Physics
Physics
Problem
Explain in not more than two sentences why the minimum speed required to leave Earth’s gravitational field is greater than the speed needed to stay in a close circular orbit by a factor of .Intuitive explanation
Escape velocity must overcome all gravitational potential energy to reach infinity, while orbital speed only needs enough kinetic energy to balance the gravitational force pulling inward—so escape velocity is times larger. The key insight is that escape requires converting kinetic energy into potential energy across an infinite distance, whereas an orbit trades off centripetal acceleration against gravity at a fixed radius.
Intuitive explanation
Escape velocity must overcome all gravitational potential energy to reach infinity, while orbital speed only needs enough kinetic energy to balance the gravitational force pulling inward—so escape velocity is times larger. The key insight is that escape requires converting kinetic energy into potential energy across an infinite distance, whereas an orbit trades off centripetal acceleration against gravity at a fixed radius.