Question

A satellite is projected vertically upwards from an earth station. At what height above the earth's surface will the force on the satellite due to the earth be reduced to half its value at the earth station? (Radius of the earth is 6400 km.)

Concept of Physics - 1 , HC VERMA , Chapter "The Force".

Answer 1

Hi..

Hope this helps u!!

Answer 2

Hello Dear.


Assume that the height will be h.; {from the earth surface} .
We know that the formula,
At the earth station,

F= GMm / R²

Where the symbol GMm and R is :-
M is the mass of the earth.
m is the mass of satellite 
R is the radius of earth.

So now, The force exert on the satellite due to the earth at which the height
h=F/2 .
$F_{h}$ = G Mm / (R + h)² = F/2
or GMm /(R+h)² = GMm/2R² .
(R+h)² = 2R²

h² + 2Rh - R² = 0

h = (-2R +_ 2√2R ) / 2
h  = R (√2- 1) 
h   = 6400 (√2 -1 )
h   = 6400 (0.414)
h   = 2649.6 km.

Hence the height from the earth surface is h = 2650 km (approx) .


Hope it Helps. :-)