A space probe is on a circular orbit around the sun at a distance of \(r_0 = 1 \,\text{AU}\) (astronomical unit). It collides with an asteroid in its trajectory, losing all of its kinetic energy. As a result, the space probe falls directly towards the sun.

How long (in days) does it take for the space probe to arrive at the sun? Round to the nearest integer.

**Details and Assumptions:** The Earth orbits the sun in an elliptical orbit with semi-major axis \(1 \text{ AU},\) and has an orbital period of 365.25 days. The planets (including the Earth) have a negligible impact on the orbit of the probe. The diameter of the sun is negligible compared to the orbital radius \(r_0.\)

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