Final answer:
To calculate the radius of an object with a mass of 10⁹ Suns and convert it to light years.
Step-by-step explanation:
To calculate the radius of an object with a mass of 10⁹ Suns, we need to use the formula for gravitational force: F = (G * M₁ * M₂) / r². Rearranging the formula to solve for r, we get r = √((G * M₁ * M₂) / F). Plugging in the given values, where M₁ is the mass of the object and M₂ is the mass of the Sun, we can find the radius.
To convert the radius from light years, we need to use the speed of light. We know that light travels at a speed of approximately 9.461 × 10¹² km/year. Multiplying the radius by this conversion factor, we can find the radius in light years.