# Crater Box

 Astronomy: Crater Formation Grade Range: Elementary School, High School Format: Hands-on

The Crater Box is a simple way to show how craters form. This is an easy hands-on experiment that younger students will enjoy, if only because they get to throw balls in a sand box. This demonstration fits well into a high-school astronomy course, since you can demonstrate how to calculate the size of an object based on the dimensions of the crater it leaves behind.

## Materials

• A Large, Flat Box
• A Mix of Coarse and Fine Sand
• Small Balls of Varying Size and Mass
• Yard Stick
• Ruler (optional)

## Safety Precautions

Please read the Physical Demonstration section of the Demonstration Safety page before performing this demonstration.

## Demonstration

1. Ask a student to drop one of the balls into the box, from about one foot above the sand. Let them drop a few different types of balls, so they can see how the mass of the ball affects the outcome.
2. Ask the student to now drop a ball from two feet up. Can they see a difference in the depth of the crater? What about the width?
3. Ask the student to now drop a ball from three feet up. Ask again if they can see a change in the width or depth of the crater.
4. Optional: If students would like, they can use the ruler to measure the width and depth of the hole at the different heights. Do they see a trend forming?

## Why This Works

### Short Explanation

Crater formation is easy to see and understand. An object comes in from outer space, strikes a planet or moon, and that impact results in a hole on the surface. We can replicate this using this box of sand and set of balls, and look at what you need to make bigger craters.

When you drop the different balls in at different heights, you see that the more mass the ball has, the bigger the crater it makes. This is because the amount of energy our ball has depends on two things: how big it is, and how fast it is going when it hits the sand. Since we are dropping the balls instead of throwing them, we can have them all be moving at about the same speed when they hit the sand. This means that the only thing that changes the outcome is how much mass each ball has. In other words, the bigger and heavier the ball, the bigger the hole it will make!

We can see that the craters are all forming in similar ways, whether they are big or small. This is because craters have three stages of formation. The first stage is the Contact Stage, when the ball hits the surface. The second stage is the Excavation Stage, when some of the sand is sent flying by the impact, and we see the hole widen up from the ball's impact. The final stage is the Modification Stage, when we see the walls of the hole collapse a bit, and the flying sand lands again. The craters are not very big, however, and that is because it takes a lot of energy to make the sand move out of the way without scooping it. In fact, to double how wide the hole is you need to drop the ball eight times higher, and to double how deep it is you would have to drop the ball from sixteen times higher!

### Full Explanation

Crater formation is easy to see and understand. An object comes in from outer space, strikes a planet or moon, and that impact results in a hole on the surface. However, the dimensions of the crater formed, and what factors into the dimensions of it, are a bit harder to comprehend.

When we drop a ball into the sand, and as we drop it from higher heights, we can see the three stages of crater formation happening. We first see what is called the Contact Stage, when it first strikes the surface. The ball will sink into the surface, compressing some of the sand, and creates a pressure wave in the sand itself. As this pressure wave travels out through the sand, it pushes some of the sand around the ball up and away from the impact. This is the Excavation Stage, when we see the bits of sand being flung up around the ball, and we see the crater's width form. Right after this we see the Modification Stage, when some of the sand forming the crater wall collapses into it, finishing the shape and size of the crater.

When we drop the ball from differing heights, we are affecting how much energy it has when it strikes the sand. In this case, we are looking at the relationship between Potential Energy (PE = mgh) and Kinetic Energy (KE = 1/2 mv^2); By increasing the drop height, we are increasing the final velocity of the ball, which affects the final dimensions of the crater. When a crater forms, the initial crater before any collapse will normally be spherical, and will have a depth and width that are proportional to the size of the object. If we measure the width and depth of the craters formed by the balls in the sand, we should start to see a trend that both of these factors are increasing. They both increase slowly, however, with the width of the crater growing faster than the depth of it. This is because of the spherical shape a crater takes on; the volume of a sphere can be calculated with a cubed diameter, and the crater formed will never have a volume greater than 1/3 of an imaginary sphere placed within it. We can combine these terms to find:

 Diameter d1/3 ∝ 1/2 mv2 = mgh Depth d1/4 ∝ 1/2 mv2 = mgh

If we want to see the crater from the two foot drop get twice as wide, we would have to drop it from eight feet high! Also, in order to see the crater get twice as deep, we would have to drop the ball from sixteen feet! If we drop objects from the edge of the atmosphere, however, they will reach a max velocity because of the air slowing it down. In that case, we would instead have to adjust the object's mass is in order to see larger craters. This is why little meteoroids falling to earth don't usually leave a mark, but bigger ones will!