Assume there are suddenly only two objects in the universe; a 1000kg weight and Earth. The weight (somehow)?

Question

begins to fall from ten million km distance. How fast will it be going when it hits (relative to Earth). I believe it will never exceed the "Escape Velocity" of Earth, even if it is a light year away. What about 100 light years, etc.? Anyone?

Answer 1

Imagine you turned it around, like playing a movie in rewind. Suppose you have a 1000kg weight leaving Earth at some high speed, at it comes to a stop and falls back at a distance of 10 million km (or 100 light years) or whatever. (It doesn't matter for now what the speed is.) A convenient thing about Newtonian physics is that it always works the same backwards and forwards.

So your belief is right. The velocity of the object when it arrives at Earth will never exceed escape velocity, because then it would escape if you flipped things backwards.

To get the actual answers -- how fast they'll be going -- you set the gravitational potential energy (G * mass of Earth * 1000 kg / distance) at the top to the kinetic energy (1/2 * 1000kg * velocity^2) plus gravitational potential at the bottom.

You get 11,177 m / s for 10 million km and 11,180 m / s for 1000 LY (which you expect, since it almost escapes).

Answer 2

Objects can move faster entering the earth's atmosphere if they are already moving at a high speed. It is likely that the object would pick up much speed traveling the great distance, and would hit the planet at a higher speed than that of a 'free fall' in our atmosphere.

Such as comets and asteroids, they can impact earth at thousands of miles an hour. That is why many of them (some the size of a state) could wipe out the entire planet. The imense heat and pressure from the collision causes the matter to transform into energy. According to Albert Einstein's theory, a normal size house, if converted to pure energy, could melt the ice caps and possibly split the planet in half.

I can't tell you the speed it would ACTUALLY be traveling, you would have to know way too many factors to even try guessing that.

--- In the link provided, you can click the "Launch Interactive" link under the picture and it will show you more on the matter to energy theory. That whole site has good information on many topics. Hope it helps some.

Answer 3

If it has no velocity when it starts to fall, then when it reaches the earth's atmosphere, it will be very close to, but slightly less than, escape velocity. When it hits, it will be much slower, because of friction with the atmosphere.

At the heights that you mention, escape velocity (square root of 2GM/R, where R is the distance; M is earth's mass, not the object's mass; and G is a constant) is very, very low. If the object starts at a velocity greater than escape velocity, then it continues to have a velocity greater than escape velocity until the atmosphere slows it.

Answer 4

You are correct, as long as you assume
that it started from rest relative to earth.
( It could be approaching at greater than
escape velocity to begin with.)

Answer 5

well if there are only these two objects in the universe, and one begins to "fall" that means it is falling towards the other one, so it all depends on the intial velocity and mass of the objects in question. bodies that are in motion remain in motion unless acted upon by an outside force. hope this helps!!!!!