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- https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/Book%3A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/13%3A_Gravitation/13.04%3A_Gravitational_Potential_Energy_and_Total_EnergyThe acceleration due to gravity changes as we move away from Earth, and the expression for gravitational potential energy must reflect this change. The total energy of a system is the sum of kinetic a...The acceleration due to gravity changes as we move away from Earth, and the expression for gravitational potential energy must reflect this change. The total energy of a system is the sum of kinetic and gravitational potential energy, and this total energy is conserved in orbital motion. Objects with total energy less than zero are bound; those with zero or greater are unbounded.
- https://phys.libretexts.org/Courses/Prince_Georges_Community_College/General_Physics_I%3A_Classical_Mechanics/54%3A_Gravity/54.06%3A_Escape_VelocityIf a particle leaves the surface of a planet with an initial velocity equal to the escape velocity, then the body will move more and more slowly as the particle moves farther from the planet, finally ...If a particle leaves the surface of a planet with an initial velocity equal to the escape velocity, then the body will move more and more slowly as the particle moves farther from the planet, finally reaching a velocity of zero at r=∞. (We assume only the particle and the planet are present, and ignore all other bodies.)
- https://phys.libretexts.org/Workbench/PH_245_Textbook_V2/05%3A_Module_4_-_Special_Applications_of_Classical_Mechanics/5.01%3A_Objective_4.a./5.1.03%3A_Gravitational_Potential_Energy_and_Total_EnergyThe acceleration due to gravity changes as we move away from Earth, and the expression for gravitational potential energy must reflect this change. The total energy of a system is the sum of kinetic a...The acceleration due to gravity changes as we move away from Earth, and the expression for gravitational potential energy must reflect this change. The total energy of a system is the sum of kinetic and gravitational potential energy, and this total energy is conserved in orbital motion. Objects with total energy less than zero are bound; those with zero or greater are unbounded.
- https://phys.libretexts.org/Bookshelves/College_Physics/College_Physics_1e_(OpenStax)/34%3A_Frontiers_of_Physics/34.02%3A_General_Relativity_and_Quantum_GravityWe know from "Special Relativity" that relativity is the study of how different observers measure the same event, particularly if they move relative to one another. Einstein’s theory of general relati...We know from "Special Relativity" that relativity is the study of how different observers measure the same event, particularly if they move relative to one another. Einstein’s theory of general relativity describes all types of relative motion including accelerated motion and the effects of gravity. General relativity encompasses special relativity and classical relativity in situations where acceleration is zero and relative velocity is small compared with the speed of light.
- https://phys.libretexts.org/Bookshelves/University_Physics/Physics_(Boundless)/5%3A_Uniform_Circular_Motion_and_Gravitation/5.8%3A_Energy_ConservationAn object reaches escape speed when the sum of its kinetic energy and its gravitational potential energy is equal to zero.
- https://phys.libretexts.org/Courses/Muhlenberg_College/MC%3A_Physics_121_-_General_Physics_I/13%3A_Gravitation/13.04%3A_Gravitational_Potential_Energy_and_Total_EnergyThe acceleration due to gravity changes as we move away from Earth, and the expression for gravitational potential energy must reflect this change. The total energy of a system is the sum of kinetic a...The acceleration due to gravity changes as we move away from Earth, and the expression for gravitational potential energy must reflect this change. The total energy of a system is the sum of kinetic and gravitational potential energy, and this total energy is conserved in orbital motion. Objects with total energy less than zero are bound; those with zero or greater are unbounded.
- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/09%3A_Work_Power_and_Energy/9.11%3A_Gravitational_Potential_Energy_and_Total_EnergyBut the total energy at the surface is simply the potential energy, since it starts from rest. [Note that we do not use Equation ??? at the surface, since we are not in orbit at the surface.] T...But the total energy at the surface is simply the potential energy, since it starts from rest. [Note that we do not use Equation ??? at the surface, since we are not in orbit at the surface.] The kinetic energy can then be found from the difference in the total energy change and the change in potential energy found in Example 13.4.1.
- https://phys.libretexts.org/Bookshelves/University_Physics/Radically_Modern_Introductory_Physics_Text_II_(Raymond)/13%3A_Newtons_Law_of_Gravitation/13.07%3A_Use_of_Conservation_Lawswhere m is the mass of the bullet, M is the mass of the moon, R is the radius of the moon, and v initial is the minimum initial velocity required for the bullet to escape. At apheli...where m is the mass of the bullet, M is the mass of the moon, R is the radius of the moon, and v initial is the minimum initial velocity required for the bullet to escape. At aphelion and perihelion, the radial part of the velocity of the asteroid is zero and the speed equals the tangential component of the velocity, v = v t . Thus, at aphelion and perihelion we can eliminate v in favor of the angular momentum:
