The Size of the Solar System We are making a scale solar system, where 40 AU - the distance from the
Sun to Pluto - is the equivalent of 100 yards. That means the Sun will be on the
0-yard line, and Pluto is at the 100-yard line.
Remember from last lab that to do conversions we first use an equality to find
our conversion factor:
some # of units of original measurement
=
some # of units of converted measurement
We then multiply the original measurement we're trying to convert by a
fraction which has both sides of our conversion factor:
Original Measurement
some # of units of converted measurement
X
=
some # of units of original measurement
Converted measurement
Example:
We want to convert AU distances in our solar system to yard lines on our
football field. In this case, we have the following conversion factor:
40 AU
=
100 yards
Let's say we want to find out on which yard line we want to put Earth on our
football field. If you look in your book (as you'll have to do for the other planets'
orbits), Earth is 1 AU from the sun - so that's our original measurement. We plug
this into our conversion formula above and get:
100 yards Earth's yard line
=
1 AU
X
=
40 AU
2.5 yards
We also want to do this to scale the planets' diameters. However, when we
talk about planetary sizes, 1 AU is way too big a measurement – planetary
diameters are usually measures in kilometers. So first we use the fact that
1 AU = 150 million kilometers.
This also means that on our football field our planetary diameters will be
better measured in inches, so we have to convert that, too. So, we take our
previous example where 1 AU in space is the equivalent of 2.5 yards on the
football field, and convert 2.5 yards to inches:
36 inches
2.5 yards
X
=
90 inches
1 yard
We combine this all to tell us that 150 million km in space (1 AU) is equal to
90 inches on our football field (2.5 yards). Thus, if we want to convert km sizes
of planets to inch sizes on our football field, we multiply by 90 inches, then divide
by 150 million km.
Example:
Let's say we want to find out how large Earth's diameter is on our football field. If
you look in your book (again, as you'll have to do with the other planets) Earth
has a diameter of 12,756 km. We plug this into our formula, first starting with our
conversion factor:
150 million km
=
90 inches
We then multiply Earth's real diameter by a fraction made out of our conversion
factor:
Earth's diameter
90 inches =
12,756 km
X
=
150,000,000 km
0.0075 inches
To complete the scale model for Earth, then, we'd put an object that is .0075
inches across at the 2.5 yard line.