I usually tell this analogy in the spring. I use it as a hook during the Algebra unit on Quadratics, when introducing problems involving projectiles (Mission to Mars lesson). I am sharing it now because it is timely, being that the rover Curiosity just landed on Mars this week.
(Note 1: It would be useful to show the web video “7 Minutes of Terror,” depicting the latest Mars landing before sharing the following tale.
Note 2: The video has now been updated in 2021 for the rover Peseverance.)

If you view images of the command center just after the Mars landing of the space probe Curiosity, you will see people cheering, hugging, and even popping bottles of champagne. It looks to me like the lockerroom after a Super Bowl win… as it should, because what this elite group of engineers, scientist and austronats have accomplished is the Ultimate Touchdown, ever. In fact, NASA refers to the landing as “touch down.”

To greater appreciate this phenomenal feat, let’s compare and contrast NASA’s touchdown to one thrown by an NFL quarterback. Imagine you are throwing a football to a receiver running downfield, but since the earth is moving along it’s orbit, we need you to be running forward also. In fact, you are running faster than the receiver, so after you throw the ball, you will eventually pass the receiver and thus need to look over your shoulder to watch him catch it.

Oh yeah, and you are not running in lines on a field, you are both on a track that has no straight aways. You are in the inside lane; your receiver is in the outside lane. You throw the ball, and as you pass your receiver you watch it drift to the outside lane as it bends around the track as well.

But we remember that a projectile launched into space needs to exit earth’s atmosphere through a small “window.” Therefore, instead of you running, you are driving a car with the passenger side window open. You must throw the ball out the window to the receiver who is running .. no wait … a spacecraft must enter Mars atmosphere through a small window as well, so the receiver must be driving a car also with the driver side window open. You must throw the ball out your window, watch it drift to the outside lane as you blow by the receiver’s car and have the ball fly into his open window.

Oh yeah, and another thing to consider. Earth and Mars each rotate on their own axis. OK, so the cars are spinning! While they are spinning in their respective lanes, you time your throw so the ball travels out your window, drifts through the curves in the track to intercept the path of the car in the outside lane at the exact moment when the window is in just the right position for the ball to enter the car and land in the receiver’s lap. Touchdown.

Come on! If you completed that pass, you would cheer, hug and pop champagne too. In a football game, all eyes follow the long bomb for a few seconds. In our game, all eyes are fixed on the sky for 8 months. If a quarterback throws an incomplete pass, he wastes a million dollars of his teams money. If you miss this interplanetary pass, you blow $2.6 billion of taxpayer money. This is big league pressure we are talking about.

It’s an Ultimate Touchdown to be sure. Here is the coolest part. You are going to learn in your high school algebra class some of the very mathematics that he takes to launch a rocket to Mars.

Hut, hut, hike!