Your water bottle is full of water at room temperature. picky you wants the water 1.00 kelvin warmer. instead of heating it up in the microwave or on the stove, you decide to drop it from 1 meter multiple times, reasoning that most of the gravitational pe eventually goes to heating up the water (pe → ke just before hitting the ground → a change in internal energy of the water in the water bottle). assuming all this energy goes into heating up the water, how many times do you have to drop the water bottle from 1 meter to warm it up the required amount?

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.

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