Earth's Accel.: Is 10^(-22)m/s^2 Correct?

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Homework Help Overview

The discussion revolves around calculating the acceleration of the Earth due to the gravitational interaction with a free-falling 60-kg person, given the mass of the Earth as 6 x 10^24 kg. The original poster questions the validity of the resulting acceleration value of 10^(-22) m/s^2, expressing that it seems unusual.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of Newton's second law and question the appropriateness of the equations used for the scenario. Some participants inquire about the gravitational attraction equation and whether the assumption of constant gravitational acceleration (g) is valid for the given situation.

Discussion Status

The discussion is active, with participants exploring different equations and interpretations of the problem. There is a suggestion to consider an alternative equation for gravitational attraction, indicating a productive direction in the conversation.

Contextual Notes

Participants note the potential relevance of the distance from the Earth's surface in determining the validity of the calculations, as well as the implications of assuming g is constant.

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Homework Statement
A 60-kg person is free-falling from the sky to Earth. What is the acceleration of the Earth of the mass of the Earth is 6*10^24 kg?
Relevant Equations
F=ma
let a be the acceleration of Earth, m=60kg, M=6*10^24 kg, g=10 m/s^2
Ma=F=mg
=> 6*10^24*a=60*10
=> a=10^(-22) m/s^2
is this correct because the answer is a bit strange?
 
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Oydpuuodouflj6r9 said:
Homework Statement:: A 60-kg person is free-falling from the sky to Earth. What is the acceleration of the Earth of the mass of the Earth is 6*10^24 kg?
Relevant Equations:: F=ma

let a be the acceleration of Earth, m=60kg, M=6*10^24 kg, g=10 m/s^2
Ma=F=mg
=> 6*10^24*a=60*10
=> a=10^(-22) m/s^2
is this correct because the answer is a bit strange?
Welcome to PF. There is another equation that may be more appropriate for this question. Do you know of an equation that gives the gravitational attraction between two masses separated by a distance r (to their centers of mass)?

EDIT -- Although as @PeroK is pointing out below, if the person is falling close to the surface of the Earth, the equation that you used may be valid. Does it say anything about how far away from the surface the person is?
 
Oydpuuodouflj6r9 said:
Homework Statement:: A 60-kg person is free-falling from the sky to Earth. What is the acceleration of the Earth of the mass of the Earth is 6*10^24 kg?
Relevant Equations:: F=ma

let a be the acceleration of Earth, m=60kg, M=6*10^24 kg, g=10 m/s^2
Ma=F=mg
=> 6*10^24*a=60*10
=> a=10^(-22) m/s^2
is this correct because the answer is a bit strange?
What is strange about that?
 
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berkeman said:
Welcome to PF. There is another equation that may be more appropriate for this question. Do you know of an equation that gives the gravitational attraction between two masses separated by a distance r (to their centers of mass)?
I would assume that we can take ##g## to be approximately constant for this problem.
 

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