The sun goes around the center of our galaxy once every 250 million years. The sun is also 2.55×1020 m from the center of our galaxy. What is the acceleration of our sun towards the center of the galaxy in m/s2?

1.62E-10

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To find the acceleration of our sun towards the center of the galaxy, we need to understand the concept of centripetal acceleration.

Centripetal acceleration is the acceleration directed towards the center of a circular path, experienced by an object moving in a circular motion. It can be calculated using the equation:

ac = v^2 / r

Where:
ac = Centripetal acceleration
v = Velocity of the object
r = Radius of the circular path

In this case, the sun is moving in a circular path around the center of our galaxy. We are given that the sun takes 250 million years to complete one orbit, which is equivalent to the time period of circular motion, T. To find the velocity, v, we need to divide the circumference of the circular path by the time period:

v = 2πr / T

Plugging in the given values, we have:
r = 2.55 × 10^20 m
T = 250 million years = 250 × 10^6 years = 7.89 × 10^15 seconds (since there are 365.25 days in a year)

Now, we can substitute the values of r and T into the equation for velocity to find v.

v = 2π(2.55 × 10^20 m) / (7.89 × 10^15 s)

Calculating this, we get v ≈ 2.041 × 10^5 m/s.

Finally, we can substitute the velocity value into the centripetal acceleration formula to find the acceleration towards the center of the galaxy.

ac = (2.041 × 10^5 m/s)^2 / (2.55 × 10^20 m)

Calculating this, we get ac ≈ 1.63 × 10^-10 m/s^2.

Therefore, the acceleration of our sun towards the center of the galaxy is approximately 1.63 × 10^-10 m/s^2.