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You don't need to go that far. Newton's 2nd Law does the job nicely.

F = M x A" The force on the body is equal to the product of (mass) times (acceleration) "

The thrust (force) of the rocket motors is constant, so the product of the spacecraft's

(mass) times its (acceleration) is constant.

As it burns fuel from its tanks, its total mass shrinks. In order for the product of

(mass) x (acceleration) to remain constant, the acceleration increases.

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