Simple harmonic motion of the earth

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SUMMARY

The discussion clarifies that the rotation of the Earth and its revolution around the Sun do not qualify as simple harmonic motion (SHM). While both movements are periodic, they are not linear and do not exhibit the characteristics of SHM, which requires a restoring force proportional to displacement from an equilibrium position. The Earth's orbit is elliptical, and thus, neither position nor velocity aligns with a sine wave. Although Uniform Circular Motion (UCM) shares some mathematical similarities with SHM, it fundamentally differs in its definition and characteristics.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM) principles
  • Knowledge of Uniform Circular Motion (UCM) concepts
  • Familiarity with periodic motion and its mathematical representations
  • Basic grasp of elliptical orbits in celestial mechanics
NEXT STEPS
  • Study the mathematical definitions and equations of simple harmonic motion
  • Explore the principles of Uniform Circular Motion and its applications
  • Investigate the characteristics of elliptical orbits in celestial mechanics
  • Learn about restoring forces and their role in SHM
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in the dynamics of planetary motion and oscillatory systems.

monty37
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is the rotation of the Earth and the revolution of it around sun simple harmonic in nature?
it is periodic but not linear.
 
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monty37 said:
is the rotation of the Earth and the revolution of it around sun simple harmonic in nature?
it is periodic but not linear.

The orbit is an ellipse, not a circle. So neither the position nor the velocity exactly describe a sine wave, so its not simple harmonic motion.
 
SHM is caused by a restoring force that is linearly proportional to the extension of an object from its equilibrium position. Like a spring, the force that it pushes back with is directly proportional to how much you squeeze it.

The result is periodic motion that is sinusoidal with time.

As a planet moves in orbit, even if it is a perfect circle, there is no movement from or to an equilibrium position. Uniform Circular motion is also periodic, and when you examine the component of motion in a single dimension, this too is sinusoidal. This conveniently allows many of the same formulas to be used when solving advanced problems of both SHM and UCM.

But at its fundamental definition, Uniform Circular Motion is not Simple Harmonic Motion.
 

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