In 1993 the spacecraft Galileo sent home an image of asteroid 243Ida and a tiny
ID: 1745493 • Letter: I
Question
In 1993 the spacecraft Galileo sent home an image of asteroid 243Ida and a tiny orbiting moon(now known as Dactyl), the firstconfirmed example of an asteroid-moon system. In the image the moonwhich is 1.5 km wide, is 100 km from the center of the asteroid,which is 55 km long. The shape of the moon's orbit is not willknown; assume it is circular with a period of 27h. (a) What is themass of the asteroid? (b) The volume of the asteroid, measured fromthe Galileo images, is 14100km3. What is thedensity(mass per unit volume) of the asteroid?Explanation / Answer
a) Given that Distance of the moon from the center from the center of theasteroid is (r) = 100 km = 100000m = 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
Hire Me For All Your Tutoring Needs
Integrity-first tutoring: clear explanations, guidance, and feedback.
Drop an Email at
drjack9650@gmail.com
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.