Question

The International Space Station operates at an altitude of 350 km. Plans for the final construction show that material of weight 4.22 ✕ 106 N, measured at the Earth's surface, will have been lifted off the surface by various spacecraft during the construction process. What is the weight of the space station when in orbit?

Answer 1

The weight of the station becomes
`3.756* 10^(6)N`

Step-by-step 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

`W=mass* g_(surface)\\\\\therefore mass=(W)/(g_(surface))\\\\mass=(4.22* 10^(6)N)/(9.81)\\\\\therefore mass=430173.292kg`

Now we know that the variation of acceleration due to gravity with height above surface of earth is given by

`g(h)=g_(surface)(1-(2h)/(R))`

where R = 6371 km is Radius of earth

Applying values we get the value of 'g' at height of 350 kilometers equals

`g(350)=9.81* (1-(2* 350)/(6371))=8.732ms^(-2)`

hence the weight in orbit becomes

`W_(orbit)=mass* g_(orbit)\\\\W_(orbit)=430173.292* 8.732\\\\ \therefore W_(orbit)=3.756* 10^(6)N\\`