Although
the science and mathematics behind space exploration
is mind-boggling, many key concepts relate back
to the fundamentals that many of us are familiar
with. For example, modern orbital mechanics
calculations still rely directly on the work
of Kepler and Newton, among others.
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.
Johannes
Kepler(German, 1546-1601)
derived mathematical models (ellipses)
for orbital motions.
Isaac
Newton(English, 1643-1727)
developed the laws of motion and gravity.
He also developed integral calculus and
differential calculus, which are probably
the most important fields of mathematics
in modern science.
Gottfried
Leibniz(German, 1646-1716)
independently developed integral and differential
calculus. His notation and terminology
is the standard today.
to 
, the geometry of elliptical
orbits (as proposed by Kepler)
yields,
.
gives
altitude predictions.
