Measure the Speed of the ISS With Your iPhone

Can you spot the ISS? It can be that “star” that appears to be like like a small line, around the tree. The telephone took a one-second publicity, and that’s how far the station moved in that time. That is pretty great. Oh, observe that this is ideal by the star Betelgeuse in the constellation Orion. (Speaking of which, I am a small dissatisfied that Betelgeuse apparently won’t go supernova at any time before long.)

My plan now is to use the length of that line and the publicity time of the picture to calculate the velocity of the ISS. Bear in mind that average velocity (in just one dimension) is defined as transform in posture (∆x) divided by the transform in time (∆t). As an equation, it appears to be like like this:

Illustration: Rhett Allain

Calibrating With the Stars

But wait! I have the time, but I never have the length. Images never record the sizing of factors, they capture the angular sizing, which relies upon in part on how far away they are. Hold your thumb up at arm’s length and evaluate it to the moon. They glimpse about the same, ideal? They have a related angular sizing, even however your thumb is (almost certainly) a good deal smaller.

But what about your phone’s camera? The sizing of factors you see in a picture also relies upon on the camera’s field of watch (FOV). When I get a new telephone, I like to established up a nice experiment to measure the FOV (alternatively than just looking it up). Here’s just one I did for the Apple iphone six.

But in this circumstance, I never need to have that. I can use the picture by itself to uncover a scaling variable for angular measurements, since it consists of one thing I know about: I can use the angular sizing of Orion to identify the angular sizing of the ISS line. Precisely, I’m likely to attract a line from Betelgeuse (Orion’s ideal shoulder) to Rigel (his still left foot), which I know has an angular length of .3247 radians (many thanks WolframAlpha).

(Truly, working with a constellation is a fantastic way to measure field of watch for a telephone much too, considering that it does not matter exactly where you stand even on the tallest mountain, the angular sizing of Orion will be the same, since those stars are so far away.)

Now I’m likely to use the Tracker online video investigation application to measure the ISS line in that picture. Here’s what I get:

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