What is the Difference Between Escape Velocity and Orbital Velocity?
🆚 Go to Comparative Table 🆚Escape velocity and orbital velocity are two distinct concepts related to the motion of objects in space. Here are the main differences between them:
- Definition: Escape velocity is the minimum velocity required for an object to overcome the gravitational potential of a massive body and escape to infinity. Orbital velocity, on the other hand, is the velocity with which an object revolves around a massive body.
- Formula: The formula for escape velocity is $$Ve = \sqrt{2gR})$$, where g is the acceleration due to gravity and R is the radius of the planet. The formula for orbital velocity is $$Vo = \sqrt{gR}$$.
- Relation: Escape velocity and orbital velocity are proportional, with escape velocity being equal to the square root of 2 times the orbital velocity, i.e., $$Ve = \sqrt{2}Vo$$.
- Purpose: Escape velocity is required for an object to break free from the gravitational pull of a massive body, such as a planet or star. Orbital velocity is the speed at which an object orbits another body, and it is fast enough to counteract the force of gravity that pulls the orbiting object down.
In summary, escape velocity is the minimum speed required for an object to escape the gravitational pull of a massive body, while orbital velocity is the speed at which an object orbits around a massive body. These two velocities are related through the square root of 2.
Comparative Table: Escape Velocity vs Orbital Velocity
The difference between escape velocity and orbital velocity lies in their purpose and the speed required for each. Here is a table summarizing the key differences:
| Escape Velocity | Orbital Velocity |
|---|---|
| Refers to the minimum amount of velocity required for an object to break free from the gravitational influence of a celestial body (e.g., Earth) | Refers to the minimum amount of velocity required for an object to orbit around another object (e.g., a satellite orbiting Earth) |
| The escape velocity of a satellite near Earth is given by the formula: $$v_e = \sqrt{\frac{2GM}{R}}$$, where $$M$$ is the mass of Earth, $$R$$ is the radius of Earth, and $$G$$ is the gravitational constant | The orbital velocity of a satellite at a certain height, $$h$$, is given by the formula: $$v_o = \sqrt{\frac{GM}{R + h}}$$, where $$M$$ is the mass of Earth |
| Escape velocity is denoted by $$v_e$$ | Orbital velocity is denoted by $$v_o$$ |
| Escape velocity can be represented as $$\sqrt{2gR}$$ | When a satellite is moving in its orbit near Earth, the orbital velocity, $$vo$$, can be represented as $$\frac{vo}{\sqrt{2}}$$ |
| Escape velocity is √2 times greater than orbital velocity |
The relationship between escape velocity and orbital velocity can be expressed mathematically by dividing the escape velocity equation and the orbital velocity equation.
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