If planets orbit a central star too slowly, they will be attracted by gravity and fall into the star. Suppose a planet moves radially (not orbiting the sun or spinning on its axis) from its orbit and is embedded into the sun's equator. Taking the mass of the sun to be M, what is the mass of the planet in terms of M that increases the sun's average period of 27 days by 10%? You may find it useful to assume that the planet is far much smaller than the sun and that the sun is consistent at all points.