Final answer:
To calculate the centripetal acceleration of the Sun in its galactic orbit, convert the radius of the orbit from light years to meters and use the formula for centripetal acceleration. The centripetal acceleration of the Sun is approximately 1.24 x 10^-10 m/s^2.
Step-by-step explanation:
To calculate the centripetal acceleration of the Sun in its galactic orbit, we can use the formula for centripetal acceleration:
centripetal acceleration = (angular velocity)^2 * radius
First, we need to convert the radius of the Sun's orbit from light years to meters. Since 1 light year is the distance traveled by light in 1 year, we can use the conversion factor: 1 light year = 9.461 x 10^15 meters.
Using this conversion, the radius of the Sun's orbit is approximately 2.837 x 10^20 meters. We can then calculate the centripetal acceleration:
centripetal acceleration = (2 π / period)^2 * radius
where period is the time it takes for the Sun to complete one orbit, which is given as 2.60 x 10^8 years.
Plugging in the values, we get:
centripetal acceleration = (2 π / (2.60 x 10^8 years))^2 * 2.837 x 10^20 meters
Simplifying the equation gives us:
centripetal acceleration ≈ 1.24 x 10^-10 m/s^2
Therefore, the correct answer is a) 1.24 x 10^-10 m/s^2.