A meteoroid passes through a position in space where its speed is very small relative to Earth's and it is at a perpendicular di
stance of 19 Earth radii above Earth's surface. The meteoroid is moving in such a way that Earth captures it. What is the speed of the meteoroid when it is one Earth radius above the ground
If we call 1 the position in space where the meteoroid of mass m speed is very small relative to Earth's (whose mass is and radius is ) and it is at a perpendicular distance of above Earth's surface, and 2 the position when it is above the ground, then, since in this case mechanical energy is conserved, we can write:
which means:
where K is the kinetic energy and U the gravitational potential energy. Since we can write:
which means:
And since (the distance of an object to the center of the Earth is Earth's radius plus the height of the object), we have: