Respuesta :
Answer:
Venus will take 223.015 days to make one orbit around the sun .
Explanation:
Given that,
Distance[tex]r = 1.50\times10^{11}\ m[/tex]
Distance[tex]r'=1.08\times10^{11}\ m[/tex]
We need to calculate the time period for Venus
Using Kepler's third law
For Earth,
[tex]T^2\propto r^3[/tex]....(I)
For Venus,
[tex]T'^2\propto r'^3[/tex]....(II)
Ratio of equation (I) and (II)
[tex]\dfrac{T'^2}{T^2}=\dfrac{r'^3}{r^3}[/tex]....(I)
Put the value in the equation
[tex]\dfrac{T'^2}{T^2}= \dfrac{1.08\times10^{11}}{1.50\times10^{11}}[/tex]
[tex]T'^2=\dfrac{1.08\times10^{11}}{1.50\times10^{11}}\timesT^2[/tex]
[tex]T'^2=(\dfrac{1.08\times10^{11}}{1.50\times10^{11}})^{\dfrac{3}{2}}\times1[/tex]
[tex]T=0.6109\ earth year[/tex]
[tex] T=0.611\times365[/tex]
[tex]T=223.015\ days[/tex]
Hence, Venus will take 223.015 days to make one orbit around the sun
For making one orbit to the sun the venus will take 223.015 earth days
What time venus will take to orbit once to the sun?
It is Given that,
The Earth orbits the sun once per year at the distance [tex]=1.50\times10^{11} m[/tex]
Venus orbits the sun at a distance [tex]=1.08\times10^{11} m[/tex]
For calculating the Time period of venus
From Kepler's third law
For Earth,
[tex]T^{2} _{e} =r^{3} _{e} ...............(1)[/tex]
For Venus,
[tex]T^{2} _{V} =r^{3} _{V} ...............(2)[/tex]
From the ratio of equations (I) and (II) we will get
[tex]\dfrac{T^{2}_{v} }{T^{2}_{e} } = \dfrac{r^{3}_{v} }{r^{3}_{e} }[/tex]
By putting the values in the equation
[tex]\dfrac{T^{2}_{v} }{T^{2}_{e} } = \dfrac{(1.08\times 10^{11} )^{3} }{{(1.50\times 10^{11} )^{3} }}[/tex]
[tex]T_{v} ^{2} = \dfrac{(1.08\times 10^{11} )^{3} }{{(1.50\times 10^{11} )^{3} }}\times1[/tex]
[tex]T_{v} =0.911 earth year[/tex]
[tex]T_{v} = 0.611\times 365 days[/tex]
[tex]T_{v} = 223.015 days[/tex]
Thus for making one orbit to the sun the venus will take 223.015 earth days
To know more about Venus and earth follow
https://brainly.com/question/2559768
Hence, Venus will take 223.015 days to make one orbit around the sun
