Question

The distance to the other planets in the Solar System from the Earth depends on where they are in their orbit. The closest that Mars gets to the Earth is 0.5 AU. At this time it is observed to have an angular diameter of 18 arcseconds. The furthest it gets from Earth is 2.5 AU. What would its angular diameter be for this observation

Answer 1

3.6 arcsec

Step-by-step explanation:

angular diameter = diameter / distance

diameter is constant

so angular diameter ∝ 1 / distance

angular diameter = k / distance

For first case ,

18 = k / .5

for second case let angular diameter be D .

D = k / 2.5

dividing ,

D / 18 = .5 / 2.5 = 1 / 5

D = 18 / 5 = 3.6 arcsec

3.6 arcsec is the answer .