If a planet was suddenly stopped in its orbit supposed to be circular, show that it would fall onto the sun in a time `sqrt(2)/(8)` times the period of the plant's revolution.

Explanation

To solve the problem of how long it would take for a planet to fall into the Sun if it were suddenly stopped in its circular orbit, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Conditions:**
- The planet is initially in a circular orbit around the Sun with radius \( R \).
- The gravitational force provides the necessary centripetal force to keep the planet in orbit.

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