In 1993 the spacecraft Galileo sent home animage (Figure 13-48) of asteroid 243
ID: 1744874 • Letter: I
Question
In 1993 the spacecraft Galileo sent home animage (Figure 13-48) of asteroid 243 Ida and a tiny orbiting moon(now known as Dactyl), the first confirmed example of anasteroid–moon system. In the image, the moon, which is 1.5 kmwide, is 100 km from the center of the asteroid, which is 55 kmlong. The shape of the moon's orbit is not well known; assume it iscircular with a period of 27 h. (a) Whatis the mass of the asteroid? (b) Thevolume of the asteroid, measured from the Galileo images, is 14100km3. What is the density (mass per unit volume) of theasteroid?Explanation / Answer
a) Given that Distance of the moon from the center from the center of theasteroid is (r) = 100 km = 105m Length of the asteroid (L) = 55 km long. The moon's orbit is circular with a period of (T) =27 h. =27*60*60s = 97200s Universal law of gravitation is (G) =6.67*10-11N.m2/kg2 We know that from the Kepler's thrid law we get M = 42r3/GT2 Now substitute all the above values to get the requiredanswer b) Givven that The volume of the asteroid is (V) =14,100km3. = 14,100*109m3 The density of the asteroid is given by = M/V ( M from thepart a ) Now substitute all the above all the values to get therequired answer Now substitute all the above values to get the requiredanswer b) Givven that The volume of the asteroid is (V) =14,100km3. = 14,100*109m3 The density of the asteroid is given by = M/V ( M from thepart a ) Now substitute all the above all the values to get therequired answerRelated Questions
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