# The Naked Scientists Forum

### Author Topic: Would an accelerating object accelerate faster under gravity's influence?  (Read 679 times)

#### jeffreyH

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##### Would an accelerating object accelerate faster under gravity's influence?
« on: 14/11/2015 23:48:50 »
If the gradient of the gravitational field strength of an object at all radial points are known in advance can we learn something via the following. If we have calculated the acceleration due to gravity from a particular altitude down to the surface what would happen if we accelerated an object down to the surface at exactly this rate of increasing acceleration? Would this prevent any further increase in velocity due to gravity or would gravity still impart an increase in this acceleration?
« Last Edit: 15/11/2015 09:40:03 by chris »

#### evan_au

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##### Re: What would happen in this scenario?
« Reply #1 on: 15/11/2015 06:41:01 »
Please clarify the question. One way of doing this is to express the problem in mathematical notation.
Quote from: jeffreyH
we have calculated the acceleration due to gravity from a particular altitude down to the surface
If we assume an airless body (eg the Moon), and calculate the gravitational acceleration as a function of the radius from the center of the Moon:
Gravitational Acceleration = g(r).
g: gravitational acceleration
r: radius from center of the Moon

For "normal" velocities and "normal" masses, g(r) can be approximated by Newton's law of gravitation:
g(r) = GM/r2
Where:
G: Gravitational Constant
M: Mass of the Moon
r: radius from center of the Moon

Assuming that there is no tangential velocity (which could put it in an orbit that never hits the Moon's surface), you calculate the final impact velocity vf by integrating this acceleration g(r) from initial radius Ri to the Moon's radius Rm, and adding any initial radial velocity vi.

Quote
what would happen if we accelerated an object down to the surface at exactly this rate of increasing acceleration?
Here I am confused. If we let the object free-fall, it would experience acceleration g(r) without us having to do anything.

However, the active voice "we accelerated" implies that we do not let if free-fall, but do something to it. What is this "something"?
Is it to double the acceleration? So the object accelerates at 2g(r)?
Are there unstated assumptions different from what I have assumed above?
Something else?

#### alancalverd

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##### Re: What would happen in this scenario?
« Reply #2 on: 15/11/2015 09:14:41 »
If you double the force, you double the acceleration, regardless of the source of that force. Newton, I, "Principia", 1713 (Cambridge).

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##### Re: What would happen in this scenario?
« Reply #2 on: 15/11/2015 09:14:41 »