Escape Speed – Class 11 | Chapter – 8 | Physics Short Notes Series PDF for NEET & JEE
Escape Speed: Escape speed is the minimum speed an object needs to escape the gravitational pull of a celestial body, such as a planet or a star. It is the speed required for an object to achieve an infinite distance from the celestial body, assuming there is no other force acting on it.
The escape speed is independent of the mass of the object escaping, and depends only on the mass and radius of the celestial body. This means that the escape speed for a spacecraft leaving Earth is the same whether it is carrying a single astronaut or a full crew of astronauts and their equipment.
Formula of Escape Speed
The escape speed (v) of an object can be calculated using the following formula:
v = √(2GM/r)
Where,
- v is the escape speed
- G is the gravitational constant
- M is the mass of the celestial body
- r is the distance between the object and the center of the celestial body.
Unit of Escape Speed
Unit of escape speed or the escape velocity is metre per seconds (m.s-1) which is also the SI unit of escape speed.
Dimensional Formulas:
| Dimensional formula of universal gravitational constant = M-1L3T-2 |
| Dimensional formula of the mass of the earth = M1L0T0 |
| Dimensional formula of distance to the centre of the earth = M0L1T0 |
| Therefore, the dimensional formula of escape speed after substituting in the equation is = M0L1T-1 |
Importance of Escape Speed
Escape speed is an important concept in space exploration and astronomy. Here are some of the reasons why:
- Launching spacecraft: Escape speed determines the minimum speed at which a spacecraft must travel to escape the gravitational pull of a planet or other celestial body. This is important for launching spacecraft into space and for interplanetary travel.
- Planetary exploration: Understanding the escape speed of a planet or moon is important for planning space missions to explore and study these bodies. It can help determine the feasibility of landing on the planet or moon and returning to Earth.
- Understanding celestial bodies: The escape speed of a celestial body can provide valuable information about its mass and size. This information can help scientists better understand the body’s composition, formation, and evolution.
- Gravitational interactions: Escape speed is also important in understanding the gravitational interactions between celestial bodies. For example, it helps explain why moons and asteroids can remain in orbit around a planet or why comets can orbit the sun.
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