 = a3
P2 = 868.25
P = 29.47 years
3. Show that Pluto is closer to the Sun at perihelion than Neptune at aphelion. Pluto’s semi-major
axis is 5.906 x 109 km and its orbit has an eccentricity of 0.249. Neptune’s semi-major axis is
4.498 x 109 km and its orbit has an eccentricity of 0.009. (2 points)
Pluto at perihelion = a(1 – e) = 5.906 x 109 (1 – 0.249) = 4,435,406,000 km
Neptune at aphelion = a(1 + e) = 4.498 x 109 (1 + 0.009) = 4,538,482,000 km
4. It takes Venus 0.62 Earth-years to go around the Sun once. On average, how far is Venus from the
Sun? (2 points)
P = 0.62 years
P2 = 0.3844 = a3
a = 0.727 AU
5. If Jupiter’s orbital period is 11.86 Earth-years, find the distance (in km) from Jupiter to the Sun
when it is moving slowest. Jupiter’s eccentricity is 0.048. Hint: Use more than one equation to
solve. (2 points)
Jupiter moves slowest at aphelion. We can determine Jupiter’s semi-major axis (a) using
Kepler’s Third Law (P2 = a3). P2 = 140.66 = a3, so a is 5.2 AU. 5.2 AU = 780,000,000 km (7.8 x
108 km). 7.8 x 108 (1 + 0.048) = 817,440,000 km.