Newton's law of universal gravitation
Every two masses attract each other along the line joining them:
\[F = G\frac{m_1 m_2}{r^{2}}\]
- \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the two masses, and \(r\) is the distance between their centers.
- The force is proportional to the product of the masses, so a heavier body pulls harder.
- The force is inversely proportional to the square of the distance: doubling \(r\) cuts the force to one quarter.
Why this matters on the translunar coast
- The spacecraft is always pulled by Earth, but the strength of that pull depends on how far away it is.
- Near Earth the pull is strong; far out it is weak. The force is not a constant that the spacecraft carries with it — it is a property of the current separation.
- That is why the deceleration is not uniform along the path: the same spacecraft feels a different force at every point of the journey.