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.

Thomas and Michael at blackboard calculating the speed of Mecury    

    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.

Graph of speed of each planet vs distance

     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 Neptune, through the Kuiper Belt, with its Dwarf Planets, and finally out to the remote Oort Cloud with its primordial debris and frozen potential comets.

     In other words the “influence” of the Sun extends far, far past Neptune. For a non-mathematician, or a group of elementary age children, this helps to explain how the Sun can keep such a huge family from wandering off into the galaxy.

Thomas and Michael at the balckboard

Thomas Tang and Michael Kauper explore the Solar System mostly during day care hours in South Minneapolis.

rev. 03-2010

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