The gausss law for gravity: ∮g⃗ ⋅da⃗ =−4πgmin. a spherical planet is discovered with mass m, radius r, and a mass density that varies with radius as ρ=ρ0(1−r/2r), where ρ0 is the density at the center. determine ρ0 in terms of m and r. hint: divide the planet into infinitesimal shells of thickness dr, then sum (i. e., integrate) their masses. express your answer in terms of the variables m and r.

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.

Because its reliable.   there is no pollution  the chances of a radiation leak is low

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