NASA Celestia Guided Activity

Jupiter Challenge: 1

Find the exact number of Earths’ that can fit inside Jupiter

(You will have to pretend that Earth is made of marshmallow and can squeeze into all of the space of Jupiter.)

The Inside Story: Diameter versus Volume

The diameter of Earth is approximately 13,000 kilometers. Jupiter’s diameter is approximately 143,000 km. That makes Jupiter’s diameter 11 times greater than Earth’s diameter. However, Jupiter’s volume is way over 1,000 times greater than Earth’s volume! How is that?

Solution:
Diameter and volume of spheres are related, but not in a one-to-one manner. In other words, even though Jupiter’s diameter is 11 times greater than Earth’s diameter, that doesn’t mean that Jupiter’s volume is 11 times greater than Earth’s volume. To find the relationship between diameter and volume of a sphere, you have to look at the formula for a sphere.

You may already know these facts. Radius (r) is the distance from the center of a sphere to its edge. Diameter (d) is the distance from one edge of a sphere, through its center, to the opposite edge. Therefore the diameter is equal to two times the radius (d = 2r).

The formula for the volume of a sphere:

Note that the radius (r) of a sphere is cubed (r x r x r) in the equation! So, if you doubled the size of its diameter (or radius), the new volume would not be twice as large, but 23 (2 x 2 x 2). That’s 8 times larger! Since the diameter (and radius) of Jupiter are both 11 times greater than that of Earth, Jupiter’s volume is 113 (11 x 11 x 11), or about 1,330, times greater than Earth’s!

Now it is up to you to do the exact math:

Challenge Bonus:

A ping pong ball is 1.5 inches in diameter, and a softball is 4.5 inches in diameter. That means that a softball is 3 times the size of a ping pong ball. Can you say how many times greater (in volume) a softball is compared to a ping pong ball? You should be able to do this one in your head.

Planet	Diameter (km)	Radius (km)	Volume (km^3)
Earth	12,756
Jupiter	142,796