What is the relationship between height and gpe

Let the force exerted by Earth on an object of mass 'm' at height 'h' where the gravitational acceleration is 'g' be 'F' and the potential energy of the object be 'E'.

We know,
F = mg
(for a body experiencing gravitational pull of magnitude 'g')

And, E = mgh
Replacing mg = F in E, we get:
E = F x h

That is the relation between potential energy for a body at height 'h' and the gravitational force it experiences at that height.

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.