Foundations of Space Dynamics. Ashish Tewari
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where the relative position of mass
(2.41)
The gradient of
On comparing Eqs. (2.40) and (2.42), we have
(2.43)
The acceleration of the mass
(2.44)
and is independent of the test mass,
The concept of gravitational potential between a pair of isolated masses,
(2.45)
or
(2.46)
where
(2.47)
is the net gravitational potential experienced by the
The potential energy,
(2.48)
to be the net work done by the gravitational forces to assemble all the particles, beginning from an infinite separation,
The gradient of
(2.49)
Hence the right‐hand side of Eq. (2.37) is expressed as follows:
A substitution of Eqs. (2.38) and (2.50) into Eq. (2.37) yields the important result that the total energy of the system is conserved:
(2.51)
or
To demonstrate another constant of the