Name: _____________________________________________
Kepler’s Laws Practice
Date: ____________________
Part 1 – Kepler’s Second Law: A line joining a planet & the Sun sweeps out equal areas in equal time.
In the ellipse below there are two areas (A and B), which represent the same time interval. Count the
number of blocks in area A and area B. Estimate partial blocks to the best of your ability. A
Blocks in A: ~51
Blocks in B: ~51
B
1. Suppose a planet is orbiting along this ellipse’s edge. If the time passed is the same for each
segment of the ellipse, should the number of blocks included also be the same?
Yes, according to Kepler’s Second Law.
2. For which arc (A or B) would the planet cover more of its orbit?
Area B, since the distance along the ellipse is longer.
3. If arc B is greater in length than arc A, and the time to travel those distances is the same, along
which arc is the planet moving faster? Explain.
Area B, which has a longer distance but travels it in equal time.
4. Why doesn’t our planet have large changes in orbital speed, even though Kepler’s second law
would indicate that the speed does change?
Because Earth’s orbit is not very eccentric.
Part 2 – Kepler’s Third Law: The squares of the orbital periods of the planets (the time it takes them to
move around the Sun) are proportional to the cubes of their semi-major axes:
P2 = a3
1. Rewrite the above equation with Earth’s numbers substituted: 12 = 13
2. Complete the table below, verifying that P2 = a3.
Planet
Mercury
Venus
Earth
Mars
Jupiter
P (days)
87.66
226.3
365
686.2
4343.5
P (yr)
0.24
0.6196
1.00
1.879
11.892
a (km)
58,343,169
107,710,466.4
149,597,870
227,388,762.4
777,908,924
a (AU)
0.390
0.72
1.00
1.52
5.2
P2
0.058
0.3839
1.00
3.531
141.42
a3
0.0593
0.373
1.00
3.51
140.608