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grantP
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Homework Statement
to find KE of an orbiting body, do I use 1/2mv^2 or 1/2Gm1m2/r??
Conceptual problem: Finding gravitational KE
- Thread starter grantP
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- Conceptual Gravitational
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SUMMARY
To find the kinetic energy (KE) of an orbiting body, one can use either the formula 1/2mv² or 1/2Gm₁m₂/r, depending on the context of the problem. In a circular orbit, the gravitational force acts as the centripetal force, leading to the relationship mv²/r = GMm/r². Consequently, the kinetic energy can be expressed as KE = 0.5GMm/r, which is derived from the gravitational potential energy (GPE) equation. The total energy of an orbiting body is represented as KE + GPE = -0.5GMm/r.
PREREQUISITES- Understanding of Newton's laws of motion
- Familiarity with gravitational force and potential energy
- Knowledge of circular motion dynamics
- Basic algebra and manipulation of equations
- Study the derivation of gravitational potential energy in orbital mechanics
- Learn about the conservation of mechanical energy in orbital systems
- Explore the differences between kinetic energy and gravitational potential energy
- Investigate the implications of varying orbital radii on kinetic energy
Students studying physics, particularly those focusing on mechanics and gravitational systems, as well as educators seeking to clarify concepts related to orbital motion and energy conservation.
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