Let’s utilize the car again, but this time we will get the real numbers from the accelerometer in our smartphone. Let’s assume we start at a red lithe and then accelerate at a speed of 2 m/s2 (meters per second squared) for five seconds. From the above equation Δv1 will be 2 x 5 = 10 m/s, so this is our speed. Now, after driving for a while, we accelerate again at a speed of 1 m/s2 five more seconds. Δv2 is therefore 1 x 5 = 5 m/s. Adding these two changes, our speed is now 15 m/s. And so on.
The only problem is that inertial measurement is not as correct as Doppler over long periods of time because compact errors will accumulate. This means that you must periodically recalibrate the system using a different method.
Optical navigation
On Earth, humans have long navigated by the stars. In the northern hemisphere you just need to find Polaris. It is called the North Star because the Earth’s axis of rotation points directly at it. That’s why it appears stationary while the other stars seem to revolve around it. If you point your finger at Polaris, you will be pointing north and you can utilize that orientation to go in any direction.
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 30 degrees latitude. You see, it’s straightforward. And once you’re able to measure your position, just do it twice and record the time interval to calculate your speed.
But celestial navigation works because we know how the Earth rotates, and that doesn’t aid with spacecraft. Well, can we just utilize the stars like you utilize the cows on the side of the road? NO. The stars are so far away that astronauts would have to travel for many, many generations to detect any change in their position. Like an airplane flying over the sea, it appears to be standing still even when traveling at 25,000 miles per hour.
But we can still utilize the basic idea. For optical navigation in space, spacecraft can locate other objects in the solar system. By knowing the exact location of these objects (which change over time) and their position relative to the viewer, you can triangulate the location. Again, by taking multiple position measurements over time, you can calculate velocity.
After all, although spacecraft do not have speedometers, it is possible to indirectly track their speed with a little physics. But this is just another example of how flying in space really is completely different – and much more complicated – than driving or flying on Earth.