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Chapter 8: Problem 44

Define escape velocity.

Short Answer

Expert verified
Answer: The escape velocity of Earth is approximately 11.2 km/s or 40,320 km/h. It can be calculated using the formula: Escape velocity = sqrt((2 * G * M) / R), where G is the gravitational constant, M is the mass of Earth, and R is Earth's radius.

Step by step solution

01

Definition of Escape Velocity

Escape velocity is the minimum velocity an object must have to escape the gravitational pull of a celestial body, such as a planet or a moon, without any additional propulsion.
02

Gravitational Force

The gravitational force between two objects can be calculated using Newton's Law of Universal Gravitation: F = (G * m1 * m2) / r^2 where F is the gravitational force, G is the gravitational constant (approximately 6.674 * 10^(-11) N(m/kg)^2), m1 and m2 are the masses of the objects, and r is the distance between the centers of the objects.
03

Escape Velocity Formula

The escape velocity can be calculated using the following formula: Escape velocity = sqrt((2 * G * M) / R) where M is the mass of the celestial body (such as the mass of Earth), R is the radius of the celestial body (distance from the center to the surface), and G is the gravitational constant.
04

Example Calculation

To calculate the escape velocity for Earth, use the following values: - Earth's mass (M) = 5.972 * 10^24 kg - Earth's radius (R) = 6.371 * 10^6 m - Gravitational constant (G) = 6.674 * 10^(-11) N(m/kg)^2 Plug these values into the escape velocity formula: Escape velocity = sqrt((2 * 6.674 * 10^(-11) * 5.972 * 10^24) / (6.371 * 10^6)) Escape velocity ≈ 11.2 km/s or 40,320 km/h. So, an object would need a velocity of at least 11.2 km/s to escape Earth's gravitational pull without additional propulsion.

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