<p>The major axis is just the sum of the distance at perigee plus the distance at apogee. This is 400 km + 1500 km + the <em>diameter</em> (not radius) of the Earth, and the semi-major axis is half of that.</p>

<p>However, the semi-minor axis is harder to determine. Therefore, why not use an <a href="https://en.wikipedia.org/wiki/Orbital_eccentricity#Calculation" rel="nofollow noreferrer">alternative method to calculate the eccentricity</a>?</p>

<p>$$e = \frac{r_a-r_p}{r_a+r_p}$$</p>

<p>Here, the $r$'s are the distance to the <em>center</em> of the Earth, not the apside altitudes. Can you take it from here?</p>

CC BY-SA 3.0
2018-04-21T09:14:28.387Z
2018-04-21T09:14:28.387Z
Glorfindel
<p>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 ($b$).</p>

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

CC BY-SA 3.0
2018-04-20T23:15:23.750Z
Why would you *need* to do this?
James K
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2018-04-20T23:50:43.550Z
I'm voting to close this question as off-topic because this was cross posted on Physics SE.
StephenG - Help Ukraine
CC BY-SA 3.0
2018-04-21T00:56:06.497Z
@JamesK I need the eccentricity and semi-major axis to input into an orbit generation/propagation code.
user12120
<orbit><earth><orbital-elements><orbital-mechanics><satellite>
Calculate eccentricity from apside altitudes?
user12120
# Calculate eccentricity from apside altitudes?

(Asked by: username_0 on 2018-04-20)

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 ($b$).

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

**Tags:** orbit, earth, orbital-elements, orbital-mechanics, satellite
> **Comments:**
> **username_1**: Why would you *need* to do this?  
> **username_2**: I'm voting to close this question as off-topic because this was cross posted on Physics SE.  
> **username_0**: @JamesK I need the eccentricity and semi-major axis to input into an orbit generation/propagation code.  

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## 1 answers

### Answer by username_3 on 2018-04-21. Score: 0 | Accepted answer

The major axis is just the sum of the distance at perigee plus the distance at apogee. This is 400 km + 1500 km + the *diameter* (not radius) of the Earth, and the semi-major axis is half of that.

However, the semi-minor axis is harder to determine. Therefore, why not use an [alternative method to calculate the eccentricity](https://en.wikipedia.org/wiki/Orbital_eccentricity#Calculation)?

$$e = \frac{r\_a-r\_p}{r\_a+r\_p}$$

Here, the $r$'s are the distance to the *center* of the Earth, not the apside altitudes. Can you take it from here?


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