Given the following orbital elements, how should I calculate the minimum and maximum speed of the satellite?
Mean Orbital Altitude: $950$ km
Inclinination: $23.1$ deg
Eccentricity: $0.1$
Right ascension of the ascending node: $94$ deg
Satellite mass: $150$ kg
I'm thinking about using Vis-Viva equation, but I'm not sure how to calculate the semimajor axis and the distance between the satellite and Earth.
Best Answer
You are already on the right track with the vis-viva equation. For using it you need to extract some simple facts from the given orbital elements of the ellipse.
In an elliptic orbit the mean radius is the semi-major axis $a$. Therefore, from
you get the mean radius (i.e. the semi-major axis $a$) by adding the mean altitude to the radius of the earth ($6370\text{ km}$). $$a = 6370\text{ km} + 950\text{ km}$$
And from
and the definition of the eccentricity $\epsilon$ you can calculate the minimum and maximum radius of the ellipse: $$r_\text{min}=a(1-\epsilon)$$ $$r_\text{max}=a(1+\epsilon)$$