Question

If Earth's moon were replaced by a neutron star with a radius of 12 km, what would the angular diameter (in arc seconds) of the neutron star be as seen from Earth? (Hint: Use the small-angle formula, angular diameter (in arc seconds) 2.06 ✕ 105 arc seconds = linear diameter distance , where the linear diameter and the distance both have the same units.)

Answer 1

The angular diameter in arc seconds is 2.06 * 10^5 arc seconds.

Step-by-step explanation:

To calculate the angular diameter of the neutron star as seen from Earth, we can use the small-angle formula:

Angular Diameter (in radians) = Linear Diameter / Distance

Given the hint that 2.06 * 10^5 arc seconds correspond to the linear diameter-distance ratio, we can set up the equation as:

Angular Diameter (in radians) = (2.06 * 10^5 arc seconds) * (Linear Diameter) / (Linear Diameter)

Since the linear diameter of the neutron star is given as 12 km, we can plug in this value:

Angular Diameter (in radians) = (2.06 * 10^5 arc seconds) * (12 km) / (12 km)

Angular Diameter (in radians) = 2.06 * 10^5 arc seconds

The angular diameter in arc seconds is 2.06 * 10^5 arc seconds.