Asix kilogram cat is resting on top of of book shelf that is one meter high. what is the cats potential energy relative to the floor?

PE=1/2 mV^2

replace the values in the above formula, and you'll get your answer

The formula for Gravitational Potential Energy is: mass * g * height. The (g) is specific to the planet in which you're calculating in, which, assuming you mean a cat on Earth, is 9.8 m/s^2. The height is 1, and the mass is 6. Therefore, inputting that into the equation will give you: 

6 * 9.8 * 1, 
potential energy = 58.8J ; correct to 3 significant figures. 

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.