I'm looking for a creative method to measure the following set-up with a few stipulations:?

Question

How could you accurately measure the distance between two baseball-sized spheres that are very close to one another (about 1-30cm) but you must not come within 4 feet of the spheres. That is, you cannot touch them or come near them...imagine a forcefield around them. Using light/lasers seems like possible solution, but is there a simpler way? What is the best way to set-up this measurement?

Answer 1

You could use accurate angular measurements from two remote points measuring angles from tangent edges of the spheres. You would have to very accurately measure the distance between the two remote points to get an accurate result. After taking the angular measurements, you would have enough data to compute the radius of the spheres and the positions of the radius points.

Answer 2

EDITED: There is a more basic way, not involving any form of rangefinder, but I wouldn't call it simpler. I'm assuming you want the distance BETWEEN the spheres (which are of only approximately known diameter) as stated, not the center-to-center distance. Also that not only you, but any tool, must remain at least 4 feet away. You can't directly measure your own distance from the spheres without using a rangefinder, so you can't use projection or angle measurements to derive the distance, and in any case a measurement taken from a single viewpoint would be inaccurate due to the sight line grazing the spheres at points displaced from the closest two points. So I'm proposing that you determine the centerline of the two spheres and construct a path parallel to it and a known distance from it, from which you take right-angled sightings of the spheres.
Let's say the spheres are displaced horizontally. Set up an approximately horizontal plane that cuts the spheres in half. (Ideally you do this with a flat board, sighting along it in such a direction that both spheres are visible, finding the centers of the spheres by halving their subtended angles, and tilting the board as needed.) Note the following procedure works for spheres that are equal or unequal in size. Sighting along this plane, position your line of sight to line up the left edges of the spheres, as measured by an edge of a right angle template (eg a right triangle drawing tool) in the line of sight and perpendicular to the plane. Make a point on the plane where the template's right angle vertex is. Repeat at a different distance along the line of sight and draw the left-edge line of sight defined by the two points. Then repeat the procedure for the right edges of the spheres. Then draw a line on the plane equidistant between these two lines of sight. This is the centerline of the two spheres. Mark a path parallel to the centerline and at a known distance at least 4 feet + the larger sphere radius away, sight at right angles to the path to the two facing edges of the spheres (again using the right-angle template), and mark the corresponding points along the path. The separation distance of the two points is that of the spheres.

Answer 3

use a Laser Range finder. From one specific point find the range of one then find the range of the other. if done correctly then you should come up with there distance from the chosen point. Then useing the Pathagorian therom you can calculate the lentgh of the missing side of your triangle.

Answer 4

Stand exactly 5 feet in front of them and put a ruler exactly 5 feet behind them. If you see 22cm of the ruler between them, they are 11cm apart.

I hope I didn't do your homework for you.

Answer 5

what????