Scale Model of the Solar System

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This is an outdoor experiment:

Objective:

Students will gain a new perspective on our place in space, the relative size of the planets and the sun compared to space, and a sense of the distances between stellar and solar system objects. Students will discover that space is really full of nothing but empty space, and that this big planet we live on is less than trivial against all of what is really out there, except for the fact that we occupy this tiny planet.

Introduction:

One of the most important aspects of Astronomy is getting a sense of the sheer size of the Universe. I think it is useful to create your own scale model of the solar system and see for yourself just how small our world actually is in comparison to our local neighborhood of planets, moons, and our sun. Your task will be to create a scale model of the solar system using a tennis ball, or something in your possession of similar size, which will represent the sun. Your scale model will include both the distance from the sun to each listed object, and the relative size of each object relative to the tennis ball.

Materials and Equipment Needed:

1. Tennis ball, or something of similar size

2. Paper, pencil, and given dimensions generously provided by me

3. Calculator

4. An open space

5. Walking shoes (hiking stick is optional)

6. A bag lunch to take on your 12 billion kilometer walk

7. Yardstick, meterstick, or tape measure (1 meter has 39.77 inches)

8. A map of the United States is helpful

Procedure:

In the accompanying page are the actual sizes of the sun and its nine planets, and average distances of each planet out from the sun, as well as a few other interesting objects. You will set up a mathematical proportion which will allow you to determine how far away from the tennis ball each planet is, and also how big each planet is relative to that tennis ball. If the tennis ball is to represent the sun, then the tennis ball diameter represents 1,392,000 km. You will need to measure the diameter of your tennis ball, and then you will have your mathematical relationship which will allow you to solve for the other values. For example: If you measure your tennis ball to be 10 cm, then your relationship is:

10 cm = 1,392,000 km ... this is your ratio for determining the scale diameter and distance for everything in the Solar System. This can be written as a simple ratio looking like 10 cm/1,392,000 km

(yes, I know that a tennis ball is really more like 7 cm in diameter, but the 10 m value for this example is easier to teach with)

Yhe actual distance from Earth to Sun us 149,600,000 km

Your value for X is the scale model distance from the tennis ball Sun to little sand grain-sized Earth.

The entire equation will look like: 10 cm/1,392,000 km = X cm/149,600,000 km

IN ORDER TO SOLVE FOR "X" JUST REARRANGE THE EQUATION (10 cm)(149,600,000 km)/1,392,000 km = X

*Remember, to convert from X centimeters to X meters, you divide by 100.*

In the same fashion, to figure out how big the Earth would be in comparison to a Sun the size of a tennis ball, you set up the equation with the same ratio:

10 cm/1,392,000 km = X cm/12,756 km

Rearranged to solve for X looks like: (10 cm)(12,756 km)/1,392,000 km = X

Your value for X is now the size of the earth relative to the tennis ball. Remember, to convert from centimeters to millimeters, you multiply by 10.

YOU ALWAYS USE THE SAME RATIO OF 10 cm/1,392,000 km AND THE ONLY OTHER NUMBER YOU CHANGE WILL BE THE ACTUAL DISTANCE OR ACTUAL DIAMETER OF THE PLANETS. THE RATIO STAYS THE SAME.

Once you have all of your values calculated for each of the planets, you will apply the same relationship to Proxima Centauri (the closest neighboring star to our sun) and to the Andromeda Galaxy (the closest major galaxy to our Milky Way).

Now, go outside and go on a walking tour of the solar system. Place the tennis ball at a height of about 2 meters and estimate the length of your stride and walk from the sun (tennis ball) out to Pluto. On the way, stop at each planet location and look back at the tennis ball and get an idea of how small it may appear in the sky if your were actually on the surface of another planet. Since Pluto is an average of almost 6 billion kilometers from the sun, you will be walking a relatively long way and you may get tired on your journey. Bringing a bag lunch will keep you energized for this trek. A warm jacket will also help when you get to Pluto, since the temperature out there is a not so balmy -220oC!

Once you are at "Pluto," you can look back at the tennis ball and get an idea of just what our solar system is really made of. While you are standing at Pluto, you can try to figure how far away the next tennis ball would be. Using the same mathematical relationship, calculate the distance to Proxima Centauri, the closest neighbor to the sun and then to the Andromeda galaxy. A bit more calculating is in order here. If light travels 300,000 km/sec … how far will light travel in one year? How far will light go in 4.3 years and in 2,900,000 years? (This is recent satellite data which indicates that Andromeda may be closer to 2,900,000 light years away, than the printed text value of 2,200,000 light years).

As you stand at Pluto, imagine how far away our nearest neighbor star is, and then on this scale just how far away the nearest major galaxy.

Important data for your design: Actual dimensions

Object Diameter (km) Mean Distance from the Sun (km)

Solar System Object Diameter (km) Distance from Sun (km )
Sun 1,392,000  
Mercury 4,878 57,900,000
Venus 12,104 108,200,000
Earth 12,756 149,600,000
Mars 6,794 227,900,000
Jupiter 142,800 778,000,000
Saturn 120,540 1,427,000,000
Uranus 51,200 2,871,000,000
Neptune 49,500 4,497,000,000
Pluto 2,300 5,913,000,000
Proxima Centauri   4.3 light years
Andromeda Galaxy   2.9 million light years

*remember, light travels at 300,000 km/s how far will it travel in 1 year?*

Set up a mathematical proportion which will enable you to make your scale model

calculated calculated

size of celestial object distance from sun to celestial

in centimeters* object in meters*

*(be careful to keep track of units and be consistent between cm, m, mm, and km)*

What are the scale diameters of the solar system objects if your experiment.

Object used to represent the sun Diameter of object in cm

For every object in the list below, please fill in the appropriate blank with the scale model values for diameter and distance. Please convert all units for the diameter measurements to mm, and all units for distance measurements to m ... except the final two values which should be in km.

Sun Diameter

Scale Model Mercury Diameter is Mercury Distance

Scale Model Venus Diameter Venus Distance

Scale Model Earth Diameter Earth Distance

Scale Model Mars Diameter Mars Distance

Scale Model Jupiter Diameter Jupiter Distance

Scale Model Saturn Diameter Saturn Distance

Scale Model Uranus Diameter Uranus Distance

Scale Model Neptune Diameter Neptune Distance

Scale Model Pluto Diameter Pluto Distance

Scale Model Proxima Centauri Distance

Scale Model Andromeda Galaxy

If Proxima Centauri is actually 4.3 light years from here, how long would it take to travel there at the speed of the Voyager spacecraft (45,000 km/hr)

Now that you have completed your scale model and gone outside to visualize it, please respond to the following questions.

1) After doing this exercise, how "big" does the earth now seem to you?

2) Throughout history, mankind has viewed the earth’s resources as being unlimited. Following this lab, what is your perspective on earth’s resources now, and how do you believe we should act regarding these resources?

3) Carl Sagan once described the Earth as a "pale blue dot" against the absolute immense black emptiness of space. Considering that our sun is one of about 200 billion suns in our galaxy alone, with incredible distances between suns, one might quickly despair into a melancholic stupor. What are your thoughts about your own significance against such an incredible vastness as deep space?


       

Any questions you may have regarding the actual numbers regarding diameter and distance can be found at the Scale Model Lab site in this course. When you have completed this work, please submit the responses and then return to the Planet Introduction folders, or go directly to Inner Rocky Worlds for your study.


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