9. Can someone help me with this word problem, I’m confused. According to Kepler's third law of planetary motion, the square of the time (T) needed for a planet to make one revolution varies directly with the cube of the averagedistance (d) of the planet from the sun. Which choice represents this relationship?O T = kdO T = dkO T = kd?O T =国A 3:35et OT= kd3%3DO T = dk3O T = kd²O T² = #

Name: 9. Can someone help me with this word problem, I’m confused. According
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Description: 9. Can someone help me with this word problem, I’m confused. According to Kepler's third law of planetary motion, the square of the time (T) needed for a planet to make one revolution varies directly with the cube of the averagedistance (d) of the pl

We know newtons law of gravitation F=GmMr2mrω2=GmMr2mr2πT2=GmMr2T2=4πGMr3here r=kT2 α k3T2=dk3…

Answered: According to Kepler's third law of…

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9. Can someone help me with this word problem, I’m confused.

According to Kepler's third law of planetary motion, the square of the time (T) needed for a planet to make one revolution varies directly with the cube of the average
distance (d) of the planet from the sun. Which choice represents this relationship?
O T = kd
O T = dk
O T = kd?
O T =
国
A 3:35
e
t

OT= kd3
%3D
O T = dk3
O T = kd²
O T² = #

Expert Solution

Step 1

We know newtons law of gravitation

$F = \frac{GmM}{r^{2}} {mrω}^{2} = \frac{GmM}{r^{2}} mr {(\frac{2 π}{T})}^{2} = \frac{GmM}{r^{2}} T^{2} = (\frac{4 π}{GM}) r^{3} here r = k T^{2} α k^{3} T^{2} = {dk}^{3}$

Where d is proportionality constant.

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