1. What is the angular diameter of the Sun, as seen from Mercury, a perihelion? At aphelion?Mercury is at 0.31 AU (= 46.5 million km)from the Sun at perihelion, and 0.47 AU (= 70.5million km)from the Sun at aphelion. Perihelion:angular diameter 1,400,00057.31.7346,500,000 Aphelion:angular diameter 1,400,00057.31.1470,500,000 2.The Hubble Space Telescope has a resolution of about 0.05”. What is the size of the smallest feature can distinguish on the surface of the Moon (distance = 380.000 km)? On Mercury, at closest approach to Earth?We use the angular diameter formula, with angular diameter in units of seconds:angular size= 206,265(actual size/ distance)actual size= distance × angular size/ 206,265Moon:actual size0.05380,000206265= 0.092 km = 92 mMercury:actual size0.0576,500,000206265= 19 km3. Calculate Venus’s angular diameter, as seen by an observer on Earth, when the planet is a) at its brightest, distance is 0,47 AU,b) at greatest elongation, distance is 0,72 AU,c) at the most distant point in its orbit, distance is 1,7 AU. The formula for angular diameter in seconds of arc isangular diameter = 206,000(actual diameter / distance)The true diameter of Venus is 12 ×104km, and the various distances are given in the first two sections of the chapter.a.When Venus is brightest, Distance = 0.47 AU = 7.05 ×107km;angulardiameter 4712 1020626535.17.05 10kmkmarc seconds
b.At greatest elongation,Distance = 0.72 AU = 1.08 ×108 km;angulardiameter 4812 1020626522.91.08 10kmkmarc secondsc.At superior conjunction,Distance = 1.7 AU = 2.55 ×108 km;angulardiameter 4812 102062659.72.55 10kmkmarc seconds