Proportion of planetary-period to the distance-from-the-sun

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SUMMARY

Kepler's law of planetary motion establishes that the square of a planet's orbital period (T^2) is proportional to the cube of its distance from the Sun (r^3). In the case of Mars and Venus, Mars is approximately twice as far from the Sun as Venus. However, this does not imply that the orbital period of Mars is twice that of Venus. The correct relationship indicates that if Mars is at a distance of 2r, then T^2 for Mars is 8 times that of Venus, leading to a period for Mars that is 2 times longer than that of Venus.

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1. =Homework Statement
Kepler's law of planetary motion says that the square of the period of a planet (T^2) is proportional to the cube of the distance of the planet from the Sun (r^3). Mars is about twice as far from the Sun as Venus. How does the period of Mars compare with the period of Venus?


Homework Equations





The Attempt at a Solution


Does this mean that the period of Mars is about twice as long as Venus'?
T^2=Kr^3
2T^2=K2r^3
?
 
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glassy said:
1. =Homework Statement
Kepler's law of planetary motion says that the square of the period of a planet (T^2) is proportional to the cube of the distance of the planet from the Sun (r^3). Mars is about twice as far from the Sun as Venus. How does the period of Mars compare with the period of Venus?


Homework Equations





The Attempt at a Solution


Does this mean that the period of Mars is about twice as long as Venus'?
T^2=Kr^3
2T^2=K2r^3
?

Short answer , No.

When you write 2T^2 did you mean 2 * T^2 or did you mean (2T)^2

Similarly, your K2r^3 : K * 2 * r^3 or K * (2r)^3 or (K * 2 * r)^3
 

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