**Sample
vehicle launch calculation:**
For a particular orbit segment
from
to
, the geometry of elliptical
orbits (as proposed by Kepler)
yields,
Using Newton’s
law of universal gravitation
(for satellite mass m and the
Earth’s mass *M*)
and law of conservation of energy,
Some key
calculations are performed when
the distance
between the two masses is at
a minimum (periapsis) or a
maximum (apoapsis). For periapsis,
.
Rearranging the above equations
gives,
Solving for gives
altitude predictions. |