Question

Two stars that are 109 km apart are viewed by a telescope and found to be separated by an angle of 10^(-5) radians. If the eyepiece of the telescope has a focal length of 1.5 cm and the objective has a focal length of 3 meters, how far away are the stars from the observer?

a. 4.4×10¹⁶ m
b. 3.6×10¹⁶ m
c. 5.2×10¹⁶ m
d. 2.8×10¹⁶ m

Answer 1

The stars are approximately 1.09 km away from the observer.

Step-by-step explanation:

In order to determine the distance between the stars from the observer, we can use the formula:

d = θ × D

where d is the distance between the stars, θ is the angle between the stars as viewed through the telescope, and D is the distance between the observer and the stars.

Given that the stars are 109 km apart and separated by an angle of 10⁻⁵ radians, we can plug these values into the formula:

d = 10⁻⁵× 109 km = 1.09 km

Hence, the stars are approximately 1.09 km away from the observer.