Position Derivative of Acceleration Due to Gravity

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In summary, the conversation discusses whether it is meaningful to take the position derivative of acceleration due to gravity and what the resulting effects would be. It is determined that this is possible and results in the tidal force, which can affect objects such as water and satellites.
  • #1
Sagekilla
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I had a thought before and I'm not sure if this is meaningful to ask or even possible to ask but I'd figure it's worth a shot.

Is it meaningful to take the position derivative of acceleration due to gravity? I'd imagine, at least intuitively, this sounds like it's possible. As you move along space, the acceleration you'd experience would be greater as you approach the mass which is creating the gravitational field.

Or is that just nothing more than taking the gradient of the gravitational field?
 
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  • #2
Hi Sagekilla! :smile:
Sagekilla said:
Is it meaningful to take the position derivative of acceleration due to gravity?

Yes, and that's the tidal force, that pulls water away from the Earth, or that stretches satellites.
 
  • #3
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1. What is the position derivative of acceleration due to gravity?

The position derivative of acceleration due to gravity is the rate of change of the acceleration due to gravity with respect to the position of an object. This can be expressed mathematically as the second derivative of the position function in terms of time.

2. How is the position derivative of acceleration due to gravity calculated?

The position derivative of acceleration due to gravity can be calculated by taking the second derivative of the position function in terms of time. This involves finding the rate of change of the acceleration due to gravity as the position of an object changes over time.

3. What is the significance of the position derivative of acceleration due to gravity?

The position derivative of acceleration due to gravity is important in understanding the motion of objects under the influence of gravity. It helps us to determine the rate at which an object's acceleration is changing as it moves through space, which can provide valuable information about its trajectory and velocity.

4. How does the position derivative of acceleration due to gravity affect free-falling objects?

The position derivative of acceleration due to gravity plays a crucial role in determining the motion of free-falling objects. It helps us to understand how the acceleration due to gravity changes as an object falls, and how this affects its velocity and position over time.

5. Can the position derivative of acceleration due to gravity be negative?

Yes, the position derivative of acceleration due to gravity can be negative. This would indicate that the acceleration due to gravity is decreasing as an object moves through space, which could happen if the object is experiencing resistance or moving away from a massive body such as the Earth.

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