How Can Astronauts Tell How Fast They’re Going? | WIRED

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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 r1. At 1:00:15, it’s position vector is r2.

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.

To get closer to the actual velocities, we’d have to use much smaller time intervals. In fact, if we make Δt small enough, that curved path can be approximated by a series of tiny line segments, giving us a pretty accurate velocity at any instant.

Velocity Is Relative

There’s one more thing we need to think about. Imagine you’re pedaling a bicycle with a little speedometer attached to the wheel, and it says you’re going 4 miles per hour. But you aren't riding on the road; you’re on the deck of a cruise ship, which is moving at 10 mph. So how fast are you going?

Well, there’s no single right answer; it depends on your frame of reference. With respect to the ship, you’re going 4 mph. But with respect to the water, your speed depends on your direction. If both ship and bike are heading west, you’d be going 14 mph. If you turned the bike around and headed east, you’d be going 6 mph. What’s more, as an observer on the shore would see, in the latter case you’d be pedaling forward and moving backward at that speed.

Often the reference frame is obvious, like the surface of the Earth. But in space, it's not always so clear. For spacecraft like the Orion on its recent trip around the moon, there are two obvious reference frames. The first is the Earth. We can measure the speed as it moves toward or away from us. This usually makes sense because that's where the flight started and where mission control sits.

But for NASA’S Artemis IV mission, which is scheduled to touch down on the lunar surface in 2028, it would be silly to use Earth as a reference frame. You could have a positive Earth-speed but be stationary with respect to the moon—not very helpful in landing maneuvers. Instead, the lander will use the moon as a reference frame. Or if you wanted to travel around the solar system, it would make sense to use the sun as your reference .

The fact is, there is no stationary reference point anywhere in the universe. All motion is relative to other motion. So now, if your brain is sufficiently scrambled, let's get into some of the ways we can measure speed in space.

Doppler Speed

Perhaps the most common method uses the Doppler effect. You already know about this. If you stand by some train tracks, you hear a high-pitched sound as a train approaches, and it shifts to a low-pitched sound as it passes, right? NNEEEEEEEEE—rrrrrraaaaaa …

What’s happening is that the sound waves are getting bunched up as the train moves toward you. That means more wave peaks hit your ear