Question

Find the acceleration due to gravity at a distance of 12000 km from the centre of the earth

Answer 1

Explanation:

g=GMe/Re

G=gravity constant

Me=6.02×10^24kg

Re=6400km

on equating these in equation a g=9.8m/s² at

surface of earth

let us assume an object is moved a distance

h from surface of earth

so then then the value of g decreases as an object moves away from earth then the equation

is g'=G×Me/(Re+h)²

so here h=12000km=12000×10³m=12×10⁶m

g=GMe/Re²

g'=GMe/(Re+12×10^6m)²

now

we can cancel someconstants by dividing

g/g'=GMe/Re²/GMe/(Re+12×10^6)²

now GMe cancels

g/g'=(Re+h)²/Re²

g×Re²/(Re+h)²=g'

9.8× (6400×10^3)²/12000+6400

9.8×(6400×10³)²/(18400×10³)²=

=9.8× 6400×6400×10⁶/18400×18400×10⁶

9.8×1/2.875×1/2.875=1.185633m/s²