If a rock fell 20,000 meters to Earth Question

  • Context: Undergrad 
  • Thread starter Thread starter Jack981
  • Start date Start date
  • Tags Tags
    Earth Rock
Click For Summary

Discussion Overview

The discussion revolves around the question of how long it would take for a rock to fall 20,000 meters to Earth, assuming no air resistance and only Earth's gravitational influence. Participants explore the implications of changing gravitational acceleration as the rock approaches Earth, considering the need for integration in their calculations.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant suggests that the problem involves integration due to the changing acceleration as the rock falls, referencing the gravitational equation g=m1(m2)G/r^2.
  • Another participant questions the necessity of using an elliptic integral, proposing a simpler approach using a free body diagram and Newton's law of gravity.
  • Some participants discuss the significance of the change in gravitational acceleration over a 20 km fall, with one noting that the time difference between calculations using constant surface gravity and variable gravity is minimal (only 0.17 seconds).
  • A participant expresses difficulty in incorporating time into the equations, indicating a need for clarification on how to express the relationship between time and radius.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of complex mathematical approaches versus simpler methods. There is no consensus on the best way to approach the problem, and the discussion remains unresolved regarding the optimal method for calculating the fall time.

Contextual Notes

Some assumptions about the problem, such as the effects of air resistance and the simplifications made in the gravitational model, are not fully explored. The discussion also highlights the dependence on definitions of gravitational acceleration at varying distances from Earth.

Jack981
Messages
2
Reaction score
0
I was thinking about this question:

So if a rock fell 20,000 meters to Earth assuming no air resistance and no other gravitational forces from anything but Earth, how long would it take the rock to hit Earth? Keep in mind acceleration is changing through the gravity equation as the rock gets closer and closer to Earth -> g=m1(m2)G/r^2.

(I'm not sure if its necessary but if it is, say the rock is 5 kg).

I put undergrad because this was not a question that came up in class and I think it involves integration.

This is not a hw/cw question it is a question I came up with on my own.
 
Physics news on Phys.org
Welcome to PF, Jack. Do you have any specific questions about the question you were thinking about?
 
Hello, I wanted to know if anyone had a possible solution to the question which is how much time it would take to hit Earth. I've been trying to figure it out but can't figure out how to fit time into the overall equation because I always just get the equations in terms of radius.
 
If you search PF, sometimes you can find similar inquiries. @HallsofIvy did a good development on this topic in this PF thread. I must admit I stall out on the subject of the elliptic integral. Maybe you can take it further.
 
Am I missing something here? Why do you need an elliptic integral? Set up a free body diagram where the force found from Newton's law of gravity is equal to the mass of the ball times its acceleration. The equation is separable and so is fairly easily integrated (twice) to get the separation between the two bodies as a function of time. Maybe I am missing something here?
 
  • Like
Likes   Reactions: PeroK and russ_watters
Jack981 said:
So if a rock fell 20,000 meters to Earth assuming no air resistance and no other gravitational forces from anything but Earth, how long would it take the rock to hit Earth? Keep in mind acceleration is changing through the gravity equation as the rock gets closer and closer to Earth -> g=m1(m2)G/r^2.
20 km? How much does g really change? Do you really need to bother with that? If you decide no, do you know how to do the problem then?
 
russ_watters said:
20 km? How much does g really change? Do you really need to bother with that? If you decide no, do you know how to do the problem then?

The time difference between calculations using constant surface and variable gravity for ##20km## is only ##0.17s##, I believe.
 
Jack981 said:
I was thinking about this question:

So if a rock fell 20,000 meters to Earth assuming no air resistance and no other gravitational forces from anything but Earth, how long would it take the rock to hit Earth? Keep in mind acceleration is changing through the gravity equation as the rock gets closer and closer to Earth -> g=m1(m2)G/r^2.

(I'm not sure if its necessary but if it is, say the rock is 5 kg).

I put undergrad because this was not a question that came up in class and I think it involves integration.

This is not a hw/cw question it is a question I came up with on my own.

https://www.physicsforums.com/threa...ith-varying-acceleration.866218/#post-5437928
 

Similar threads

Undergrad Relativistic Space Travel: Optimizing Proper Time [Project Hail Mary]
  • · Replies 36 ·
2
Replies
36
Views
5K
Undergrad Does Special and General Relativity Affect Aging of Apollo Astronauts?
  • · Replies 10 ·
Replies
10
Views
4K
Undergrad Do We Need ESC in Earth's Atmosphere?
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad General relativistic comparison to Newtonian physics
  • · Replies 21 ·
Replies
21
Views
2K
Undergrad Mysterious Agent Blows Up Moon: Can Earth Survive?
  • · Replies 9 ·
Replies
9
Views
4K
Graduate Measuring Relativistic Velocities on Earth: A Question
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Gravity transition directly at the underside of a "shell planet"
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Question on the particles that formed the Earth.
  • · Replies 16 ·
Replies
16
Views
2K
Calculate the speed of the rock as it enters Earth's atmosphere
  • · Replies 8 ·
Replies
8
Views
4K
Two rocks launched up/collison (Kinematics)
  • · Replies 10 ·
Replies
10
Views
2K