Suppose the gravitational force varies inversely as the \\\\(n\\\\)th power of distance, then the time period of a planet in circular orbit of radius \\\\(R\\\\) around the sun will be proportional to.
F=\\\\(\\dfrac{GmM}{R^n}=m\\omega^2R\\rightarrow\\omega=\\sqrt{\\dfrac{GM}{R^{n+1}}}\\\\) hence time period is proportional to \\\\(R^{\\dfrac{n+1}{2}}\\\\)