Answer to Question #105129 in Classical Mechanics for Joe Se

Question

Let's use Kepler's laws for the inner planets. Use the following distances from the sun to calculate the orbital period for each of these planets. Express your answer in terms of Earth years to two significant figures. Answer for the highlighted planet in each question.

Note: Use Kepler's law directly. Don't just Google the answers, as they will be a little bit different.

When you have calculated them, only submit the value for Earth.

Planet Distance from the sun Period of orbit around the sun

a. Earth 150 million km ___ Earth years
b. Mercury 58 million km ___ Earth years
c. Venus 108 million km ___ Earth years
d. Mars 228 million km ___ Earth years

Answer 1

a) Period of orbit around the sun is 1 Earth year.

b) Period of orbit around the sun is 0.24 Earth years.

$$\frac{T_{Mercury}}{T_{Earth}}=\left(\frac{R_{Mercury}}{R_{Earth}}\right)^{1.5}=\left(\frac{58}{150}\right)^{1.5}=0.24$$

c) Period of orbit around the sun is 0.61 Earth years.

$$\frac{T_{Venus}}{T_{Earth}}=\left(\frac{R_{Venus}}{R_{Earth}}\right)^{1.5}=\left(\frac{108}{150}\right)^{1.5}=0.61$$

d) Period of orbit around the sun is 1.9 Earth years.

$$\frac{T_{Mars}}{T_{Earth}}=\left(\frac{R_{Mars}}{R_{Earth}}\right)^{1.5}=\left(\frac{228}{150}\right)^{1.5}=1.9$$