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

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In summary, Kepler's law of planetary motion states that the square of a planet's period is proportional to the cube of its distance from the Sun. If Mars is twice as far from the Sun as Venus, then its period is not necessarily twice as long as Venus'. This is because the equation for Kepler's law can be interpreted in multiple ways, depending on the values of the variables.
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glassy
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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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  • #2
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
 

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

What is the "Proportion of planetary-period to the distance-from-the-sun"?

The proportion of planetary-period to the distance-from-the-sun is a measurement used to compare the time it takes for a planet to orbit around the sun to its distance from the sun. It is typically expressed as a ratio or percentage.

How is the "Proportion of planetary-period to the distance-from-the-sun" calculated?

The calculation of the proportion of planetary-period to the distance-from-the-sun involves dividing the orbital period of a planet (measured in Earth days) by its average distance from the sun (measured in astronomical units, or AU). The resulting number represents the proportion between these two factors.

What does the "Proportion of planetary-period to the distance-from-the-sun" tell us about a planet?

The proportion of planetary-period to the distance-from-the-sun can tell us about the relative speed of a planet's orbit and its distance from the sun. A higher proportion indicates a longer orbital period and/or a greater distance from the sun, while a lower proportion suggests a shorter orbital period and/or a closer distance to the sun.

Why is the "Proportion of planetary-period to the distance-from-the-sun" important in studying planetary motion?

Studying the proportion of planetary-period to the distance-from-the-sun can provide valuable insights into the dynamics of planetary motion, including the effects of gravity and the relationships between a planet's speed, distance, and orbital period. This information can help us better understand the formation and evolution of our solar system.

How does the "Proportion of planetary-period to the distance-from-the-sun" vary among different planets?

The proportion of planetary-period to the distance-from-the-sun varies greatly among different planets due to their varying sizes, distances from the sun, and orbital speeds. For example, the proportion for Earth is approximately 1:1, while for Neptune it is about 164:1. This shows the vast differences in orbital dynamics between planets.

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