Welcome! Today we'll explore the concept of escape velocity. To break free from Earth's gravitational pull, a rocket must reach a minimum speed of approximately 11.2 kilometers per second. This is the speed needed to overcome Earth's gravity and enter interplanetary space.
The escape velocity is calculated using a specific formula. It equals the square root of two times the gravitational constant G, times the mass of Earth M, divided by Earth's radius r. This formula shows that escape velocity depends on the planet's mass and size. The larger and more massive the planet, the higher the escape velocity needed.
Now let's calculate the actual escape velocity for Earth. We use Earth's gravitational constant of 6.67 times 10 to the minus 11, Earth's mass of 5.97 times 10 to the 24 kilograms, and Earth's radius of 6.37 times 10 to the 6 meters. Substituting these values into our formula gives us 11,200 meters per second, which equals 11.2 kilometers per second.
Let's simulate a rocket launch. As the rocket accelerates from zero, its speed gradually increases. We can see the rocket moving away from Earth as it gains velocity. The yellow arrow shows the current speed, and when the rocket reaches 11.2 kilometers per second, it will have enough energy to escape Earth's gravitational pull completely.
To conclude, let's compare escape velocities across different celestial bodies. Earth requires 11.2 kilometers per second. The Moon, being smaller and less massive, only needs 2.4 kilometers per second. Mars requires 5.0, while the massive Jupiter needs 59.5 kilometers per second. The Sun, with its enormous mass, requires an incredible 617.5 kilometers per second to escape its gravitational pull.