Orbital radius vs period question

In summary, the orbital radius and period of a planet are directly related, as stated in Kepler's third law of planetary motion. A larger orbital radius leads to a longer period, as the weaker gravitational pull from the planet's star causes the planet to take longer to complete one orbit. The formula for calculating orbital period is T = 2π√(a^3/GM), where T is the period, a is the orbital radius, G is the gravitational constant, and M is the mass of the central star. The orbital radius is not the same as the distance from the planet to its star, and the orbital period does not directly affect a planet's temperature, but the distance from the planet to its star, determined by the
  • #1
cheeselover87
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Homework Statement


a satellite has period T and orbital radius R. If you wish to increase the period to 8T what must the new orbital radius be? (answer is 4R, I just don't know how to get it)


Homework Equations





The Attempt at a Solution

 
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  • #2
First think of the relationship between orbital radius and the period.

(Centripetal force = gravitational force of attraction)
 

FAQ: Orbital radius vs period question

What is the relationship between orbital radius and period?

The orbital radius and period of a planet are directly related. This means that as the orbital radius increases, the period also increases. This relationship is known as Kepler's third law of planetary motion.

How does the orbital radius affect the time it takes for a planet to orbit its star?

The larger the orbital radius, the longer it takes for a planet to complete one orbit around its star. This is because the further a planet is from its star, the weaker the gravitational pull, and therefore, it takes longer for the planet to complete its orbit.

What is the formula for calculating orbital period?

The formula for calculating the orbital period of a planet is T = 2π√(a^3/GM), where T is the period, a is the orbital radius, G is the gravitational constant, and M is the mass of the central star.

Is the orbital radius the same as the distance from the planet to its star?

No, the orbital radius is the distance between the planet and the center of its star. The distance from the planet to its star may vary depending on the shape of the planet's orbit.

How does the orbital period of a planet affect its temperature?

The orbital period of a planet does not directly affect its temperature. However, the distance from the planet to its star, which is determined by the orbital radius and period, can impact the planet's temperature. A longer period and larger orbital radius may result in a colder planet, while a shorter period and smaller orbital radius may result in a warmer planet.

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