Dare Mighty Things. That was the hidden message in the parachute of the Mars Perseverance rover. It’s not fairly as mighty, however I’m going to dare one thing myself: I’m going to strive to determine how far the descent stage would land from the rover.
OK, let me again up actual fast. Just in case you do not know how this works, right here is the fundamental 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 bottom. Then the descent stage used its remaining gas to shoot away from the touchdown web site.
It’s this fly-away stage that I wish to analyze. If I can get the acceleration because it leaves, then possibly I can mannequin its trajectory to see the place it could land. Yes, NASA is aware of precisely the place it landed—they even have a picture of its crash site. But it is enjoyable to see if I can do that simply from the one rover video.
OK, let’s get began. The plan is to make use of angular dimension of the descent stage to get the space from the rover in every body of the video. But what’s angular dimension, and what does it should do with place? Here is a fast experiment for you. Take your thumb and maintain it at arm’s size out of your face and shut one eye. Yes, actually do that. Now discover one thing within the room that your thumb covers up. What occurs if you deliver your thumb nearer to your eye? It appears greater and covers up much more stuff within the background. The precise dimension of your thumb did not change, simply its angular dimension.
Suppose there may be another object—possibly it is a stick of size L in your subject of view. Imagine you could can draw a line out of your eye to every finish of the stick. It would seem like this.
The stick is form of like part of a circle with a radius r centered in your eye. This means 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 next can be true.