originally posted by: solve
a reply to: mblahnikluver
It looks smallish, hard to tell how far or close that thing is...
Actually, it is unusually easy
to determine its size and distance from the camera using 15 seconds of googling the camera specs and
trigonometry that I learned in the 8th grade (thank you Mr. Mihalik!).
The bottom line is that the object is about the size of a large pizza box, and is sitting on the ground roughly 60 feet from the rover.
Here is the analysis:
For starters, here is a detailed technical description of the Pancam: Link
The relevant numbers are that it is on a mast 1.5 meters above the Martian surface, its field-of-view is 16°x16° and its images are 1024x1024
- Note that this means each degree is 64 pixels.
- 16° is a narrow angle, which minimizes distortion near the edges of the frame.
- The object in question is near the center of the frame, which makes the distortion negligible.
What really makes this analysis so easy is...
...that the both the object and the rover are on level ground with respect to each other.
...that the horizon is visible, flat and on the same level as the object & rover.
...that the camera is ~level to the horizon (actually, it's tilted 0.336° to the right, but this is negligible).
If the rover was looking up a hill or down into a crater at the object, or if there were hills closer than the horizon, this would be much more
The camera, at 1.5 meters off the ground, is looking down at the object. It is ~306 pixels below the horizon, which equates to 4.8°
sin 4.8° = 1.5 meters / x
x = 1.5 meters / sin 4.8°
x = 1.5 meters / 0.084
x = 17.85 meters
This is how far the object is from the camera.
Now then, the object is 106 pixels wide, which equates to 1.66°
sin 1.66° = x / 17.85 meters
x = sin 1.66° * 17.85 meters
x = 0.029 * 17.85 meters
x = 0.518 meters, or 51.8cm
This is how wide the object is.
edit on 24-6-2017 by Saint Exupery because: I moved the bottom line from the bottom line to near the top so as not to bore the entire
internet with my bloviating.