Asteroid in a circular orbit about the Sun

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Homework Help Overview

The discussion revolves around calculating the orbital period of an asteroid in a circular orbit around the Sun, specifically with a radius of 3.04 astronomical units (AU). The context includes references to the Earth's orbital characteristics as a basis for comparison.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need for relevant equations, including Newton's law of gravitation and Kepler's laws, to determine the period of the asteroid. There is uncertainty about how to apply these equations effectively.

Discussion Status

Participants are actively exploring the necessary equations and concepts related to orbital mechanics. Some have suggested deriving Kepler's equation by equating centripetal and gravitational forces, indicating a productive direction in the discussion.

Contextual Notes

There is a request for step-by-step guidance to enhance understanding, and participants are considering the implications of using different equations related to orbital dynamics.

sstoning
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If the Earth's period is 365.25 days and its distance to the (center of the) Sun is one astronomical unit (AU), what is the period, to the nearest day, of an asteroid in a circular orbit about the Sun with a radius of 3.04 AU?

please show steps so that I can learn.

thanks a lot.
 
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What are the relevant equations that you think are needed here?
Newton's law of gravitation maybe?
 
I think the equation for the period of a planet is needed; but I'm not sure how to use it.
 
Kepler's equation relating period to radius.
If this isn't given, it can be derived by equating the equation for centripetal force to the equation for universal gravitational force.
 

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