Newtons law of gravitation can be used to show that if an...

newton's Law of Gravitation can be used to show that if an object weighs w pounds on the surface of the earth, then its weight at distance x from the center of the earth is W(x) = wR^2/x^2 (for x ≥ R) where R = 3,960 miles is the radius of the earth. At which altitude would an 130-lb person weigh 129.5lbs? (Round your answer to two decimal

It is a law of physics that the gravitational force exerted by the Earth on an object above the Earth's surface varies inversely as the square of its distance from the Earth's center. Thus, an object's weight $w(x)$ is related to its distance $x$ from the Earth's center by a formula of the form $$ w(x)=\frac{k}{x^{2}} $$ where $k$ is a constant of proportionality that depends on the mass of the object. (a) Use this fact and the assumption that the Earth is a sphere of radius $4000 \mathrm{mi}$ to obtain the formula for $w(x)$ in Example $4 .$ (b) Find a formula for the weight $w(x)$ of a satellite that is $x$ mi from the Earth's surface if its weight on Earth is $6000 \mathrm{lb}$. (c) How much work is required to lift the satellite from the surface of the Earth to an orbital position that is 1000 mi high?

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