If I attach the same engine to a 1,000 kg spacecraft and a 10,000 kg spacecraft in orbit, the 1,000 kg spacecraft will accelerate more quickly. If I drop a 1 kg rock and a 10 kg rock on the moon, they accelerate at the same rate. What is the difference?
I think what I may be asking is “why is gravity the a and not the f in f=ma.”
EDIT: BY all means please feel free to discuss, but I consider the question answered by u/mmmmmmBacon12345
mmmmmmm….. Bacon…..
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The gravitational force on an object is proportional to that object’s mass, but so is the object’s inertia. If you increase an object’s mass tenfold, you increase the gravitational force on it tenfold—but you also make it ten times harder to accelerate, and these factors offset one another perfectly.
You’ve said it yourself by quoting “f=ma”: the force (f) grows by a factor of ten, but so does mass (m). Since they’re on opposite sides of the equation, they cancel each other out. Better yet, rewrite it as “a=f/m”: increase the mass and thereby the gravitational force, and your acceleration increases by a factor of 10/10, which simplifies to 1/1, which is just 1, which means your acceleration remains the same.
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