Doc Al said: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.
Yes. Your speed with respect to the Earth will never exceed the speed of light.tkav1980 said:Is there a point where the strength of Earth's 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?
Doc Al said:Yes. Your speed with respect to the Earth will never exceed the speed of light.
Doc Al said: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.
It's not that gravity (or the resulting proper acceleration) depends on the speed, but the effect of that acceleration does.dtyarbrough said: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.
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.It should take approximately 9360 hours to reach the speed of light at a rate of 9m/sec/sec.
tkav1980 said: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 Earth's 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?
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".tkav1980 said: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?
Terminal velocity in a vacuum is the maximum velocity that a falling object can reach when the only force acting upon it is gravity. In a vacuum, there is no air resistance to slow down the object, so it will continue to accelerate until it reaches its terminal velocity.
The formula for calculating terminal velocity in a vacuum is v = √(2mg/ρAC), where v is the terminal velocity, m is the mass of the object, g is the acceleration due to gravity, ρ is the density of the object, A is the cross-sectional area of the object, and C is the drag coefficient of the object.
Understanding terminal velocity in a vacuum is important in fields such as physics and engineering. It helps us predict how objects will behave when falling in a vacuum, and it is also used in designing spacecraft and other objects that will experience freefall in a vacuum.
The factors that affect terminal velocity in a vacuum include the mass and shape of the object, the acceleration due to gravity, and the density and drag coefficient of the object. Objects with a larger mass and a higher drag coefficient will have a higher terminal velocity, while objects with a lower density and a lower drag coefficient will have a lower terminal velocity.
No, terminal velocity in a vacuum will vary depending on the factors mentioned above. Objects with different masses, shapes, and drag coefficients will have different terminal velocities. However, in a perfect vacuum where there is no air resistance, all objects will eventually reach the same terminal velocity of 9.8 meters per second squared due to the acceleration of gravity.