If the earth exerts a 500 N gravitational force on an object in near space, how much force does this object exert on the earth, and by what law can this be asserted?
According to Newton's third law of motion, every action has an equal and opposite reaction. So, if the Earth exerts a gravitational force of 500 N on an object in near space, then the object exerts an equal and opposite force of 500 N on the Earth.
To understand how this works, we need to know Newton's law of universal gravitation. The equation for this law is:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force between two objects,
G is the gravitational constant (approximately equal to 6.674 × 10^-11 N(m/kg)^2),
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.
In this case, the object in near space is exerting a force of 500 N on the Earth. Since the mass of the Earth is much larger than the mass of the object, we can assume that the mass of the Earth remains constant while calculating the force exerted by the object on Earth.
Let's rearrange the equation to solve for the mass of the object (m2):
m2 = (F * r^2) / (G * m1)
Given that the gravitational force (F) is 500 N and let's assume the distance (r) between the Earth and the object is constant, we can find the mass of the object.
However, without knowing the mass of the Earth (m1) or the distance (r), it's not possible to determine the exact force that the object exerts on the Earth. But we can conclude that the object exerts an equal and opposite force (500 N) on the Earth based on Newton's third law of motion.