Final answer:
If it takes a planet 2.8 × 10⁸ s to orbit a star with a mass of 6.2 × 10³0 kg, the average distance between the planet and the star is approximately A. 1.43 × 10⁹ meters.
Step-by-step explanation:
To find the average distance between the planet and the star, we can use the formula for the period of an object in circular orbit:
T = 2π√(r³/GM)
where
T is the period (given as 2.8 × 10⁸ s)
r is the average distance between the planet and the star (what we're trying to find)
G is the gravitational constant
M is the mass of the star (given as 6.2 × 10³⁰ kg).
Rearranging the formula, we get:
r = (T²GM)/(4π²)
Substituting the given values, we have:
r = ((2.8 × 10⁸ s)² × (6.67 × 10⁻¹¹ Nm²/kg²) × (6.2 × 10³⁰ kg))/(4π²)
Simplifying the expression, we find that the average distance between the planet and the star is approximately 1.43 × 10⁹ meters.
So therefore the correct answer is A. 1.43 × 10⁹ meters.