How deep would the water covering be on a perfectly spherical Earth?

[FRDE]

I vaguely remember something similar turning up here some time ago.

The answer given was that if earth were the size of a base/basket/billiard ball then the vertical distance between the deepest trench and the highest mountain would be about the thickness of a fingernail.

I can’t remember which ball, but with that sort of ratio it doesn’t seem to matter that much.

[wolfstu]

Now that the basic mathematical answer has been given, it may be of interest to consider that the Earth is not perfectly spherical, or of uniform density. For the real earth, a global ocean wouldn’t have a spherical surface.

@The European Space Agency

The irregular gravity field shapes a virtual surface at mean sea-level called the ‘geoid’. This is the surface of equal gravitational potential of a hypothetical ocean surface at rest and so defines ‘the horizontal’ - meaning that if a ball were placed on this hypothetical surface it would not roll, despite the presence of virtual slopes. The geoid is important for understanding more about ocean currents and is also employed as a reference for traditional height systems and monitoring sea-level change. In addition, the geoid is used for levelling and construction.

Determining the shape of the geoid to very high precision is the goal of the recently launched GOCE mission (Gravity field and steady-state Ocean Circulation Explorer).

[Snarky_Kong]

@DesertDog

Well, according to Wiki, the difference between the polar radius and equatorial radius of the Earth is 22km with a mean radius of 6371km That’s a difference of .00345 (22/6371)

An American pool ball is 2.25in +/- .005in in diameter. Dividing the diameter by two to get the radius and dividing that into the tolerance, you get a difference of .00444 Doubling the tolerance. because it is plus or minus after all, doubles the difference to .00888 (.005/1.125 or .010/1.125).

If you want to see an oblate planet, go look at Saturn.

2.25 +/- 0.005 gives radii of 1.1225 and 1.1275 respectively for a variation of 0.005 or +/- 0.0025. The difference is then 0.00444, not 0.0088.

[Chronos]

Of course, for the real Earth, if you had a global ocean the shape of the geoid would be different.

[DesertDog]

@Snarky_Kong

2.25 +/- 0.005 gives radii of 1.1225 and 1.1275 respectively for a variation of 0.005 or +/- 0.0025. The difference is then 0.00444, not 0.0088.

Oops. I forgot to halve the tolerance when I halved the diameter to get the radius. Still, .00444 is less round than .00345