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

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Using Newton's version of Kepler's third law, the orbital period of a planet can be determined by the formula T^2 = (4π^2/GM) * r^3, where T is the orbital period, G is the gravitational constant, M is the mass of the star, and r is the distance from the star. In this scenario, with a planet twice the mass of Earth orbiting at 1 AU from a star of the same mass as the Sun, the mass of the planet does not affect the orbital period. The orbital period remains the same as Earth's, which is one year. Participants are encouraged to share their calculations or any difficulties they encounter for further assistance. Understanding these principles is essential for exploring celestial mechanics.
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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.

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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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