The acceleration due to gravity at the north pole of Neptune is approximately 10.7 m/s^2. Neptune has mass 10^26kg and radius 25000km and rotates once around its axis in a time of about 16h.

Question

What is the gravitational force on an object of mass 4.8kg at the north pole of Neptune?What is the apparent weight of this same object at the Neptune's equator? (Note that Neptune’s “surface” is gaseous, not solid, so it is impossible to stand on it.)

Answer 1

The acceleration of gravity on the surface of Neptune is
g' = G M/R^2,
where M is the planet's mass.
M g' will be the weight registed at the poles. G is the universal constant of gravity

The "apparent weight" at the equator will be reduced from M g' by the centripetal force M R w^2, where w is the rotational angular velocity in radians/s), which you can deduce from the 16 hour length of a day.