3 ms·

> He came up with a law of motion to explain how two balls of different weights, dropped from the same height, hit the ground simultaneously. I've been thinkin

> He came up with a law of motion to explain how two balls of different weights, dropped from the same height, hit the ground simultaneously. I've been thinking about this for a while. The two balls hit the ground at the "same time" because relative to the earth, they are about the same mass (ball #1 is only 1/2 the mass of ball #2, and the difference between that and the mass of the earth is negligible). Once you start making ball #1 and ball #2 massively different, one of the balls begins to attract the earth itself more than the other ball. For example... 1) Take a basketball, drop it. Measure the time. 2) Take a miniture blackhole, drop it. Measure the time. While earth's pull will be the same on both the basketball and the blackhole, the blackhole's pull on earth will be much much grater than the basketball's and hence the additive acceleration will be larger. But, if you drop them at the same time, next to each other, things will even out since the earth will move towards them both as it moves towards the one. What do I win?

bane 15y ago
And if you drop them at the same time, Ball #1 would probably arc towards the blackhole changing the length of time it took to hit...if it manages to stay outside of the blackhole's event horizon.
andrewingram 15y ago
The problem becomes even more interesting when you start considering that it matters which frame of reference the timing is done from, if each ball has its own timer contained within then you get to have fun with relativity.
archgoon 15y ago
There is no mass for which one ball attracts the earth more than the other ball if the other (fixed mass) ball is less than the mass of the Earth. The ratio of the two forces, the force between the varying mass ball (vmb) and the Earth and the varying mass ball and the fixed mass ball (fmb), is constant°: m_earth/m_fmb. °Assuming equal distance between the two objects. It's still constant w.r.t. mass if you allow different distances, you just pick up a ratio term of the two distances. Again, you don't 'start' attracting one ball more than the Earth. You're _always_ attracting the Earth more. Now that I've put it that way, we can see that the mass doesn't matter, since the previously neglected force is _only_ operating between the direction of the two masses, so there is no additional acceleration in the direction of the earth. If you pretend the earth is a infinite plane (which is typical) than we can see that this will have no effect on the fall time. Since the distance to the earth starts being equal, and the accelerations (relative to the earth) are equal, the time will be equal. If, however, you instead acknowledge that the earth is a sphere, and we really started the two objects at rest at the same radius but different angles, than you have a restricted three body problem and I should probably not try to solve that before I've had coffee. Thank you very much. It will be a good day.
- powertower 15y ago
  > There is no mass for which one ball attracts the earth more than the other ball if the other (fixed mass) ball is less than the mass of the Earth. Are you talking about inertia? If ball #1 or #2 does not have the mass (and hence gravitational pull) to overcome Earth's inertia ... the Earth does not move towards it. But wouldn't that force or energy still be conserved and transferred into the ball's own acceleration?
  - archgoon 15y ago
    >If ball #1 or #2 does not have the mass (and hence gravitational pull) to overcome Earth's inertia ... the Earth does not move towards it. That is false. I think you are thinking of friction.
laxatives 15y ago
If the blackhole pulls harder on the earth than the basketball pulls the earth, the earth also pulls harder on the blackhole than the basketball
dakr 15y ago
It is important to keep in mind that black holes do not "pull" things towards them, they have the same kind of gravity that any other object has, and are also affected by gravity in the same way as other objects. A "miniature" black hole will land at the same time as the basketball.

bane 15y ago

And if you drop them at the same time, Ball #1 would probably arc towards the blackhole changing the length of time it took to hit...if it manages to stay outside of the blackhole's event horizon.

andrewingram 15y ago

The problem becomes even more interesting when you start considering that it matters which frame of reference the timing is done from, if each ball has its own timer contained within then you get to have fun with relativity.

archgoon 15y ago

There is no mass for which one ball attracts the earth more than the other ball if the other (fixed mass) ball is less than the mass of the Earth. The ratio of the two forces, the force between the varying mass ball (vmb) and the Earth and the varying mass ball and the fixed mass ball (fmb), is constant°: m_earth/m_fmb. °Assuming equal distance between the two objects. It's still constant w.r.t. mass if you allow different distances, you just pick up a ratio term of the two distances. Again, you don't 'start' attracting one ball more than the Earth. You're _always_ attracting the Earth more. Now that I've put it that way, we can see that the mass doesn't matter, since the previously neglected force is _only_ operating between the direction of the two masses, so there is no additional acceleration in the direction of the earth. If you pretend the earth is a infinite plane (which is typical) than we can see that this will have no effect on the fall time. Since the distance to the earth starts being equal, and the accelerations (relative to the earth) are equal, the time will be equal. If, however, you instead acknowledge that the earth is a sphere, and we really started the two objects at rest at the same radius but different angles, than you have a restricted three body problem and I should probably not try to solve that before I've had coffee. Thank you very much. It will be a good day.

powertower 15y ago
> There is no mass for which one ball attracts the earth more than the other ball if the other (fixed mass) ball is less than the mass of the Earth. Are you talking about inertia? If ball #1 or #2 does not have the mass (and hence gravitational pull) to overcome Earth's inertia ... the Earth does not move towards it. But wouldn't that force or energy still be conserved and transferred into the ball's own acceleration?
- archgoon 15y ago
  >If ball #1 or #2 does not have the mass (and hence gravitational pull) to overcome Earth's inertia ... the Earth does not move towards it. That is false. I think you are thinking of friction.

laxatives 15y ago

If the blackhole pulls harder on the earth than the basketball pulls the earth, the earth also pulls harder on the blackhole than the basketball

dakr 15y ago

It is important to keep in mind that black holes do not "pull" things towards them, they have the same kind of gravity that any other object has, and are also affected by gravity in the same way as other objects. A "miniature" black hole will land at the same time as the basketball.