Explanation The universal gravitational constant is 6.67 × 10 − 11 N ⋅ m 2 / kg 2 , mass of the earth is 5.97 × 10 24 kg , radius of earth is 6.37 × 10 6 m . The formula for gravitational potential energy is, U = − G m M r Here, U is the gravitational potential energy m is mass of module M is mass of moon r is the distance between moon and the module G is the universal gravitational constant The formula for kinetic energy is, K = 1 2 m v 2 Here, K is the kinetic energy v is the velocity The formula for total energy is, E = U + K Here, E is the total energy of the system. Substitute 1 2 m v 2 for K and − G m M r for U in the above expression. E = − G m M r + 1 2 m v 2 For projectile at a height above surface of earth: Substitute E 1 for E , r 1 for r and v c for v in the above expression. E 1 = − G m M r 1 + 1 2 m v c 2 (1) Here, v c is the escape speed of the earth The expression for value of r 1 is, r 1 = r e + h Here, r e is the radius of earth h is the height of projectile from the surface of the earth The formula for escape speed is v c = 2 G M r e (2) Here, G is the universal gravitational constant M is the mass of earth r e is the radius of earth For projectile on surface of earth: Substitute E 2 for E , r e for r and v c 3 for v in the above expression

Physics, Books a la Carte Edition (5th Edition)

5th Edition

ISBN: 9780134020853

Author: James S. Walker

Publisher: PEARSON

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force betwe…

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Chapter 12, Problem 53PCE

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The height above the earth at which speed of the projectile is one-third of the escape speed of the earth,

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Chapter 12, Problem 52PCE

Chapter 12, Problem 54PCE

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Physics, Books a la Carte Edition (5th Edition)

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The height above the earth at which speed of the projectile is one-third of the escape speed of the earth,

Solution Summary: The author explains the universal gravitational constant, mass of the earth, distance between moon and module, and the formula for kinetic energy.

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The height above the earth at which speed of the projectile is one-third of the escape speed of the earth,

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