Scientists wish to locate an orbiting laboratory at a height where the local value of g is exactly 1% less than its surface value.
(i) Derive an equation relating altitude h to the given fractional decrease in g.
(ii) Using this equation, calculate the required altitude (to the nearest metre) for the laboratory. Use R=6.4×106m.
(iii) Assuming instead that engineers dig a vertical tunnel inside Earth, find the depth at which g would be reduced by the same 1%. Compare the altitude and depth values obtained.