The speed of an object falling toward Earth due to gravity depends on the distance from the Earth's center. According to Newton's law of universal gravitation, the force of gravity acting on an object is proportional to the mass of the object and inversely proportional to the square of the distance between the centers of the two objects. Mathematically, the equation is expressed as:
F=G⋅m1⋅m2r2F = frac{G cdot m_1 cdot m_2}{r^2}F=r2G⋅m1⋅m2
Where:
- F is the force of gravity
- G is the gravitational constant
- m₁ and m₂ are the masses of the two objects (in this case, the mass of the object falling and the mass of the Earth)
- r is the distance between the centers of the two objects (the distance from the object to the center of the Earth)
When an object falls towards the Earth, its distance from the Earth's center decreases, which means the value of 'r' decreases. As 'r' decreases, the force of gravity increases because it is inversely proportional to the square of the distance. This increased gravitational force causes the object to accelerate, resulting in an increase in speed as it falls.
In simpler terms, as an object falls closer to the Earth's center, it experiences a stronger gravitational pull, which accelerates it and increases its speed. Therefore, the speed of the falling object does depend on the distance from the Earth's center.