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Table 1
Equatorial to polar radii ratio Re/Rp as a function of η, k and α, for Υ = coskθ and Υ = sinkθ.
| Υ = coskθ | Υ = sinkθ | Υ = sinkθ | |||||||||||
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| η = 0.2 | |||||||||||||
| k | 0.5 | 2.0 | 3.0 | 6.0 | 0.5 | 2.0 | 3.0 | 6.0 | 0.5 | 2.0 | 3.0 | 6.0 | |
| α = 0.00 | 1.100 | 1.100 | 1.000 | 1.000 | 1.100 | 1.100 | 1.000 | 1.000 | α′ = 0.0 | 1.100 | 1.100 | 1.000 | 1.000 |
| − 0.50 | 1.037 | 1.061 | 1.069 | 1.081 | 1.142 | 1.218 | 1.246 | 1.293 | +1.0 | 1.083 | 1.061 | 1.053 | 1.043 |
| − 0.25 | 1.065 | 1.078 | 1.083 | 1.090 | 1.113 | 1.134 | 1.142 | 1.154 | +1/3 | 1.091 | 1.078 | 1.074 | 1.068 |
| +0.25 | 1.143 | 1.125 | 1.120 | 1.112 | 1.093 | 1.082 | 1.079 | 1.074 | − 1/5 | 1.109 | 1.125 | 1.130 | 1.139 |
| +0.50 | 1.192 | 1.153 | 1.141 | 1.125 | 1.088 | 1.072 | 1.067 | 1.058 | − 1/3 | 1.120 | 1.153 | 1.165 | 1.185 |
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| η = 0.8 | |||||||||||||
| k | 0.5 | 2.0 | 3.0 | 6.0 | 0.5 | 2.0 | 3.0 | 6.0 | 0.5 | 2.0 | 3.0 | 6.0 | |
| α = 0.00 | 1.400 | 1.400 | 1.400 | 1.400 | 1.400 | 1.400 | 1.400 | 1.400 | α′ = 0.00 | 1.400 | 1.400 | 1.400 | 1.400 |
| − 0.50 | 1.159 | 1.274 | 1.306 | 1.347 | 1.515 | 1.719 | 1.794 | 1.918 | +1.0 | 1.350 | 1.274 | 1.247 | 1.202 |
| − 0.25 | 1.268 | 1.333 | 1.350 | 1.372 | 1.437 | 1.499 | 1.523 | 1.564 | +1/3 | 1.374 | 1.333 | 1.317 | 1.292 |
| +0.25 | 1.545 | 1.474 | 1.455 | 1.431 | 1.379 | 1.346 | 1.333 | 1.312 | − 1/5 | 1.427 | 1.474 | 1.491 | 1.521 |
| +0.50 | 1.693 | 1.552 | 1.515 | 1.466 | 1.366 | 1.312 | 1.292 | 1.259 | − 1/3 | 1.456 | 1.552 | 1.589 | 1.651 |
Notes. α′ = − α/ (1 + α); Re(α = 0) /Rp(α = 0) = 1 + η/ 2 given by the Roche gravity-rotation potential that identifies the surface of rigid rotators. The Υ = sinkθ function is used first with α and then with α′.
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