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You asked what would happen to your weight if the earth's mass doubled (due to a density increase) without changing in size.


There are three very useful equations in this context.


First, weight = mass * gravity.
Second, force = mass * acceleration.
Third, gravity = (g-constant (your mass * earth's mass))/distance between the masses squared.


It happens that the first two equations mean the same thing. For this to be true, weight would have to be a force (it is, and it's called "newtons"), and gravity would have to be an acceleration (that's also true).


So what we need to do here is figure out how much gravity the earth would have if its mass doubled. Since the earth does not change in size, in your problem, the distance doesn't either. We can then set distance = 1 in the third equation. Likewise, the gravitational constant doesn't change; that's why it's called a "constant".


So what do we have? It's clear that the gravity acting on you and earth doubles if we do nothing but double the earth's mass.


Since your weight = your mass times gravity, and gravity has doubled as we've shown, the answer is simple: YOUR WEIGHT WOULD DOUBLE TOO.

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15y ago

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