If the earth suddenly shrinks to $$\frac{1}{64}$$th of its original volume with its mass remaining the same, the period of rotation of earth becomes $$\frac{24}{x}$$h. The value of x is __________.
If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth $$\alpha \mathrm{h}\left(\mathrm{h}<<\mathrm{R}_{\mathrm{e}}\right)$$ from the earth surface. The value of $$\alpha$$ will be _________.
(use $$\left.\mathrm{R}_{\mathrm{e}}=6400 \mathrm{~km}\right)$$
Two satellites S1 and S2 are revolving in circular orbits around a planet with radius R1 = 3200 km and R2 = 800 km respectively. The ratio of speed of satellite S1 to be speed of satellite S2 in their respective orbits would be $${1 \over x}$$ where x = ___________.