SOLUTION: Kepler’s Third Law of planetary motion states that the square of the period T of a planet (the time taken for a complete revolution around the sun) is proportional to the cube of
Algebra.Com
Question 1025907: Kepler’s Third Law of planetary motion states that the square of the period T of a planet (the time taken for a complete revolution around the sun) is proportional to the cube of its average distance d 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) Based on the idea of proportionality, if the average distance away from the sun was to double, would the period double also? If not, what is the percentage change? (d) Neptune is approximately 30 times as far away from the sun as Earth. Without using the specific number of kilometers, what is the period of Neptune? Does your answer correspond with the value from other sources?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Kepler’s Third Law of planetary motion states that the square of the period T of a planet (the time taken for a complete revolution around the sun) is proportional to the cube of its average distance d from the sun.
-----
(a) Express Kepler’s Third Law as an equation.
T^2 = k*d^3
-----------------------
(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.
T^2 = k*(150x10^6)^3
k = T^2/(150x10^6)^3
-------------------------
(c) Based on the idea of proportionality, if the average distance away from the sun was to double, would the period double also? If not, what is the percentage change?
Note: T = sqrt(k*d^3)
If d is doubled, T^2 = k*(2d)^3
T^2 would equal 8k*d^3
T would be 2sqrt(2)*sqrt(kd^3)
Percent change = 2sqrt(2) = 283%
--------------------------------
(d) Neptune is approximately 30 times as far away from the sun as Earth. Without using the specific number of kilometers, what is the period of Neptune? Does your answer correspond with the value from other sources?
I'll leave that to you.
Cheers,
Stan H.
-----------
RELATED QUESTIONS
Kepler’s Third Law of planetary motion states that the square of the period T of a planet (answered by KMST)
Please help me solve this :
Kepler’s Third Law of planetary motion states that the... (answered by rothauserc)
Hi, Please help me solve part D. Thank you.
Kepler’s Third Law of planetary motion... (answered by Theo)
Kepler’s third law of planetary motion may be given as T=kr^3/2 where T is the time... (answered by richwmiller)
Kepler's Third Law of planetary motion states that the square of the period T of a planet (answered by stanbon)
Kepler’s Third Law of Planetary Motion states that the square of the period of... (answered by josgarithmetic,math_tutor2020)
Kepler’s third law of planetary motion may be given as where T is the time for one... (answered by richwmiller)
hey guys this is a two part problem not doing so great on I could use your help please.
(answered by ankor@dixie-net.com)
Kepler's third law of planetary motion states that the square of the orbital period of... (answered by Theo)