jbird3000 hit it on the head, but no one seemed to notice, so I’ll elaborate: Along with mass, every object also has a property called inertia (that is–basicly–the tendency to resist any change in velocity) the two are related. The more mass, the more inertia. Ever notice how hard it is to get that studebaker rolling for a push-start, but than, once it’s moving, it’s eaiser to push. That has to do with that whole “object at rest will remain at rest” thing. The more massive an object, the more resistant it will be to any change in velocity (weather that be starting from a stopped position, or stopping from a moving one)
So, the inertia of an object counteracts the stronger force of gravity that results from the greater mass–thus ensuring that, in a vacuum, objects will fall at the same rate, regardless of mass
Critical1 in the case you’re discussing, the black hole, for lack of a better term, “bends space” in it’s immediate vicinity–it changes the geometry of the space nearby. It’s true that you, measuring with an Euclidian ruler wouldn’t see it as a straight line–but the ruler’s faulty, not the definition of straight.
Yes, stupid me, I was assuming an infinitely rigid earth. Of course, in the real earth, the part under the heavier object would deform slightly upwards and the heavier one would hit first.
Though wouldn’t inertia apply to those tidal forces as well? The more massive object would cause a more massive bulge, which would take longer to move…
Yes, but the force on the bigger bulge is larger than the force on the smaller bulge so the bigger bulge will be bigger even with inertia.
I did not intend to refer to rigidity, but that the earth would spin slightly. Compare it to a rigid car which is moving forwards, but when it slams on the brakes, often the right side will decelerate faster than the left side, causing the left side to continue forwards more than the right side, so that the front left corner will suffer more damage than the front right corner will (or vice versa). Similarly, in the OP, my intention was to say that if the more massive abject is on the left, the earth will swing upwards on the left more than on the right.
Several posters have mentioned inertia, saying that the greater attraction of the more massive objects is negated by the fact that inertia will require the more massive objects to take more time to reach the speeds of the less massive objects. But is this counterbalance exact? Could it be that the more massive objects will reach each other sooner than the less massive, even though they have to fight the interia? Or could it be that the inertia is significant enough that the less massive objects will win?
Well, according to physics the cancellation is exact, as andy_gl has already pointed out:
Gravitational force is proportional to mass: F=mg
Acceleration is force divided by mass: a=F/m
So a = g, regardless of mass.
One problem that has been alluded to already is that for a very massive object, the Earth will also accelerate toward the object. The result is that they meet at their combined center of gravity. Since the Earth moves “up” a bit more for a heavier falling object, the heavier object will actually hit sooner.
Just semantics. Incorrect semantics, by the way. Here’s what you said:
[ul][li]Objects don’t have gravity. [/li][li]Objects have mass.[/li][li]Massive objects have an attractive force.[/li][li]This force is called gravity.[/ul][/li]
All you’ve done is add extra steps to say the same thing:
[ul][li]If A is an object and objects have mass, then A has mass.[/li][li]If A is an object and has mass, then A is a massive object.[/li][li]If A is a massive object, and massive objects have an attractive force, then A has an attractive force. [/li][li]If A has an attractive force, and that force is called gravity, then A has gravity.[/ul][/li]
And to elaborate on what FriendRob said, there are actually two components to acceleration in a gravitational interaction between objects A and B: The acceleration of A towards B, and the acceleration of B towards A. In calculating A -> B, A’s mass does indeed cancel exactly, and vice versa. But in the total interaction, both masses do come into play.
Well, the confusing thing is that objects have a specific gravity which is not the same as mass. When someone starts talking about “gravity of an object” I can get confused thinking they are actually talking about specific gravity.
Likewise, I have also gotten confused when people talk about “density” without qualifying it. Most of the time they mean mass density, but sometimes they mean number or energy density. It would be nice if we named things very differently so as to avoid such confusion. That’s why certain people get picky over terminology. It is all semantics but semantics can sometimes be important.
This deformation will occur when the objects are in place, but before they are dropped. If the distances the objects are dropped are measured between the objects and the deformed Earth, the heavier object is farther from the Earth’s center when you drop it. It’s no longer obvious that the heavier object will hit first. Another reason why assuming the Earth is the same is “not a trivial assumption”.
While I don’t agree that it is “just semantics,” I did indeed make a misstatement.
As objects do not “have gravity”, they also do not “have an attractive force.”
In my last post, replace “All massive objects have an attractive force for all other massive objects” with “There exists an attractive force between all massive objects.”
Take this physics question:
“Jimmy is in a car going 30 kph and throws a ball going 20 kph out of ahead of him, how fast is the ball moving?”
In grade school the answer is “50 kph” but for a student in Modern Physics in college it’s a wee bit under that.
Is the grade school being misled? No, for all practical purposes that is the right answer. There is no reason to bring up relativity at that level. It is a basic principle of teaching that you feed students little bits at a time. You don’t throw Special Relativity at them unless it matters.
Teaching (in any field) requires such accommodations. The formula for the swing of a pendulum is an approximation for small angles. Hooke’s law for springs likewise, etc. etc. The first time you are taught about square roots you are told that negative numbers can’t have square roots. Later on they teach you about imaginary numbers but not about quaternions.
But never mistake that a simplfication at the grade school level is the depth of knowledge of the field. It isn’t.
Spot on ftg.
It’s simply a convenient approximation that a mass will accelerate toward the earth at 9.8 m/s/s.
For high school or first year physics, it works fine. Any errors in the approximation aren’t going to show up in questions involving small masses and distances.
Physicists and mathematicians know it’s an approximation, and also know that Newtonian gravity is an approximation of general relativity. Many physicists suspect that general relativity is an approximation for something else as yet undiscovered or unproven.
For a simple example of when the approximation breaks down,
try working out how long it takes for a 1 kg hammer dropped from the moon’s orbit to hit the earth.
Using the approximation, the answer is about 8800 s.
If the initial acceleration is recalculated to account for the greater initial distance, the answer is about 530,000 s.
Of course, the actual acceleration varies as the hammer gets closer to earth, and the real answer is about 419,000 s.
Thus, distance can greatly affect the answer.
Mass also affects the answer. If instead of a hammer, I drop a small object with mass of the the moon from the moon’s orbit, it will hit the earth in about 417,000 s.
So yes, the stuff that’s being taught is an approximation. Everyone knows about it. It’s useful in lots of situations. Why worry about it?
Dont forget the fact that you didn’t specify that this was in a vacuum (thank god for Jimmy). Also, due to conservation of momentum, the act of throwing the ball means the car slows down slightly. 