Gavity Question

[PeterPesto]

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I know that 9.8 m/s^2 is an approximation for objects close to Earth.

So I was doing a Kaplan question, which says that two objects are dropped, with a difference in 1 meter in height. It says that the object dropped at the lower height will start to pull away in distance from the second object. The rationale is that the force of gravity gets stronger with shortened distances. So the rate at which the lower object's acceleration is greater than the higher dropped object. The force is increasing, therefore the acceleration must be increasing as well, hence the separation distance increases.

Do you agree with this?

 

[PiBond]

I know that 9.8 m/s^2 is an approximation for objects close to Earth.

So I was doing a Kaplan question, which says that two objects are dropped, with a difference in 1 meter in height. It says that the object dropped at the lower height will start to pull away in distance from the second object. The rationale is that the force of gravity gets stronger with shortened distances. So the rate at which the lower object's acceleration is greater than the higher dropped object. The force is increasing, therefore the acceleration must be increasing as well, hence the separation distance increases.

Do you agree with this?

Yes, but the difference is really friggin' small

 

[ilovemcat]

I know that 9.8 m/s^2 is an approximation for objects close to Earth.

So I was doing a Kaplan question, which says that two objects are dropped, with a difference in 1 meter in height. It says that the object dropped at the lower height will start to pull away in distance from the second object. The rationale is that the force of gravity gets stronger with shortened distances. So the rate at which the lower object's acceleration is greater than the higher dropped object. The force is increasing, therefore the acceleration must be increasing as well, hence the separation distance increases.

Do you agree with this?

Well if you glance at the formula for gravitational force between two masses, namely the earth (M) and some object (m), you get:

Fgrav = GMM/r^2

Based on the equation, if you decrease the radius, you increase the gravitational force (because they are inversely proportional).

But for those two objects you mentioned, the lower object would have a higher gravitational force but the difference would be soooooo small that for most cases it can be neglected since the earth's radius is so much larger.