Galileo's telescopes were not of high quality by modern standards. He was able to see the moons of Jupiter, but he never reported seeing features on Mars. Use the small-angle formula to find the angular diameter of Mars when it is closest to Earth. How does that compare with the maximum angular diameter of Jupiter? (Assume circular orbits with radii equal to the average distance from the sun.)

Angular diameter of Mars = 15.80 * 10^5 arc seconds

The Angular diameter of Mars is 3 times the angular diameter of Jupiter

Explanation:

Average distance of the earth from sun = 150.67 * 10^6 km

assuming the radius of Mars ( average distance from sun) = 209.33 * 10^6 km

assuming the radius of Jupiter(average distance from sun) = 768.71 * 10^6 km

The small-angle formula for mars

angular diameter = ( linear diameter / distance ) * (2.06 * 10^5 )

distance between earth and mars = 54.6 * 10^6 km

linear diameter = 2 * radius = 418.66 * 10^6 km

angular diameter = ( 418.66 / 54.6 ) * 2.06 * 10^5

                             = 15.80 * 10^5 arc seconds

small angel formula for Jupiter

Angular diameter = ( linear diameter / distance ) * (2.06 * 10^5)

distance between Jupiter and earth = 588 * 10^6 km

linear diameter = 2 * radius = 1537.42 * 10^6 km

Angular diameter = ( 1537.42 / 588) * 2.06*10^5

                             = 5.39 * 10^5 arc seconds

comparing the angular diameter of the Mars and that of Jupiter :

The angular diameter of mars / angular diameter of Jupiter

= 15.80 / 5.39 = 2.931 ≈ 3

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