Calculate eccentricity from apside altitudes? [closed]

I need to calculate the eccentricity of a satellite orbit with only the apside altitudes (height above the surface of the Earth), 400 and 1500 km. However, I don't know the semi-major axis ($a$) or semi-minor axis ($b$).

$$\text{eccentricity} = (1-(b/a)^2)^{1/2}$$

closed as off-topic by peterh, StephenG, James K, J. Chomel, Sir CumferenceApr 23 '18 at 19:26

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• Why would you need to do this? – James K Apr 20 '18 at 23:15
• I'm voting to close this question as off-topic because this was cross posted on Physics SE. – StephenG Apr 20 '18 at 23:50
• @JamesK I need the eccentricity and semi-major axis to input into an orbit generation/propagation code. – user12120 Apr 21 '18 at 0:56

$$e = \frac{r_a-r_p}{r_a+r_p}$$
Here, the $r$'s are the distance to the center of the Earth, not the apside altitudes. Can you take it from here?