Answer the following questions related to satellites moving in circular orbits around the Earth.
(i) State the mathematical relationship between the square of the orbital period T and the cube of the orbital radius r for a satellite revolving round the Earth.
(ii) If the orbital radius of a satellite is doubled, explain qualitatively whether its time period increases or decreases. Give a brief reason based on the relationship stated in part (i).
(iii) A student plots the values of T2 (vertical axis) against r3 (horizontal axis) for several artificial satellites and obtains a straight line through the origin. Explain what physical quantity is represented by the slope of this line and describe how the student could use it to estimate the mass of the Earth.