A telescope observes two points on a distant planet. The linear separation between the points is 10^6 m , and they subtend an angle of 6' (minutes of arc) at the telescope. The distance to the planet from the telescope is:

Step-by-step solution

The plane angle subtended by an arc of length s at a distance D is given by = s D , provided is measured in radians. Given: s = 10^6 m = 6' First, convert the angle into radians: 6' = ( 6 60 )^ = 0.1^ 0.1^ = 0.1 180 rad = 1800 rad Now, calculate the distance D : D = s = 10^6 1800 D = 1800 10^6 m = 1.8 10^9 m Answer: 1.8 10^9 m