Question

the period of revolution of planet A around the sun is 8 times that of planet B. how many times is the distance of planet A as great as that of planet B? give reason ​

Answer 1

There is no connection between a planet's distance from the Sun and its rate of rotation (spin on its own axis or Planetary Rotation Period). While it is true that, generally speaking, the gas giants have higher rotation rates than the earth like planets closer to the Sun, any correlation is only coincidental. Mars, for example, is further from the Sun than Earth but has a slightly slower rate of rotation - its planetary rotation period is 1.03 Earth days. Pluto. the furthest planet from the Sun, has a planetary rotation period of 6.39 Earth days. You can see in the plot below that there is no correlation between the planetary rotation period and the distance from the Sun.

Answer 2

The distance of A from  the Sun is 4 times greater than that of B  from the Sun

Explanation:

From Kepler's law we know that if T is the time period and r is the distance of the planet from the Sun then

$T^2\propto r^3$

Terefore, for the planets A and B

$\frac{T_A^2}{T_B^2}=\frac{r_A^3}{r_B^3}$

Given that

$\frac{T_A}{T_B}=8$

$\implies 8^2=\frac{r_A^3}{r_B^3}$

$\implies \frac{r_A^3}{r_B^3}=64$

$\implies \frac{r_A}{r_B}=\sqrt[3]{64}$

$\implies \frac{r_A}{r_B}=4$

$\implies r_A=4r_B$

Thus, the distance of A from the Sun is 4 times greater than that of B

Hope this helps.

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