The gravity tractor, as shown in the artist\'s rendition, is a proposed spacecra
ID: 1392550 • Letter: T
Question
The gravity tractor, as shown in the artist's rendition, is a proposed spacecraft that will fly close to an asteroid whose trajectory threatens to impact the Earth. Due to the gravitational attraction between the two objects and a prolonged period of time over which it acts (several years), the asteroid's trajectory is changed slightly, thus hopefully diverting it from impacting the Earth. If the gravity tractor's weight on Earth is 20,000 lbs and it flies with a center of gravity 160ft from the surface of the asteroid, and the asteroid is homogenous pure iron with 1290 ft diameter spherical shape, detirmine the force of mutual attraction. Idealize the gravity tractor to be a particle.
I know the answer is F = 0.5649 lbs, but can't seem to figure it out.
Explanation / Answer
mass of tractor m1 = 20000
radius of asteroid = R = 1290/2 = 645 ft
volume of asteroid = (4/3)*pi*R^3 = (4/3)*3.14*645^3 = 1.124*10^9 ft^3
mass of asteroid m2 = 1.124*10^9*490 = 5.51 *10^11 lb
distance between the centers of tractor and asteroid r =
645+160 = 805 ft
F = G*m1*m2/r^2
G = 3.32104*10^-11 lb ft^2 / pound^2
F = (3.322*10^-11*20000*5.51*10^11)/(805^2)
F = 0.5469 lb
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