You are using a gravity tractor to change the trajectory of an NEO on a collisio

Question

You are using a gravity tractor to change the trajectory of an NEO on a collision course with Earth. Unless the trajectory is altered, the NEO will impact the Earth 20 years hence. The approximately 100 meter NEO has a mass of 1.57 billion kilograms. The force exerted on the NEO is related to the product masses of the tractor and the NEO. You want to impart an acceleration of 2x10^-9 m/sec^2 to the NEO. What should the mass of the tractor be to produce a force sufficient to produce this acceleration? Neglecting the mass of the physical tractor mechanism, what would be the size of a spherical boulder from the NEO which when attached to the tractor would produce the needed mass?

Explanation / Answer

force = mass x acceleration

force =G X (mass of NEO x mass of the tractor)/ radius2

From above 2 equations it can be said that:

mass x acceleration = G X (mass of NEO x mass of the tractor)/ radius2

= 1.57 billion kilograms x 2x10-9 = 6.754 × 1011 m3 kg1 s2. ( 1.57 billion kilograms x mass of the tractor)/ 1002

= (1.57 x 1012 x 2x10-9 x1002)/6.754 × 1011 x 1.57 x 1012

mass of the tractor = 296,120.8173 kilograms

100 meter NEO has a mass of 1.57 x 1012 kilograms

1 kilogram =100 / 1.57 x 1012

296,120.8173 kilogram =  296,120.8173 x 100 / 1.57 x 1012

Therefore the size of a spherical boulder from the NEO which when attached to the tractor would produce the needed mass= 1.8861 x 10-5 meter

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