We need to consider the energy to make a concise mathematical definition of escape velocity.
Let the total mechanical energy to be Etotal.
To introduce you to the concept of escape velocity for a rocket. The escape velocity is defined to be the minimum speed with which an object of mass must move to escape from the gravitational attraction of a much larger body, such as a planet of total mass . The escape velocity is a function of the distance of the object from the center of the planet , but unless otherwise specified this distance is taken to be the radius of the planet because it addresses the question "How fast does my rocket have to go to escape from the surface of the planet?" The key to making a concise mathematical definition of escape velocity is to consider the energy.
A. If an object is launched at its escape velocity, what is the total mechanical energy of the object at a very large (i.e., infinite) distance from the planet? Follow the usual convention and take the gravitational potential energy to be zero at very large distances.
B. Consider the motion of an object between a point close to the planet and a point very very far from the planet. Indicate whether the following statements are true or false.
1. Angular momentum about the center of the planet is conserved- True or false
2. Total mechanical energy is conserved. True or false
3. Kinetic energy is conserved. True or false
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