How Can Astronauts Tell How Fast They’re Going?

Here on Earth, it’s easy to know how fast you’re driving. You get a good sense of it just by seeing trees and cows pass by. And of course you also have a speedometer that counts how many times your tires rotate per second and computes a speed based on their circumference. (Fun fact: Put bigger tires on your car and your speedometer will be wrong.)

If you’re flying over an ocean, of course, there’s no visual reference, so from inside it looks like you’re motionless. But airplanes can get their airspeed by using sensors to measure the rate at which air is passing over the wings. If there’s any wind, this won’t be the same as your speed relative to the ground, but you can get that by using GPS location data from orbiting satellites.

Now imagine you are flying to Mars. Locking in a precise velocity is critical so you don’t miss your rendezvous with the planet in its solar orbit. But there’s no trees or cows, no air, not even a GPS signal to help you out. So how do you know your rate of travel? Well, you need to use some physics. The good news is that there’s more than one way to go about it.

Speed vs. Velocity

First, a word about words: Speed is how far you go in how much time—like 50 miles an hour. For an airplane using GPS coordinates, it’s easy to calculate: Just take the distance between two locations and divide by the time it took to get from point A to point B.

But that only works if you’re going in a straight line. It doesn’t work at all for a bumblebee, whose path more resembles that of a drunken sailor. In the picture below, you can see that it travels much farther than necessary to get from one place to another.

So instead of speed, in physics we use the concept of velocity, which means speed in a given direction. Even if the bee flies at a constant speed, its velocity is always changing.

To map the bee’s path, I drew an xy coordinate plane on the scene above. (For simplicity, I’m keeping it two-dimensional.) Someone looks at their watch and records a time of 1:00:05 (five seconds after 1 o’clock); at that moment the bee is at a position defined by vector r 1 . At 1:00:15, it’s position vector is r 2 .

We can still take the change in vector position (Δr), or displacement, and divide by the change in time (Δt = 10 seconds). But what that gives us is average velocity, which might not match the bee’s actual motion anywhere in its journey.