Question

If a planet is made of uniform density material and has no topography, then which one of the following statements is correct?

• A. The geoid surface would be higher than the reference ellipsoid surface
• B. The geoid surface would be lower than the reference ellipsoid surface
• C. The geoid and the reference ellipsoid surfaces would coincide
• D. The geoid surface would be lower in some places, and higher in other places, with respect to the reference ellipsoid

Hint:

In an ideal, homogeneous, and topographically smooth planet, no gravitational anomalies exist. So, the geoid = reference ellipsoid.

Answer 1

The Correct Option is C

Step 1: Definitions. 
The geoid is an equipotential surface of Earth’s gravity field, representing mean sea level. The reference ellipsoid is a smooth mathematical surface approximating the shape of the Earth.
Step 2: Ideal conditions. 
If the planet has:
 

• Uniform density,
• No topography,
• No mass anomalies,

then the gravitational potential would be smooth and symmetrical, and the geoid would coincide with the reference ellipsoid.