Discover the Orbital Period of a Planet Using Newton's Law of Gravitation

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SUMMARY

The discussion focuses on calculating the orbital period of a planet using Newton's version of Kepler's third law. In a hypothetical solar system with a star of the same mass as the Sun, a planet with twice the mass of Earth orbits at a distance of 1 AU. The orbital period of this planet is determined to be 1 year, as the mass of the planet does not affect the orbital period when the mass of the star is constant. This conclusion is derived directly from the application of Kepler's third law, which states that the square of the orbital period is proportional to the cube of the semi-major axis of its orbit.

PREREQUISITES
  • Newton's Law of Gravitation
  • Kepler's Third Law of Planetary Motion
  • Understanding of astronomical units (AU)
  • Basic algebra for manipulating equations
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  • Study the derivation of Kepler's Third Law in detail
  • Explore the implications of mass on orbital mechanics
  • Learn about the gravitational constant and its role in celestial mechanics
  • Investigate other factors affecting orbital periods, such as eccentricity and mass ratios
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Question:

Use Newton's version of Kepler's third law to answer the following questions. (Hint: The calculations for this problem are so simple that you will not need a calculator.) Imagine another solar system, with a star of the same mass as the Sun. Suppose there is a planet in that solar system with a mass twice that of Earth orbiting at a distance of 1 AU from the star. What is the orbital period of this planet? Explain.

Any thoughts?
 
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lnl said:
Use Newton's version of Kepler's third law to answer the following questions. (Hint: The calculations for this problem are so simple that you will not need a calculator.) Imagine another solar system, with a star of the same mass as the Sun. Suppose there is a planet in that solar system with a mass twice that of Earth orbiting at a distance of 1 AU from the star. What is the orbital period of this planet? Explain.

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Show us what you've tried, and where you're stuck, and then we'll know how to help. :smile:
 

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