Three identical stars of mass M form an equilateral triangle that rotates around the triangle's center as the stars move in a common circle about that center. The triangle has edge length L. What is the speed of the stars?

Explanation

To find the speed of the stars rotating around the center of the equilateral triangle, we can follow these steps:

### Step 1: Determine the distance from the center of the triangle to each star.
In an equilateral triangle, the center of mass (centroid) is located at a distance of \( \frac{L}{\sqrt{3}} \) from each vertex (star). This is derived from the geometry of the triangle.

**Hint:** Use the properties of an equilateral triangle to find the centroid's position.

### Step 2: Write the expression for the centripetal force.
...