Question 1078498: Please help me solve this :
Kepler’s Third Law of planetary motion states that the square of the period T, in years, of a planet (the time taken for a complete revolution around the sun) is proportional to the cube of its average distance d, in millions of km, from the sun.
(a) Express Kepler’s Third Law as an equation.
(b) Find the constant of proportionality. Note that the average distance the Earth is from the
sun is 150 million kilometers, according to Wikipedia. You will also need some of your Earth
knowledge.
(c) Neptune is approximately 30 times as far away from the sun as Earth. Does your answer
correspond with the value from other sources?
(d) Suppose in another galaxy, planet X is a certain average distance away from its Sun. Another
planet, Y , is twice the average distance away from the sun as X. In percentage terms, what
is the period of planet Y in relation to planet X? (You may assume that Kepler’s law applies
not only in our own galaxy.)
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! a) T^2 = k * d^3, where k is the constant of proportionality
:
b) 1^2 = k * 150^3
k = (1 / 3375000)
:
c. T^2 = (1 / 3375000) * (30 * 150)^3
T^2 = 27000
T = 164.3168
From NASA publication Neptune's period is 165 earth years
:
d. (T(Y) / T(X)) = (2 * d(X)) / d(X)) = 2 = 200% = twice as long
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