An undiscovered planet, many lightyears from earth, has one moon in a periodic orbit. this moon takes 16101610 × 103 seconds (about 1919 days) on average to complete one nearly circular revolution around the unnamed planet. if the distance from the center of the moon to the surface of the planet is 255.0255.0 × 106 m and the planet has a radius of 3.103.10 × 106 m, calculate the moon's radial acceleration .

a = 39.8 m/s²

Explanation:

Centripetal acceleration is the acceleration that changes the direction of a body's speed without changing its module.

        a = v² / r

With the module is constant we can use the equations of uniform motion to find the speed

      v = d / t

Where the distance d is the circle length

      d = 2π r

Where r is the distance from the moon to the surface of the plant plus the radius of the plant

     r = 255.0 10⁶ +3.1 10⁶ m

     r = 258.1  10⁶ m

The time it takes to make a full turn is called a period

     t = T = 16 10³ s

Let's replace and calculate centripetal acceleration

     v = 2π r / T

calculate

     a = (2π r / T)² / r

     a = 4π² r² / T²r

     a = 4π² r / T²

     a = 4π² 258.1 106 / (16 103)²

     a = 39.8 m/s²

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