At what distance from Earth's center would a 1-kg mass experience a gravity force of 2.4 N?

To find the distance from Earth's center where a 1-kg mass experiences a gravitational force of 2.4 N, we can start with the formula for gravitational force, which is given by Newton's law of universal gravitation:

[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} ]

where ( F ) is the gravitational force, ( G ) is the gravitational constant, ( m_1 ) is the mass of the Earth, ( m_2 ) is the mass of the object (1 kg), and ( r ) is the distance from the center of the Earth.

At the surface of the Earth, the gravitational force on a 1-kg mass is approximately 9.8 N. As a mass moves away from the Earth, the gravitational force decreases according to this inverse square relationship. Therefore, we need to find the distance at which the gravitational force reduces to 2.4 N.

Setting up the equation with ( F = 2.4 , \text{N} ), we can analyze how far the mass must be positioned:

1. The formula at the surface can be established as ( F_{\text{