Drawing an ellipse

Hi

I would like to draw a realistic representation of an elliptical orbit with
a simple computer drawing program. Given the semi-major axis and
eccentricity, is there a formula that converts these into the lengths of
the major and minor axes so that I can enter these values into the the
"circle" function to make the ellipse?

TIA
Marty

"Martin Lewicki" wrote in message
...
Hi

I would like to draw a realistic representation of an elliptical orbit with
a simple computer drawing program. Given the semi-major axis and
eccentricity, is there a formula that converts these into the lengths of
the major and minor axes so that I can enter these values into the the
"circle" function to make the ellipse?

If a = semimajor axis
b = semiminor axis
c = half the distance between foci
e = eccentricity

then

a^2 = b^2 + c^2 (True for any conic section orbit)
and e = c/a (True for any conic section orbit but the
parabola, where c -- infinite)

so that

b^2 = a^2 - (e*a)^2

b = a*sqrt(1 - e^2)

Greg Neill wrote:

"Martin Lewicki" wrote in message
...

snip

So for a
semimajor axis = 2
eccentricity = 0.5

semiminor axis = 1.73205....


Easier just to write "sqrt3".

and distance of object (focus 1) from perihelion (q) is
a*(1-e)
= 1

Correct?

Looks good. And don't forget, the aphelion radius is
a*(1+e)
= 3 units

And by way of a 'reality check', you can verify that the sum of the
apoapsis and periapsis distances is equal to 2a, the length of the
major axis: here 3 + 1 = 4 = 2*2.

--
Odysseus