What is the speed of an asteroid when it collides with Earth, given its initial speed of 15 km/s at a distance of 8 Earth radii?

To determine the speed of an asteroid upon colliding with Earth, we can consider the principles of gravitational potential energy and kinetic energy. Initially, the asteroid has a kinetic energy due to its speed and gravitational potential energy due to its distance from the Earth.

When the asteroid is at a distance of 8 Earth radii from the center of the Earth, it has an initial speed of 15 km/s. As it falls toward the Earth, the gravitational pull increases, resulting in an increase in its kinetic energy and speed as it gets closer.

The gravitational potential energy decreases as the asteroid approaches Earth, converting into kinetic energy, hence increasing the asteroid's speed. The closer the asteroid gets to the Earth, the stronger the gravitational force acting on it, which accelerates it.

Using the conservation of mechanical energy is crucial to understanding how its speed changes. The initial mechanical energy (the sum of potential and kinetic energy) at a distance of 8 Earth radii will equal the mechanical energy just before impact, where the potential energy will be at a minimum and kinetic energy at a maximum.

Calculations can provide the exact speed at the moment of impact, but based on typical gravitational attraction calculations and assuming negligible air resistance for simplicity, the asteroid's speed would be