# Terminal velocity in a vacuum.

1. Dec 11, 2011

### tkav1980

I am curious if there is a terminal velocity for an object in free fall in a gravitational field based on the strength of that field. If I was falling to earth and there was no atmosphere, and I had infinite time to fall(Meaning I'd never actually reach the surface) would the strength of earth's gravity determine the maximum velocity I could achieve?

2. Dec 11, 2011

### Staff: Mentor

Not exactly sure what you mean. If you mean: Imagine the earth with no atmosphere and you dropped an object from infinity (ignoring other masses, of course)? Then the mass and radius of the earth would determine the speed with which the object hits the surface.

3. Dec 11, 2011

### tkav1980

Imagine being infinitely far away form the earth yet still able to experience its gravity with the same force as it is felt on earth. You are also in a vacuum falling towards earth. Since you are infinitely far away you will never reach it. Is there a point where the strength of earths gravity can no longer increase your velocity? Is there an upper speed limit relative to the strength of the gravitational pull from a given body?

4. Dec 11, 2011

### Staff: Mentor

Yes. Your speed with respect to the earth will never exceed the speed of light.

5. Dec 11, 2011

### tkav1980

Thank you, that was my first intuition, but that leads me to the source of my question. If an objects mass increases relative to its velocity, where aproaching c that mass approaches infinity, the energy required for more acceleration also approaches infinity. What I am not quite understanding is if gravity is a curvature of space what is the source of energy for acceleration due to gravity? I, and this is oversimplification on a grand scale I know, picture gravity like the old ball on a rubber sheet. Where the ball is simply rolling down a hill. So what is the source of the energy needed for acceleration and why is this limited to below c?

6. Dec 11, 2011

### Staff: Mentor

Let's leave general relativity aside. You've created an artificial situation, a constant gravitational field that extends to infinity. (An infinitely high hill.) So that gravitational potential energy is the source of the energy.

From special relativity, we know that as the the speed of an object approaches the speed of light, it takes more and more energy to attain an increase in speed. It would require 'infinite' energy to reach the speed of light itself.

7. Dec 11, 2011

### tkav1980

Ahh, I see your point. Thank you for taking the time to answer my questions.

8. Dec 11, 2011

### dtyarbrough

Where is it written that gravity, the force that accellerates all matter equally, regardless of mass, is in any way dependant on the speed and/or increased mass of the object. It should take approximately 9360 hours to reach the speed of light at a rate of 9m/sec/sec.

Last edited: Dec 11, 2011
9. Dec 11, 2011

### Staff: Mentor

It's not that gravity (or the resulting proper acceleration) depends on the speed, but the effect of that acceleration does.
Only if you ignore the lessons of special relativity. Speeds don't add like they do in Newtonian physics. Even though the proper acceleration remains 9.8 m/s2 (say), with each succeeding second, the speed increase with respect to an outside frame (the earth) is less. It never reaches the speed of light.

10. Dec 12, 2011

### Lsos

As was mentioned, this scenario is a VERY artificial scenario, as even Newton knew that the force of graviy falls off exponentially as you go further away from a planet. So even if you're on the edge of the universe, earth's gravity will still attract you, although by an infinitesmally small amount.

Anyway, what this all means is that indeed there is a limit to how fast earth's gravity will accelerate you. If you started out very far away at rest, earth's gravity could only get you going at ~11 km/s. This is known as escape velocity. Each body has one. It's also how fast you must go to escape earth's gravitational field. The moon missions and every space mission far away from earth had to achieve at least this speed. It's also the minimum speed at which an asteroid will hit earth's atmosphere.

Earth's gravity will ALWAYS keep slowing you down, but as you fly further away it slows you down less and less. If you're at escape velocity then you will always essentially be "outrunning" earth's gravity, so that it always slows you down but can never slow you down completely.

The escape velocity at a black hole's event horizon is the speed of light.

Last edited: Dec 12, 2011
11. Dec 12, 2011

### Elroch

It's worth mentioning that the origin of terminal velocity is an essentially constant force in one direction (gravity) opposed by a force in the opposite direction which increases with speed (air resistance). The two balance at exactly one speed. That speed is the "terminal velocity".

In empty space there is no resistance opposing gravity. Hence no terminal velocity.

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