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

[Oydpuuodouflj6r9]

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?

 

[berkeman]

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?

 

[PeroK]

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?

 

[PeroK]

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.