Scientists wish to locate an orbiting laboratory at a height where the local value of g is exactly 1% less than its surface value.
a. (i) Derive an equation relating altitude h to the given fractional decrease in g.
b. (ii) Using this equation, calculate the required altitude (to the nearest metre) for the laboratory. Use R=6.4×106m.
c. (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.