The
Speed of the Planets in Their Orbits
By
Thomas Tang and Michael Kauper, copyright 2009, rev. 2010
One day last year I was discussing the
names of the planets with the day care children We talked about Mercury being
the name for the Messenger of the Gods. The innermost planet is the speediest
planet and was named after the God with wings on his heels.
Reddish Mars, the color of blood, was named
for the God of War. Jupiter, bright and slow moving, was given the name of the
Father of the Gods. Venus, bright and beautiful, is the Goddess of Love.
In our day care home we have solar system posters, a paper solar system collage, plus the sun and planets hang from the ceiling in the Big Kids’ Room, spaced to scale, so the children are familiar with many images of our planetary family. One child wanted to know why Mercury is the fastest planet. Because Mercury is closest to the sun, so it has the shortest year, only 88 days, I replied. The children were not so easily convinced. Other planets have longer years, but they also travel much farther in their orbits. Look at the huge orbits of Jupiter and Saturn. Maybe the more distant planets actually go faster, because they have to go so much farther in their orbits.
Soon the kids were asking me how fast do
they go? We looked on the magical
Internet, and did not immediately find an answer on our favorite solar system
sites. We found the year, in earth years, for each planet; the distance from
the sun; the length of each planetary day; and how big each planet is,
especially compared to ours. We did not find out which planets move fastest.
Figure 1 Thomas Tang, right, and Michael Kauper calculate the tangential velocity of Mercury
Thomas Tang,
then 10 years old, volunteered to help me research this burning question.
Thomas and I created a chart, where we entered the mean distance of each planet
from the Sun, in millions of kilometers, and the length of its year, in earth
years. From that we calculated the circumference of each orbit, divided by the
planetary year in earth years, to get the tangential velocity components of the
planets in millions of kilometers per
earth year.
This rather non-standard velocity unit
helped us to visualize how the movement of each planet compared with the
movement of the Earth.
Our next step was to plot the tangential
velocity against the distance from the Sun. As a long time amateur astronomer,
I found this fascinating. I had never before seen this graph, not in my
astrophysics classes, not any book or magazine, even though I have been an
amateur astronomer and astronomy student for over 50 years.
According to Wikipedia, the tangential
velocity of a planet drops off as square root 1/r, where r is the distance from
the center of the Sun. The velocity formula for a circular orbit is v = square root of μ/r, where μ is a
gravitational constant.
Therefore, the speed of a planet drops off
very quickly close to the Sun and very slowly in the outer Solar System. Here
is the graph created by the authors.
The graph gave us the feeling that the
gravitational influence of the Sun drops off more and more slowly as we move on
out past
In other words the “influence” of the Sun
extends far, far past
Thomas Tang and Michael
Kauper explore the Solar System mostly during day care hours in
rev. 03-2010
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