Step 1: Recall what acceleration due to gravity depends on.
The acceleration due to gravity \(g\) depends on:
Distance from the centre of the Earth
Shape and rotation of the Earth
Step 2: Consider variation with latitude.
The Earth is not a perfect sphere; it is slightly flattened at the poles and bulged at the equator.
Also, due to Earth’s rotation:
\(g\) is maximum at the poles
\(g\) is minimum at the equator
Hence, \(g\) varies with latitude.
Step 3: Evaluate the options.
(A) Incorrect — gravity is not the same everywhere in space
(B) Incorrect — \(g\) is not the same everywhere on Earth
(C) Correct — it varies with latitude ✔
(D) Incorrect — gravity on the Moon is much smaller than on Earth
Step 4: Final conclusion.
The acceleration due to gravity varies with the latitude on the Earth.
\[
\boxed{\text{(C)}}
\]