I cannot, for the love of god, read “other things constant” and understand what it actually means.
In: 8
Like in a science experiment. You want to control something so only one factor is changing so you can measure how changing that one thing alters everything else.
So for instance if you drop an apple out a second story window, and nothing changes, gravity says the apple will fall down if you’re on the surface of the earth, because the force of gravity is F=mass of the falling object × 9.8meters/second^2.
But that’s not the real equation for gravity, that’s holding the mass of the earth, and the radius of the earth constant, ceteris paribus, as a simplification.
The actual equation for gravity between two objects is
F = G × m1×m2/r^2
G is the gravitational constant, and we multiply it by the mass of both objects, and the distance between their centers of mass. When we hold m1 and r constant, as the mass of the earth and radius of the earth at sea level, the equation simplifies to mass×9.8, because that’s just what the mass of earth times G divided by the radius of earth squared happens to be.
But if we had a way to change the mass of the earth, then we could get different results than the apple falling. If the mass of earth suddenly dropped to 0, then the apple would just hang in midair and would not fall. If the distance between them grew so vast it approached infinity, the apple would also remain still and not be drawn towards the earth.
The simplification to F=m×9.8 is useful in daily life for engineers and scientists because the mass of the earth and it’s radius is so vast that climbing to the top of mount everest or riding in an airplane has such a small effect on the force of gravity that it’s still effectively m×9.8.
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