The Earth has an equatorial bulge of 42.72 km (26.5 miles) due to its rotation. That is, its diameter measured across the equatorial plane (12756.28 km, 7,927 miles) is 42.72 km more than that measured between the poles (12713.56 km, 7,900 miles).

The planet with the largest known equatorial bulge (11808 km, 7337 miles) is Saturn.

Jupiter	Sun	71492 (Equatorial) 66854.5 (Polar)
Saturn	Sun	60268 (Equatorial) 54364 (Polar)
Uranus	Sun	25559 (Equatorial) 24973 (Polar)
Neptune	Sun	24764 (Equatorial) 24340.5 (Polar)


earth:
computed bulge: 21.89 km
actual bulge: 42.72 km

saturn:
computed bulge: 8239.7 km
actual bulge: 11808 km

The figures are vaguely in the right ballpark, but not right.

The fact that earth's gravitational field is not simply spherical does not I think account for this large a difference.

Saturn:
 normal:
  ./planet 5.6869e26 54364000 37050.56
 critical:
  ./planet 5.6869e26 54364000 23750
 broke:
  ./planet 5.6869e26 54364000 23300