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 fea

Question

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.)

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Diễm Kiều 5 years 2021-07-25T16:25:16+00:00 1 Answers 294 views 1

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  1. minhkhue
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    2021-07-25T16:26:49+00:00
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    Answer:

    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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