I wrote

The math is as follows: If you are in a cirular orbit at altitude h,
you
are r = h + R from the center of earth (with R = 6378 km) and you are
moving with respect to the center of earth at a speed of

v = sqrt(k/r),

where k = 398601 km^3/s^2 is the gravitational constant for earth
(also
called GM). Now you want to change your orbit into an elliptical one
with the highest point at radius r, and the lowest at s = 100km + R.
In
such an orbit you would at the highest point need an orbital speed of

w = sqrt(k*(2/r-1/s))

which means that you must change your speed with

dv = v - w

in order to change from the circular orbit to the elliptical orbit. If
you use the numbers as I have written them above, then the speed unit
will be km/s.

Somehow I managed to confuse "s" with "a" (which equals (r+s)/2) on the
back of my envelope, so the correct form is

w = sqrt(k*(2/r-2/(r+s))).

Sorry about that.




--
Filip Larsen