Bate, Mueller, and White - Fundamentals of Astrodynamics ... - UL FGG

4
LF=m r
TWO-BODY ORBITAL MECHANICS
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Figure 1.1-1 Newton's Law of Motion
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Ch. 1
(Ll-1)
where LF is the vector sum of all the forces acting on the mass m and r
is the vector acceleration of the mass measured relative to an inertial
referenc e frame shown as )0(Z in Figure 1.1-1. Note that equation
(1.1-1) applies only for a fixed mass system.
1.1.3 Newton's Law of Universal Gravitation. Besides enunciating
his three laws of motion in the Principia, Newton fo nnulated the law of
gravity by stating that any two bodies attract one another with a force
proportional to the product of their masses and inversely proportional
to the square of the distance between them. We can express this law
mathematically in vector notation as:
Fg = - GMm r
r 2 r
(1.1-2)
where F 9 is the force on mass m due to mass M and r is the vector from
M to m. The universal gravitational constant, G, has the value
6.67Ox10-8 dyne cm2 Igm2 •
In the next sections we will apply equation (1.1-2) to equati ;n
(1.1-1) and develop the equation of motion for planets and satellites.