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Kepler's Third Law of Planetary Motion states that the square of the period of revolution T of a planet varies directly with the cube of its mean distance a from the Sun. If the mean distance of Earth from the Sun is 93 million miles, what is the mean distance of the planet Mercury from the Sun, given that Mercury has a "year" of 88 days?
Before moving forward to answer this question, tell me if my equation set up is correct.
My equation:
T^2 = (a^3)k, where k is the constant of proportionality.
I know this does not answer the question but I need to know if the equation set up is right.
Last edited by nycguitarguy (2024-03-07 01:27:32)
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"varies directly with the cube of its mean distance a from the Sun"
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"varies directly with the cube of its mean distance a from the Sun"
I meant to type T = (a^3)k.
Updated post.
Last edited by nycguitarguy (2024-03-07 01:27:54)
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Kepler's Third Law of Planetary Motion states that the square of the period of revolution T of a planet varies directly with the cube of its mean distance a from the Sun.
T^2 = (a^3)k, where k is the constant of proportionality.
This looks right.
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FelizNYC wrote:Kepler's Third Law of Planetary Motion states that the square of the period of revolution T of a planet varies directly with the cube of its mean distance a from the Sun.
T^2 = (a^3)k, where k is the constant of proportionality.This looks right.
Perfect. I will work it out on paper and return here if I get stuck somewhere along the way. The most important skill in math is setting up the correct equation(s) when solving word problems.
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[The most important skill in math is setting up the correct equation(s) when solving word problems.
In fact, in real life, the crucial first step in any design is setting up its correct equation(s) or function(s).
The remaining steps (to find its numerical solution) could be done by one of the many CAD (computer-aided design) tools (or just by a hand-held calculator).
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FelizNYC wrote:[The most important skill in math is setting up the correct equation(s) when solving word problems.
In fact, in real life, the crucial first step in any design is setting up its correct equation(s) or function(s).
The remaining steps (to find its numerical solution) could be done by one of the many CAD (computer-aided design) tools (or just by a hand-held calculator).
Correct.
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