Question

A planet 'X' subtends an angle of 1° 25’ 30'' when light is thrown at it from two diametrically opposite points of the Earth. What is the distance of the planet from the Earth? (Radius of the Earth is 6400 k m)

Answer 1

For objects that subtend a relatively small angle we can use the following approximation:

s=rθ

Where is the actual diameter of the object in question, r is the distance to the object, and θ is the angle subtended by the object in the sky in radians we must convert degrees to radians:

0.5ºx(π/180º)=0.00873rad

s=(384000000)(0.00873)=3.35×106m

A diameter of the moon is 3.35×106m