Question

The earth orbits the sun once per year at the distance of 1.50 x 1011 m. Venus orbits the sun at a distance of 1.08 x 1011 m. These distances are between the centers of the planets and the sun. How long (in earth days) does it take for Venus to make one orbit around the sun

Answer 1

Answer:

Venus will take 223.015 days to make one orbit around the sun .

Explanation:

Given that,

Distance$r = 1.50\times10^{11}\ m$

Distance$r'=1.08\times10^{11}\ m$

We need to calculate the time period for Venus

Using Kepler's third law

For Earth,

$T^2\propto r^3$....(I)

For Venus,

$T'^2\propto r'^3$....(II)

Ratio of equation (I) and (II)

$\dfrac{T'^2}{T^2}=\dfrac{r'^3}{r^3}$....(I)

Put the value in the equation

$\dfrac{T'^2}{T^2}= \dfrac{1.08\times10^{11}}{1.50\times10^{11}}$

$T'^2=\dfrac{1.08\times10^{11}}{1.50\times10^{11}}\timesT^2$

$T'^2=(\dfrac{1.08\times10^{11}}{1.50\times10^{11}})^{\dfrac{3}{2}}\times1$

$T=0.6109\ earth year$

$T=0.611\times365$

$T=223.015\ days$

Hence, Venus will take 223.015 days to make one orbit around the sun