Question

Suppose an asteroid orbiting the sun had an orbital period of 7. 5 years. What would its orbital radius be?.

Answer 1

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:

$T = \sqrt{\frac{4*\pi ^2*r^3}{G*M} }$

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:

$T = \sqrt{\frac{4*\pi ^2*r^3}{G*M} }\\\\r = \sqrt[3]{ \frac{T^2*G*M}{4*\pi ^2} }$

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:

$r = \sqrt[3]{ \frac{(2.3655*10^8 s)^2*(6.67*10^{-11} m^3/(kg*s^2))*(1.989*10^{30} kg)}{4*3.14 ^2} } = 4.29*10^{11 }m$

So the orbital radius is 4.29*10^11 m

If you want to learn more about orbits, you can read:

brainly.com/question/11996385