# What is the terminal velocity of mass falling toward earth?

Assume no atmosphere; no friction; no extraneous factors.

What is the terminal velocity of a mass that falls from the edge of earth's gravity well to earth's surface?

Thank you in advance for your answer.

Peace
rwj

## Answers and Replies

Hootenanny
Staff Emeritus
Science Advisor
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Assume no atmosphere; no friction; no extraneous factors.

What is the terminal velocity of a mass that falls from the edge of earth's gravity well to earth's surface?

Thank you in advance for your answer.

Peace
rwj
Terminal velocity by definition requires that there be a drag force. Therefore, no drag force - no terminal velocity.

arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
Assume no atmosphere; no friction; no extraneous factors.

What is the terminal velocity of a mass that falls from the edge of earth's gravity well to earth's surface?

Thank you in advance for your answer.

Peace
rwj
What do you mean by "the edge of earth's gravity"??

As modelled by classical Newtonian mechanics, the "edge" where there is zero influence from Earth's gravity must be placed infinitely far away from the Earth.

If we imagine a a particle starting at rest at infinity, and then is solely influenced by earth's gravity, then it will hit Earth with the velocity known as "escape velocity".

Perhaps you might call this a "terminal velocity", but that would be an abuse of terms, as Hootenanny has told you already.

Is the maximum velocity of a falling mass 40,200 km/h @ earth's surface?

What do you mean by "the edge of earth's gravity"??
If we imagine a a particle starting at rest at infinity, and then is solely influenced by earth's gravity, then it will hit Earth with the velocity known as "escape velocity".
Perhaps you might call this a "terminal velocity", but that would be an abuse of terms, as Hootenanny has told you already.

A plot of gravitational potential of the earth generates a hyperbolic cross section. The sudden dip in the center is the origin of the name 'gravity well'. The 'edge' of that well occurs where minimal perpendicular velocity counters the force of gravity. I agree that the 'edge' of that well is as arbitrary as 'minimal perpendicular velocity'.

I commend you on your insight.
I will predict that a free-falling mass will reach maximum velocity of 40,200 km/h as it hits the surface of the earth.

Thanks
rwj

Hootenanny
Staff Emeritus
Science Advisor
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I will predict that a free-falling mass will reach maximum velocity of 40,200 km/h as it hits the surface of the earth.

Thanks
rwj
I'd have to disagree with you there. Your calculations are incorrect.

I'd have to disagree with you there. Your calculations are incorrect.

What, may I ask, are your better reasons and and calculations that I should doubt equal to escape velocity?

Peace
rwj

Hootenanny
Staff Emeritus
Science Advisor
Gold Member

What, may I ask, are your better reasons and and calculations that I should doubt equal to escape velocity?

Peace
rwj
Whoops! I beg your pardon, I thought you had 40 000 km/s.

You are indeed correct, the escape velocity from earth is indeed approximately 40 000 km/h.

Apologies for the mix-up!

Assume no atmosphere; no friction; no extraneous factors.

What is the terminal velocity of a mass that falls from the edge of earth's gravity well to earth's surface?

Thank you in advance for your answer.

Peace
rwj

It would probably be best that you specified either an object's starting distance from the Earth's surface or a point beginning at a given rate of acceleration m/s^2, as in theory, the further an object is placed from the Earth (and still capable of accelerating towards it), the more time it is given to accelerate and gain a higher end velocity especially considering your "no atmosphere", "no friction", "no extraneous factors" clause. 