Gravitational Force According to Newton’s Law of universal gravitation

| August 31, 2017

Question
1. Gravitational Force According to Newton’s Law of universal gravitation, the attractive force F between two bodies is given by

where m1, m2 are the masses of the two bodies
r = distance between the two bodies
G = gravitational constant 6.6742 × 10–11 newtons meter2 kilogram–2

Suppose an object is traveling directly from Planet A to Planet B. The mass of Planet A is 17.56 × 1010 kilograms, the mass of Planet B is 5.34 × 105 kilograms, and the mean distance from Planet A to Planet B is 20,000 kilometers. Set up an inequality that would answer this question: For an object between Planet A and Planet B, how far from Planet A is the force on the object due to the Planet B greater than the force on the object due to Planet A? Simplify your inequality until one side equals zero. Do not solve.

2. Find all of the zeroes (real and/or complex) of
f(x) = x² + 3x + 5

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