Q. Defined escape velocity obtain an expression for the escape velocity of a body from the surface of the earth?
To understand the concept of escape velocity, let's start with a brief explanation. Escape velocity is the minimum velocity required for an object to escape from the gravitational pull of a massive body, such as the Earth, without any further propulsion.
The escape velocity of a body from the surface of the Earth can be obtained using the following expression:
Ve = sqrt((2 * G * Me) / Re),
where:
Ve is the escape velocity,
G is the gravitational constant (approximately 6.67430 × 10^(-11) m^3 kg^(-1) s^(-2)),
Me is the mass of the Earth (approximately 5.972 × 10^24 kg),
Re is the radius of the Earth (approximately 6,371 km or 6,371,000 m).
To calculate the escape velocity, follow these steps:
1. Plug in the values of G, Me, and Re into the expression.
Ve = sqrt((2 * 6.67430 × 10^(-11) m^3 kg^(-1) s^(-2) * 5.972 × 10^24 kg) / 6,371,000 m)
2. Simplify the expression inside the square root.
Ve = sqrt(1.34420 × 10^(-9) m^3 kg^(-1) s^(-2))
3. Evaluate the square root.
Ve ≈ 11,180 m/s
Therefore, according to the calculated expression, the escape velocity from the surface of the Earth is approximately 11,180 m/s.