# Relative Size of Planets "To Scale" with Fractions of Solar System and Ratios

Mathematicians and all persons of reason are taught to question everything. And yet, from the time I was a child fascinated with the stars and planets in our solar system, I assumed that the pictures in all of the books were accurate. That couldn’t have been further from the truth. Not a single picture I every saw had a disclaimer that said, “not drawn to scale.”

This week, the children found out exactly how incorrect those pictures can be. They created an accurate to scale model of our solar system planets, including Pluto.

We started with one pound of Play-doh or the equivalent. It is likely your children will be asking you to purchase Play-doh. You need not purchase it; although, it could be fun. They are tasked to create their own scale model of our solar system with whatever material they can find. Play-doh is probably the easiest. They can also use Clay,Model Magic, Mashed Potatoes, Hummus, Tofu, etc. Zero cost material would be soil or dirt from your yard. It will harden with a little water.

I taught them how to handle this material and cut it into fifths and tenths, 5 or10 equal parts. They came up with strategies which included forming a uniform cylinder, score it in half, then cut off a perpendicular fifth; then cut the remainder in fourths giving you a total of 10 equal pieces. We practiced then cutting that tenth into tenths and more tenths until we reached a piece the size of a single grain of sand that was one 1,000,000th of the original piece.

The first step in the process is to take six tenths (or three fifths) is combine them together to make Jupiter. Then follow the remaining 10 steps on the attached pdf.

IN ORDER OF SIZE, YOU WILL HAVE CREATED THE NINE PLANETS TO SCALE. Then we looked at the ratios of the planets to Pluto as one (left column) and then Earth as one (middle column).

For example, since Mercury is a 9 to Pluto at 1 we say that:

· the ratio of the sizes of Mercury to Pluto is 9 to 1 or 9:1 or 9/1

· Mercury is nine times the size of Pluto (Mercury is 900% of Pluto)

· Pluto is one ninth (1/9) the size of Mercury (Pluto is 11.1% of Mercury)

**PLANET RELATIVE SIZE (by volume or mass)**

**PLANET**** ****PLUTO IS 1**** ****EARTH IS 1**** ****DIAMETER IN MILES**

Jupiter 1,200,000 1,200 88,730

Saturn 718,000 718 74,940

Neptune 40,000 40 30,775

Uranus 40,000 40 31,763

Earth 1,000 **1 7,926**

Venus 900 0.9 7,521

Mars 90 0.09 4,222

Mercury 9 0.009 3,031

Pluto **1** 0.001 1,430

Total 2,000,000 2,000.000

Sun1,960,000,000 1,960,000 865,000

The Sun is 1,960,000 times bigger than Earth

The Sun is 1,633 times bigger than Jupiter.

**THIS WEEK’S CHALLENGES:**

FOR ALL GRADES:

A) Create your own solar system using Play-doh, Clay, Model Magic, Mashed Potatoes, Hummus, Tofu, etc.

B) Label each planet.

FOR GRADES 3-6:

C) Use the ratios from steps 1-8 on the attached pdf to make sure the planets are actual relative size.

D) Identify the ratios between the sizes of each pair of planets.

E) **Bonus:** identify the fraction/% of each planet of the mass of the whole solar system (for example, Jupiter is 3/5=60% of whole).

For the bonus, divide each ratio number by 2,000,000 (the number of total parts of the solar system); then simplify the fraction by dividing both numerator and denominator by the same factor until there are no further common factors greater than one.

Attachment | Size |
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Relative_Size_of_Planets_Play-doh_Steps_Fractions_and_Ratios.pdf | 1.34 MB |

Relative_Size_of_Planets_Slides.pdf | 922.47 KB |