Physics, Astronomy & Cosmology / Re: what would happen if gravitational mass were different than inertial mass?« on: 10/05/2021 08:54:17 »
Aye, there’s the rub.If they \(gravitational and inertial mass) are really proportional with constant ratio, the only consequence would be the change of gravitational constant.Yes. Well done. The Gravitational constant AND/OR something else just gets multiplied by a constant. ................ We can choose constants and/or units to keep the formulae simple.
We can certainly use different formulae and constants, but what of Hamdani’s original question “What's expected to happen if gravitational mass were twice of inertial mass? What if it's only a half?”
Certainly projectile trajectories would be different. A ball thrown from the top of a building would travel a different distance compared to the distance fallen, this implies that orbits would also have a different radius. Changes to Kepler’s laws?
The rate at which a pendulum will swing should change with a new ratio of inertial to passive grav mass.
There would be a different equatorial bulge due to difference between centrifugal and gravitational force.
A plumb bob at a certain latitude would have a slightly different vertical offset, again due to difference between centrifugal and gravitational force.
A mechanical governor would expand to a different circumference, again due to difference between centrifugal and gravitational force.
There must be a lot more, but if that ratio had always been there we wouldn’t think it odd and might be speculating what it would be like if they were equal!
What would we do with the relationship
E ≈ m0c2+½m0v2
Is the energy dependant on whether mass is passive grav or inertial? in the second term it would change if motive was inertial or gravitational. Would we have m0 as the sum of inertial & gravitational?
Strangely, I always expected that the fact they are the same might be explained by some energy conservation law or, like Pound-Rebka shift, that without it you could build a perpetual motion machine.
Have you considered this:Well, it might be serious if he was originally trying to include hot air balloons, but then realised this was a flotation thing!
Newton used the idea of density instead of mass in his ideas about gravity because there was some confusion about the fact that a hot-air ballon seems to fall upwards in earths gravitational field? Maybe he was just searching for a negative gravitational charge that could be repelled instead of attracted.
I just thought I might as well throw that idea in here. It's fun. It's most certainly NOT serious.
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