By using the orbital period equation we will find that the orbital radius is r = 4.29*10^11 m
What is the orbital period?
This would be the time that a given body does a complete revolution in its orbit.
It can be written as:
[tex]T = \sqrt{\frac{4*\pi ^2*r^3}{G*M} }[/tex]
Where:
- π = 3.14
- G is the gravitational constant = 6.67*10^(-11) m^3/(kg*s^2)
- M is the mass of the sun = 1.989*10^30 kg
- r is the radius, which we want to find.
Rewriting the equation for the radius we get:
[tex]T = \sqrt{\frac{4*\pi ^2*r^3}{G*M} }\\\\r = \sqrt[3]{ \frac{T^2*G*M}{4*\pi ^2} }[/tex]
Where T = 7.5 years = 7.5*(3.154*10^7 s) = 2.3655*10^8 s
Replacing the values in the equation we get:
[tex]r = \sqrt[3]{ \frac{(2.3655*10^8 s)^2*(6.67*10^{-11} m^3/(kg*s^2))*(1.989*10^{30} kg)}{4*3.14 ^2} } = 4.29*10^{11 }m[/tex]
So the orbital radius is 4.29*10^11 m
If you want to learn more about orbits, you can read:
https://brainly.com/question/11996385
