In this experiment you will build a model solar system.
This is one of the most amazing activities you will do this semester. So enjoy it and do your best! We will do this activity together during class time.
You will need a volleyball or basketball, a number of small, round items from around the lab such as marbles, beads, and spices, a tape measure, a long string, a lab partner, and a long straight sidewalk. Oh, and you'll need your scientific calculator or spreadsheet.
But before finding a lab partner and collecting items from around the lab, do the calculations described below.
Do you remember seeing a model solar system in your elementary school classroom? It probably showed Sun and nine planets hanging from wires or strings or something. Well, guess what? That model was wrong! It wasn't even close to being an accurate model of the solar system. In this activity you will build a much more accurate model of the solar system.
The objective of this experiment is to use a volleyball to represent Sun and to lay out all of the planets in a line using objects of the appropropriate size and at the appropriate distance such that the sizes and distances are proportionally correct.
The image below shows the planets laid in a line. Their sizes are proportionally correct, relative to Jupiter, but their distances are wrong. You will do something similar in this activity, but in your case the distances will be correct.
To build any model, whether a model railroad or a model car or a model building, you have to determine a scale. The scale, or scaling factor, is used to determine the sizes of things in your model so that the proportion of the size of one object to another object is the same as for the real objects.
In the model that we will build, we will use a volleyball to represent Sun. The radius of the ball is approximately 4 in (inches) and its diameter is approximately 8 in. (To give you perspective, the diameter of a regulation men's basketball is a little over 9 in.)
The radius of the ball is 4 in. The actual radius of Sun is about 7 x 108 m. The ratio of these two numbers is our scaling factor. (It doesn't matter that they have different units in this case.) Thus,
Calculating the diameters of planets in your model
Now, to calculate the radius in inches of the planets in your model, multiply the actual radius of the planet (in meters) by the scale. For example, the radius of Mercury is 2.4 x 106 m. Let's multiply the radius of Mercury in meters times our scale. The result is
The diameter of Mercury is two times its radius. Therefore, Mercury's diameter is 0.028 in. Keep in mind that 1/8 of an inch is 0.125 in. Thus, the diameter of Mercury in our model is only about 1/5 of 1/8 of an inch. That's 1/40 of an inch!
The smallest measurement on a tape measure is usually 1/8 or 1/16 of an inch. Mercury in our model has to be approximately 1/32 of an inch. Using your tape measure, see if you can make two marks no a piece of paper that are only about 1/32 of an inch apart. That's the diameter of Mercury in our model.
Though 1/32 of an inch is approximate, you can't measure such small things with a tape measure anyway, so it's ok if we are off by a hair. You'll still get the idea.
Now, find an object that will be Mercury. Is there anything in your spice cabinet in the kitchen that you can use to represent Mercury in our model? Or maybe you have a very tiny bead. Probably something the size of a mustard seed or celery seed is about the size you need.
Put that seed in a bag or small jar and keep it for when you build the model.
Using this same method, go ahead and calculate the diameters of the other planets of the Solar System. The actual radii of the planets are listed in an Appendix of the textbook. They are also listed in the WebAssign assignment for this lab. You can enter your calculations on WebAssign to see if they are correct before looking for seeds, beads, or small marbles to use in your model.
At this point, go to the WebAssign assignment called LAB -- Build a scale model of the solar system. Enter your values for the diameters of the planets in your model. You have lots of submissions so that you can correct any calculations and resubmit. If you have trouble, be sure to email the class listserve.
For each of the planets, find an object that has about the same diameter as the diameter of your model planet that you calculated. Probably spices, small beads, and small to largish marbles will be your objects of choice. Put the objects in a jar or bag to take with you outside when you build your model.
Calculating the distances to planets in your model
The distances to planets are much larger than the diameters of planets. Thus, instead of using inches, we'll use feet. Though we'll use the same scaling factor, we have to convert inches to feet. This gives a scale of
This is 1/(2.1 x 109). Let's calculate the distance from Sun to Mercury in our model using units of feet by multiplying the actual distance from Sun to Mercury by the scale. Thus,
It's easier to write this in scientific notation as (5.8 x 1010)/(2.1 x 109) which is just 58/2.1=28 ft.
ok, stop the math for a moment. Let's imagine this. You set a volleyball or basketball on the sidewalk, and that represents Sun. You then take something the size of a celery seed and walk 28 ft from the ball and set it down. That's the planet nearest to Sun! WOW! If that doesn't blow your mind, then just you wait and see how far the other planets will be!
At this point, go to the WebAssign assignment called LAB -- Build a scale model of the solar system. Enter your values for the distances from Sun to the planets in your model. You have lots of submissions so that you can correct any calculations and resubmit. If you have trouble, be sure to email the class listserve.
Building your model.
Now you get to go outside and set up your model. You will need a 25 ft tape measure and a string. Walking off the distances with your lab partner is easiest if you measure and cut a 20 ft piece fo string.
On a long, straight sidewalk, start at Sun and walk 28 ft to Mercury. It's easiest if you and your lab partner work together to walk off one and a half lengths of string (which is 30 ft, close enough). Basically, you stand at Sun, and your partner walks one string length. Then, your partner stands there while you walk half of a string length. Then, you set down Mercury on the sidewalk.
Now, do a quick calculation of the difference in the distances of Sun to Mercury and Sun to Venus. This is about 52-28 ft, or 24 ft. That's about 2 string lengths. So, stand at Mercury while your lab partner walks one string length. Then, your lab partner should stand still as you walk one string length. Take one more step (about 4 ft.) and set down Venus.
Keep doing this until you've at least gone to Saturn. At each planet, look back at Sun. Can you believe it?
This should have been a highly illustrative lesson for you. Be prepared to discuss your experience with the class.