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The gravity tractor 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 lb and it ies with its center of gravity 160 ft from the surface of the asteroid, and the asteroid is homogeneous pure iron with 1290 ft diameter spherical shape, determine the force of mutual attraction. Idealize the gravity tractor to be a particle.

Respuesta :

mateoe1

Answer:

[tex]F_g=461lb_f[/tex]

Explanation:

First calculate the mass of the asteroid. To do so, you need to find the volume and know the density of iron.

If r = d/2 = 645ft, then:

[tex]V = \frac{4}{3} \pi r^3[/tex]

[tex]V = 1.124*10^{9}ft^3[/tex]

So

[tex]\delta_{iron}=m/V=491lb/ft^3[/tex]

[tex]m=V*\delta=5.519*10^{11}lb[/tex]

Once you  know both masses, you can calculate the force using Newton's universal law of gravitation:

[tex]F_g=G\frac{m_1m_2}{d^2}[/tex]

Where G is the gravitational constant:

[tex]G= 1.068846 * 10^{-9} ft^3 lb^{-1} s^{-2}[/tex]

[tex]F_g=461lb_f[/tex]