A Scale Model of the Solar System

This exercise is a little different. We will do all of the discussion together, and EACH of you will have a sheet to fill in.


Learning Objectives: (Total points = 75)

Part I: Introduction to our Scale: (10 points)

I will show you a number of objects. The first is a basketball, with diameter 9.4 inches. The basketball represents the Sun in this scale model of our Solar System. The Sun is really 1.39x106 km in diameter! This means that the scale of our model is 9.4 inches to 1.39x106 km, or about 1 inch for every 160,000 km, or about 1 inch for every 100,000 miles!

  1. (5 points) Write down how big you think the Earth will be in this scale model. Be honest! Don't change your answer later! Credit will be given for any answer.

    Since this is a guess, any size smaller than the 9.4 inches of the sun is reasonable!

  2. (5 points) Fill in these blanks as I give them to you. The Earth's diameter is about 12,756 km. In our scale, this is well represented by a pinhead about 0.08 inches in diameter! How close was your guess in the previous question? Were you surprised by the relative sizes of the Earth and the Sun?

    Most people are surprised at how small the Earth is relative to the Sun.

    How did I get this number? Well, 9.4 inches represents 1,390,000 km. Therefore each inch represents 1,390,000/9.4 km. So 12,756 km is represented by 12,756 km/(1,390,000/9.4 km/inch) = 0.086 inches. This is just like the scale on a map. If one inch represents 5 miles, then 7.5 miles is represented by 7.5miles/5 miles per inch=1.5 inches.

Part II: Sizes of the Objects (35 points)

Here is a table giving each object in our model of the Solar System.
  1. (20 points) As we discuss each object, fill in their scaled sizes, and write down the object we have used to represent them. We'll discuss the objects in order of increasing distance from the Sun, but we'll worry about the other columns later. For now, notice which planets are biggest, and where they are located in the Solar System.

Sun   1,391,980   9.4 basketball 0. 0.
Mercury   4,878   ______0.03_______   ____ball bearing__ 0.3871   ______11______
Venus   12,104   ______0.08_______   ____pinhead______ 0.7233   _____20_______
Earth   12,756   ______0.09_______   ____pinhead______ 1.0   _____28________
Mars   6,796   ______0.04_______   _____ball bearing_ 1.5237   ______43_______
Jupiter   142,988   ______1.0________   steel ball bearing 5.2028   __metal disk___
Saturn   120,660   ______0.8________   _____metal disk__ 9.5388   _____270_______
Uranus   51,118   ______0.3________   ___washer___ 19.18   ______540______
Neptune   49,500   ______0.3________   ___washer___ 30.0611   ______840______
Pluto   2,302   _____0.01________   __small ballbearing_ 39.44   ____1100_______

Notice that even Jupiter (the largest planet) is much much smaller than the Sun!

  1. (5 points) The moon has a diameter of 3,476 km. What sort of object should we use to represent it in our scale model? (Don't do any calculations, just compare to the other planets above.)

    The moon is between Mercury and Pluto in size, so should be represented by another ball bearing.

  2. (5 points) Without doing any calculations, about how far away from the Earth's pinhead do you think the Moon should be? Once again, any answer will earn you credit.

    Most people guessed something on the order of inches.

  3. (5 points) The moon is actually 384,400 km from the Earth. In our model, this is about 2.35 inches. Is this closer or farther than you expected? Be honest!

    Most people's guesses weren't too bad, but it is still somewhat startling to actually see with the objects just how much the moon is smaller than the Earth, and just how big the spaces between them are relative to their size.

Part III: Distances Between the Objects (20 points)

  1. (5 points) Without doing any calculations, tell me how big you think our model of the entire solar system will be? Again, any answer will earn you credit, so be honest! Will it fit on a table? Inside this room? Inside this building?

    Most people assumed the room would do, a few thought either the table or the building could hold the model.

    The distances given in the table above are the average distances between the Sun and the orbit of each planet.

  2. Using the fact that 1 AU = 1.495979x108 km, we can calculate that Mercury is (on average) 57,909,400 km from the Sun. In our scale model of the solar system, this is almost 10 yards!

    (5 points) Does this distance surprise you? Or was your guess close to accurate?

    This distance surprised some people.

  3. Clearly, we will have to leave this room to get a visual picture of the size of the solar system! As we go on a tour of our scale-model, fill in the remaining column of the Table above. (10 points)

    With the basketball Sun at the entrance to Moffitt, the steel ball bearing representing Jupiter would be near the Valley Life Sciences building, over a football field away! Uranus would have been near the West Gate of campus, and Neptune at Shattuck and Addison, and Pluto past Milvia on Addison.

Part IV: Our Place in the Universe (10 points)

  1. (5 points) The nearest star (other than the Sun) is 4.28 light years away! This is 265, 608 AU! How far away (in our scale model), do you think this star would lie? For the final time, I want your honest guess!

    By this point, most people are figuring out that the distances are VAST, and guessed fairly distant cities.

  2. (5 points) At a distance of 265,608 AU, or 4.05x1013 km, the next basketball-sized object in our scaled model is about 7,500,000 yards away, or 4200 miles ! No wonder the other stars all look faint relative to the Sun! How good was your guess?

    The distance is similar to the distance between San Francisco and Caracas, Venezuela, or between New York City and Copenhagen, Denmark.