Would an object dropped from an infinite height ultimately break the speed of light?

Question

Assuming you could have an infinitly tall frictionless vaccum which is under the earths gravitaional influence. Could one drop a pennie and expect it to hit and exceed the speed of light?

Answer 1

No.

This makes a good theoretical problem, but not a practical one. Your two conditions ("an infinite distance" and "under the earth's gravitational influence") are mutually exclusive. You can have one or the other, but never both.

Gravity decreases as the inverse of the square of the distance. At some point the gravitational influence becomes zero and the object weightless.

Answer 2

I agree. It's a good theoretical problem, but it can never be a practicality.

An infinite distance can be applied to theoretical problems, as can the earth's gravitational pull. But it's impossible to combine the two within the same problem.

If you have an infinite, frictionless distance, you can never have anything in it (ie, it'll be a vacuum, like space). Meaning to say, there can never be any gases in it, unless you're talking about imaginary gases (which are theoretical, in themselves...).

Gravity decreases at the rate of the inverse of the square of the distance. If you have a distance of 500 feet, let's say, then the gravity of the surrounding environment will lessen at a rate of 1 / 500^2 around the object.

If you have an infinite distance, then the rate at which gravity decreases its possible pull on an object would eventually reach zero (through hyperbole), thus rendering the gravitional environment around it as null.

Take a look at space. It's comprised of an infinite distance, right? Now let's go to Earth... Cape Canaveral, to be exact (I'm making this realistic. Don't hate, lol). Imagine you're on the spaceship about to blast off. It's normal Earth gravity. You can still fall down. Now, imagine you're blasting off into space. You're within orbital distance now, where gravity is really weak (if existant...). Now, if you were to keep going towards, let's say, the outer solar system... once you exit the orbital field of earth, the earth's gravitational pull around you will become zero, and you'd experience total weightlessness. Gravity will always remain at zero, until you approach an object with an immense mass (which will then pull you towards it). :-p

Also, the speed of light can never be exceeded. It's the fastest thing in the entire universe (and something we've yet to fully experiment with...). It's a milestone which can never be broken.

So to FINALLY fully answer the question, let's review the conditions. If there was an infinitely tall frictionless vacuum, the object wouldn't move. It would be weightless.

If there was a finite frictionless vacuum under the earth's gravitational pull, the penny would fall only at the speed of free-fall, never exceeding it unless it had some force accelerating it.

Light (a high-speed wave comprised of photons) is a wave. It's never to be confused as a milestone. I know too many people who say, "if you were going at the speed of light, wouldn't you BECOME light?" The answer: no. Take a look at Chuck Yeager who was the first to break the sound barrier. Was his Bell X-1 (his plane...) SOUND? Obviously not.

Hope I answered every possible scenario. :-p

Answer 3

No. If it is under the earth's gravitational influence, it would still reach terminal velocity. The reason an object reaches a terminal velocity is that the drag force resisting motion is directly proportional to the square of its speed. At low speeds the drag is much less than the gravitational force and so the object accelerates. As it speeds up the drag increases, until eventually it equals the weight. Drag also depends on the cross-sectional area. This is why things with a large surface area such as parachutes have a lower terminal velocity than small objects like cannon balls.

Answer 4

Even under Newtonian physics, a body 'falling from infinity' would not go infinitely fast. The potential energy difference between infinity and the surface of the earth is finite. Once that energy gets converted to kinetic energy, there won't be further acceleration.

On the othe rhand, under Newtonian physics, there is an infinite amount of energy between infinity and the origin for a *point mass*. This would roughly correspond to a black hole. Since the energy difference is infinite, that would allow an unbounded velocity.

The only modification for relativistic physics is that an unbounded kinetic energy does not imply an unbounded velocity like in Newtonian physics. In fact, as the velocity goes towards that of light, the kinetic energy goes to infinity, so even in the case of an infinite potential well, relativistic physics has a speed of light limit.

Answer 5

nope

in the very best case, the object would reach the escape velocity for the Earth, about 11.2 kilometers per second. That's because, if you want, the Earth sits at the bottom of a gravitational pit, and the escape velocity is what is needed for an object to escape from the pit for good - and also the speed an object gathers if arriving from "infinity".

The escape velocity increases with the (square root of the) mass of the planet / star, and decreases with the (inverse square root of the) size.

For Jupiter the escape velocity - and also the speed of an object arriving, with no friction, from infinity - is nearly 60 km / sec or 5.3x larger than for Earth. For the sun, the object would arrive with a speed of 618 kilometers per second.

So let's try for heavy, dense objects. Take a typical neutron star, 1.4 solar masses, radius 10km. Its escape velocity would be nearly 193'000 km/s, so your object would arrive at the surface at nearly two-thirds of the speed of light, not enough to observe any relativistic effects, but pretty fast.

And then you get to black holes. By definition, the Schwarzschild radius (event horizon) is set as that at which the escape velocity is equal to the speed of light. A black hole with the mass of the Earth would need to have a size of just 8.9 millemeters so if you could shrink the Earth to that minuscule size, yor object arriving from infinity would indeed land at the speed of light! One with the mass of the Sun, 2.9 kilometers.


Hope this helps.

Answer 6

No. Here we are contemplating to drop a penny in frictionless vacuum infinitely tall height. The problem is we can not have Earth's gravity functional at infinite heights. It will become clear from the following.
consider a mass m at a dist r from earth.
The force equation can be written as
GMm/(R+r)^2=mg
G=universal gravitation constant
M,m are masses of Earth and the object in question
R,r are the radius of earth and dist of object from surface of earth
g=acceleration due to gravity.
Let us see how g varies
simplifying the above equation we have
g=GM/(R+r)^2; now G&M&R are fixed.only r is varying
As r approaches infinity g will tend to zero
As the dist from earth increases the acceleration due to gravity will sharply reduce making earth's gravity ineffective.
So the problem above is flawed and it is not possible to break the speed of light.

Answer 7

No.

When the speed of an object increases the mass increases as well (not *exactly* true, but good enough for the common person because the effect is the same) so with the same force pulling it down the acceleration decreases.

Answer 8

No. An object falling to Earth from an infinite distance would (neglecting atmospheric drag) hit the surface of the Earth at 11.4 km/s (~25,000 mph). This is, not coincidentally, the escape velocity needed to escape Earth's gravity.

Answer 9

General Relativity demonstrates that the Speed of Light is an absolute speed limit. The energy speeding up the falling object would convert to mass as it approaches the speed limit

Answer 10

At the height u are talking about there wouldnt be any gravitational force under the earths influence.

Answer 11

Don't think so. Firstly, earth's gravity doesn't extend infinitely, so what would start the penny falling? And theoretically spd of lt is ultimate so can't be exceeded?