The mass of the Earth to be 5.98 X 10^24 kg. If the Earth's gravitational force causes a falling 38 kg student to accelerate downward at 9.8 m/s^2, determine the upward acceleration of the Earth during the student's fall.
According to Newton's third law action is equal to reaction. The force with which the student pulls the Earth is equal to the force with which the student is pulled by the Earth.
The force of attraction between two objects of mass M1 and M2 is given by F = G*M1*M2/r^2
As the force acting between the student and the Earth results in an acceleration of the student by 9.8 m/s^2, this gives F = G*Ms*Me/r^2 = 38*9.8 = 372.4 N
A force of 372.4 N acts on the student; this is the same force that accelerates the Earth towards the student. The mass of the Earth is given as 5.98 X 10^24 kg.
If the Earth accelerates upwards at an acceleration equal to a, 372.4 = 5.98 X 10^24*a
=> a = 372.4/(5.98*10*24) m/s^2
=> 62.27*10^-24 m/s^2
The Earth accelerates upwards at an acceleration 62.27*10^-24 m/s^2