Answer:
The weight of the station becomes [tex]3.756\times 10^{6}N[/tex]
Explanation:
Since the acceleration due to gravity decreases with increase in height we conclude that at a height of 350 kilometers the weight of the material will be lesser.
At the ground we have
[tex]W=mass\times g_{surface}\\\\\therefore mass=\frac{W}{g_{surface}}\\\\mass=\frac{4.22\times 10^{6}N}{9.81}\\\\\therefore mass=430173.292kg[/tex]
Now we know that the variation of acceleration due to gravity with height above surface of earth is given by
[tex]g(h)=g_{surface}(1-\frac{2h}{R})[/tex]
where R = 6371 km is Radius of earth
Applying values we get the value of 'g' at height of 350 kilometers equals
[tex]g(350)=9.81\times (1-\frac{2\times 350}{6371})=8.732ms^{-2}[/tex]
hence the weight in orbit becomes
[tex]W_{orbit}=mass\times g_{orbit}\\\\W_{orbit}=430173.292\times 8.732\\\\ \therefore W_{orbit}=3.756\times 10^{6}N\\[/tex]
