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Planetary Speed help: According to Kepler’s Third Law, planets closer to the sun have shorter years....

Planetary Speed help:

According to Kepler’s Third Law, planets closer to the sun have shorter years. We might ask the question, “Is this because they move faster, or because they don’t have as far to go?” Let’s investigate.

Speed is distance divided by time, so if we know how far a planet travels and how long it takes, we can calculate speed. Look up the period and orbital distance (in years and AU, respectively) of Mercury, Venus and Earth. Assuming circular orbits (the real orbits are pretty close), the distance traveled is 3.14 (= pi) times the orbital distance times 2. So in mathematical symbols, the planet’s speed is:

v = (2(pi)a)/(p)      

where v = speed

a = average distance from the sun in AU

p = orbital period in years

So I got the table below with the top row and the first column filled out. Can somebody check to see if I got the other terms correct?

a.

Compare Orbital Periods

Planet

a (AU)

Orbital period, p (years)

Average Speed, v (AU/year)

Show your full calculations!

Mercury

.613

.387

v=2pi(.613)/.387=9.952AU

Venus

.28

.723

v=2pi(.277)/.723=2.4435AU

Earth

1

1

v=2pi(1)/1=6.28AU
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