Escape Velocity & Satellites

Understanding Escape Velocity

Escape velocity is the minimum speed an object must have to break free from a planet's gravitational pull without any additional propulsion. For Earth, this velocity is approximately 11.2 km/s.

The formula for escape velocity is given by:

$$v_e = \sqrt{\frac{2GM}{R}}$$

• $v_e$ is the escape velocity
• $G$ is the gravitational constant $(6.674 \times 10^{-11} \text{Nm}^2/\text{kg}^2)$
• $M$ is the mass of the planet
• $R$ is the radius of the planet

Satellites and Their Motion

Satellites are objects that orbit planets. They can be natural, like moons, or artificial, like communication satellites.

Period of Revolution

The period of revolution is the time it takes for a satellite to complete one full orbit around a planet. It depends on the altitude of the satellite and the mass of the planet.

Orbital Speed

The speed at which a satellite travels in its orbit is called its orbital speed. It can be calculated using:

$$v = \sqrt{\frac{GM}{r}}$$

• $v$ is the orbital speed
• $r$ is the distance from the center of the planet to the satellite

Worked Example