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How Far Away From Perseverance Did the Descent Stage Land?

Dare Mighty Issues. That was the hidden message in the parachute of the Mars Perseverance rover. It is not fairly as mighty, however I’m going to dare one thing myself: I’ll attempt to determine how far the descent stage would land from the rover.

OK, let me again up actual fast. Simply in case you do not know how this works, right here is the primary touchdown sequence: The spacecraft entered the Martian ambiance after which deployed a parachute. After that, a rocket-powered descent stage slowed the rover down because it approached the floor. At the very finish of the descent stage, a cable lowered the rover to the floor. Then the descent stage used its remaining gas to shoot away from the touchdown website.

It is this fly-away stage that I wish to analyze. If I can get the acceleration because it leaves, then perhaps I can mannequin its trajectory to see the place it will land. Sure, NASA is aware of precisely the place it landed—they even have a picture of its crash site. Nevertheless it’s enjoyable to see if I can do that simply from the single rover video.

OK, let’s get began. The plan is to make use of angular measurement of the descent stage to get the distance from the rover in every body of the video. However what’s angular measurement, and what does it need to do with place? Here’s a fast experiment for you. Take your thumb and maintain it at arm’s size out of your face and shut one eye. Sure, actually do that. Now discover one thing in the room that your thumb covers up. What occurs if you carry your thumb nearer to your eye? It appears larger and covers up much more stuff in the background. The precise measurement of your thumb did not change, simply its angular measurement.

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Suppose there may be another object—perhaps it is a stick of size L in your subject of view. Think about you can can draw a line out of your eye to every finish of the stick. It could appear like this.

Illustration: Rhett Allain

The stick is type of like part of a circle with a radius r centered in your eye. This implies the size of the stick is roughly equal to the arc size that has an angle θ. Assuming the angle is measured in radians, then the following could be true.

Illustration: Rhett Allain

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