Question

2. Taking the mass of earth equal to 6 x 10^24 kg and
its radius equal to 6.4 x 10^6 m, calculate the value
of acceleration due to gravity at a height of
2000 km above the earth surface. Take
G = 6:7 x 10-11 N m² kg-2.​

Answer 1

Given:-

• Mass of earth = 6 × 10²⁴

• Radius of earth = 6.4 × 10⁶

• Height given = 200km

• G = 6.7 × 10¹¹

To Find:-

• The accceleration due to gravity 2000km above the surface of the earth.

Formulae used:-

• g = Gm/(r+ h )²

Where

• g = Acceleration due to gravity
• m = Mass
• r = Radius
• h = Height

Now,

$\implies\sf{ g_{h} = \dfrac{GM}{(r+h)^2}}$

$\implies\sf{g_{h} = \dfrac{6.7\times{10^{-11}}\times{6\times{10^{24}}}}{( 6.4\times{10^6} + 2000)^2}}$

$\implies\sf{g_{h} = \dfrac{6.7\times{10^{-11}}\times{6\times{10^{24}}}}{( 6.4\times{10^6} + 2.0\times{10^6})}}$

$\implies\sf{ g_{h} = \dfrac{6.7\times{60}\times{ 10^{-11 + 24}}}{ ((6.4 +2)\times{10^6})^2}}$

$\implies\sf{ g _{h} = \dfrac{402\times{10^{13}}}{70.56\times{10^{12}}}}$

$\implies\sf{ g_{h} = \dfrac{402}{70.56}}$

$\implies\sf{ g_{h} = 5.69m/s²}$

Therefore,. The Accceleration due to gravity at the height above the 2000km is 5.69m/s².