## Round and Round They Go!

As you introduce students to the orbits of the planets around our Sun, it is important that they understand more than just the order based on distances. If you look at the amount of time it takes to complete one orbit, you might ask why the outer planets take so much longer than the inner planets. Is it just because they have so much further to go? Or is some other factor involved? This lesson investigates.

First, if you build a scale model of the solar system, you can take pieces of string and use them to represent the orbital paths of each of the eight planets. If you then stretch the strings out from a common point, you will see that indeed the outer planets have much farther to go in order to complete one revolution. However, this alone does not explain the orbital periods. There is something more to it. The following activity can provide students with a big clue as to what the something more is.

### Materials Needed:

• Sturdy Plastic Drinking Straw (cut in half)
• String -- 18-24 inches per person
• Rubber Washers or Stoppers -- 2 per person

Assemble your "solar system model" by tying the string to one of the washers, then running the string through the straw and tying that string end to the other washer, as shown below.

Begin with lots of room. Holding the straw and washer assembly upright, pull the string until the bottom washer rests against the bottom of the straw. Hold the straw with one hand with your arm fully extended in front of your body. By rapidly rotating the wrist of the extended arm, start spinning the string/washer assembly until the string is fully extended. Continue spinning the system at a constant rate as you use your other hand to pull slowly down on the bottom washer. What do you notice about the speed at which the spinning washer is traveling as the orbit it makes gets shorter and shorter?

### Notes to Teacher:

• You need to get the spinning washer going at a quick, but steady rate before starting to pull the string. You will need to keep the spinning going as you pull until you reach a point that it will become "self-sustaining" -- then you don't have to worry about powering the spinning any more. Students may think that it is you making the washer orbit faster as its orbit radius gets smaller. Be sure to point out that it is not you. They will see this for themselves when they put their own "planets" into orbit.
• Shorter string lengths produce a more manageable assembly for younger or smaller students. They can even spin their "planet" in a vertical circle if they can't maintain the horizontal circle. While the science is not as technically correct with a vertical circle, for younger students this may be the only way they can enjoy the experience independently. Make each of them describe what they feel in the hand that is holding the straw and also what they see as the orbital circle gets smaller. This will help to get them to focus on watching the orbiting washer and not watching their neighbors or closing their eyes!
• Make a special effort to pull the string slowly enough that the washer can make complete orbits at each radius before you pull the string more. This is hard to do at larger orbits, but easy to do as the orbits get smaller.
• Do not use objects that are hard and heavy. As students practice this activity, they will inevitably hit themselves with the orbiting object. So it needs to be something soft. However, it needs to have enough mass to be an effective orbiter, so choose carefully.

1.) What does this have to do with planets orbiting the Sun? Point out that the planets more distant from the Sun have a longer orbital path AND move slower around that path than the planets closer to the Sun. Be sure students understand that there are 2 reasons the outer planets have such long orbital periods when compared to the inner planets. For the higher grades, you can investigate this mathematically in Question 2.

2.) How does this help to answer the question of why Pluto takes so much longer than Neptune to orbit the Sun? For higher grades (6 and up), have them calculate the orbital speed of Mercury and see how long it would take Pluto to make its orbit if it traveled at that speed. Then compare the time to how long it really takes Pluto to complete an orbit, and draw a conclusion. Do this for several other planets as well. Remember that you can calculate the average speed by dividing length of the orbital path by the time it takes to make one complete orbit. The orbital path (for this exercise, assume all orbits are circular) is simply 2 times pi times r, where r is the distance from the planet to the Sun. The necessary solar system data are given in a table at the end of this lesson.

3.) For grades 6 and up, this is also a great way to introduce Newton's Law of Gravitation. Students can make a graph comparing the distance of each planet from the Sun with the planet's average speed in its orbit. Look at the graph. Clearly, the farther you are from the Sun, the slower you are going and the longer it takes to make an orbit. This is very similar to the behavior of a pendulum. The longer the swing arm, the longer it takes to make one swing. You can have your students investigate this concept using their string apparatus as a pendulum to see that only the length of the swing arm (not the amount of mass of the bob) affects the period of time it takes the bob to complete one swing). Isaac Newton was the first person to realize that there must be a connection between the period of a pendulum and the period of a planet orbit. He realized that the pendulum bob was attracted to Earth, which made it swing like it did, and that the Moon was similarly attracted to Earth with the result that it orbited like it did.

Go back to your straw and string apparatus. Holding onto the string (not the straw), swing the washer over your head. Do you feel it pull on your hand? Sir Isaac Newton realized that your hand must be pulling back on the string with equal force or else the washer would fly off into space. While he realized that no string connects the Moon and Earth, he imagined an invisible string called gravity which provides a pull just like the real string. He realized that the amount of the pull was dependent on the amount of matter in each object (in this case, the masses of the Earth and Moon) since it was clear from swinging the washer on a string that a larger washer weight required more pull. He also realized that the amount of pull depended on the distance between the objects, again just like you can feel with your string. As the distance between your hand and the washer gets smaller, it is much easier to sustain the orbit. Newton worked out the mathematics and found that the pull (which we now called the gravitational pull) can be expressed as

Fg = Gm1m2/r2.

In words, the pull exerted on one body by another equals Newton's Constant times the mass of the first body times the mass of the second body divided by the square of the distance between the centers of the two bodies. Notice that in this equation, there is no distinction between which body is doing the pulling. Think about what this means. The pull of the Earth on your body is exactly equal to the pull of your body on the Earth!

Newton's model of gravity is one of the most important scientific models in history. It applies not only to apples and Moons near Earth, but to stars and distant galaxies as well. The only time you don't use Newton's model for gravity is when you get a great deal of matter in a very small space. Under those circumstances, you have to switch to Albert Einstein's model of gravity. But that is another story.

Solar System Data

 Object Mean Distance From Sun (km) Sidereal Orbital Period (days) Mercury 57,910,000 87.97 Venus 108,200,000 224.70 Earth 149,600,000 365.26 Mars 227,940,000 686.98 Jupiter 778,300,000 4332.71 Saturn 1,429,400,000 10759.50 Uranus 2,870,990,000 30685.00 Neptune 4,504,300,000 60190.00

This activity is part of the StarChild site.

http://starchild.gsfc.nasa.gov/