How can astronauts tell how fast they are going?

Let’s use our car again, but this time we get real numbers from the accelerometer in our smartphone. Say we start at a red light and then accelerate at 2 m/s² (meters per second squared) for five seconds. From the equation above, Δf₁ would be 2 x 5 = 10 m/s, so that’s our velocity. Now, after crossing for a while, we accelerate again at 1 m/s² for another five seconds. Δf₂ is then 1 x 5 = 5 m/s. Adding these two changes, our velocity is now 15 m/s. And so on.

The only problem is that inertial measurement is not as accurate as the Doppler method over long periods of time because small errors will continue to accumulate. This means that your system must be periodically recalibrated using a different method.

Optical navigation

On Earth, people have long been navigating the stars. In the northern hemisphere, find only Polaris. It is called the North Star because the Earth’s axis of rotation points right at it. This is why it stands still, while the other stars seem to revolve around it. If you point a finger at Polaris, you will point north, and you can use that orientation to go in any direction you want.

Now, if you can measure the angle of Polaris above the horizon, you will also know your latitude. If the angle is 30 degrees, you are at latitude 30 degrees. See, it’s easy. And once you can measure position, you only need to do it twice and record the time interval to find your velocity.

But celestial navigation works because we know how the Earth rotates, and that doesn’t help in a spacecraft. Oh well, can we just use the stars like you would use the cows on the side of the road? No. The stars are so far away, astronauts would have to travel for many, many generations to detect any shift in their position. Like the plane flying over the ocean, you seem to stand still even while traveling 25,000 mph.

But we can still use the basic idea. For optical navigation in space, a spacecraft can locate other objects in the solar system. By knowing the exact location of these objects (which change over time) and where they appear relative to the viewer, it is possible to triangulate a position. And again, by taking several position measurements over time, you can calculate a velocity.

In the end, even though spaceships don’t have speedometers, it is possible to track their speed indirectly with a little physics. But this is just another example of how flying in space is really, totally different– and much more complicated – than driving or flying on earth.