If it takes a planet 2.8 × 108 s to orbit a star with a mass of 6.2 × 1030 kg, what is the average distance between the planet and the star?
1.43 × 10^9 m
9.36 × 10^11 m
5.42 × 10^13 m
9.06 × 10^17 m

We can find the answer from formula for orbital velocity v=√{(G*M)/R}, where G is the gravitational constant and G=6.67*10^-11 m³ kg⁻¹ s⁻², M is the mass of the star and R is the distance from the planet to the star. Also, v=ωR, where ω is the angular velocity and R is the radius. 

ωR=√{(G*M)/R}, now, ω=2π/T, where T is the orbital period of the planet

(2π/T)*R=√{(G*M)/R}, we "put to the power of 2" both sides to get rid of the square root and get:

{(2π/T)*R}²=[√{(G*M)/R}]², 

(4π²/T²)*R²=(G*M)/R, we multiply by R:

(4π²/T²)*R³=G*M, now we solve for R and get:

R³=(G*M*T²)/4π², we take the third root to get R:

R=∛{(G*M*T²)/4π²}, plug in the numbers and get:

R=9.36*10^11 m 

And this is the average distance between the planet and the star. 

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