Question

Find the value of acceleration due to gravity at a height 3000km above the surface of earth and at a depth 8km below the surface of earth Given Re=6400km and of=9.8

Answer 1

The acceleration due to gravity at height h above the surface = g( 1 - 2h/R)

Now $g_{3000km}$
= 9.8 ( 1 - 2(3000)/6400 )

= 9.8 ( 1 - 60/64)

= 9.8 ( 4/64)

= 9.8 ( 1/16 )

= 9.8/16

= 0.6125 m/s² .

We know that acceleration due to gravity at depth d below the duration = g(1-d/R)

$g_{8km}$ = g( 1 - 8/6400)

= g ( 1 - 1/800)

= g ( 799/800)

= 9.8 × 799/800

= 9.78 m/s²