Answer: The force exerted by the object on Earth is 30.4 N, and the direction is towards the object.
Step-by-step explanation:
The gravitational force between two objects of mass M1 and M2, that are at a distance R between them is written as:
F = G*(M1*M2)/R^2
Where G is the gravitational constant, such that:
G = 6.674*1^(-11) m^3/(kg*s^2)
We know that M1, the mass of the object, is 50kg
R is the distance, in this case, is 25,600km
But this needs to be written in meters, remembering that:
1km = 1000m
Then:
25,600km = (25,600*1000)m = 25,600,000 m
And M2 is the mass of Earth, which is:
M2 = 5.972*10^(24) kg
Replacing all of those in the force equation we get
F = (6.674*1^(-11) m^3/(kg*s^2))*(50kg*5.972*10^(24) kg)/( 25,600,000 m)^2
F = 30.4 N
We know that the gravitational force is attractive, then the direction in which this force acts is towards the 50kg object.
Now, remember the second Newton's law is:
F = M*a
Then the acceleration that the object causes on Earth is:
30.4N = ( 5.972*10^(24) kg)*a
a = 30.4N/( ( 5.972*10^(24) kg)) = 5.09*10^(-24) m/s
This acceleration is almost despreciable.