An astronaut orbiting in a spaceship round the earth, has centripetal acceleration 2.45m//s^(2). Find the height of the spaceship. (Take R = 6400 km).

An astronaut orbiting in a spaceship round the earth, has centripetal

1.	An astronaut orbiting in a spaceship round the earth, has centripetal acceleration 2.45m//s^(2). Find the height of the spaceship. (Take R = 6400 km).
Answer» Solution :As centripetal acceleration EQUALS to acceleration due to gravity at that height, then `a = g_(h) = (GM)/(r^(2)) = (GM)/((R+h)^(2)) = (gR^(2))/((R+h)^(2))` `rArr a. = (gR^(2))/((R+h)^(2)) = ((R)/(R+h))^(2) = (a)/(G) = (2.45)/(9.8) = (1)/(4)` `rArr (R)/(R+h) = (1)/(2) rArr R+h = 2R ""R = h = 6400 km` `THEREFORE` SPACESHIP is at a height 6400 km.