Question 19. Escape speed from a 100 km diameter asteroid with a density of 2100

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Question 19. Escape speed from a 100 km diameter asteroid with a density of 2100 kg/m^2
N 182 (b) What is the apparent weight of this same object at Neptune's equator? (Note that Neptune's "t N 19. o -1 points YF14 13, P. 051 What is the escape speed from a 100-km-diameter asteroid with a density of 2100 kg/m3? 20. O 44 points l Previous Answers YF14 13, P.063 Two identical stars with mass M orbit around their center of mass. Each orbit is circular and has radius (a) Find the gravitational force of one star on the other. (Use any variable or symbol stated abov (G.M.M) Fig (2 R) (b) Find the orbital speed of each star and the period of the orbit. (Use any variable or symbol s 1 VRGM

Explanation / Answer

Density of asteroid p = 2100 kg/m3 ,  R = 100 km / 2 = 50 km = 50,000 m

Mass of asteroid = volume * density = (4/3) pi * R3 * p

Gravitational potential energy = PE= -G M m / R

Total energy of body = KE + PE , KE + PE = 0

(1/2) m v2 + [ - G M m / R ] = 0

v2 = 2 G M / R

v = sqrt [ 2 G * ( (4/3) pi * R3 * p ) / R ]

v = R sqrt [ (8/3) * pi * G p] = 50,000 * sqrt [(8/3) * pi * (6.67 * 10-11) * 2100]

v = 54.16 m/s

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