Communication satellites move in orbits of radius 44,400 km around the Earth. Find the acceleration of such a satellite assuming that only force acting on it is due to the Earth.

(Mass of the Earth = 6 × 1024 kg, G = 6.67× 10-11 Nm2 / kg2)


Asked by Topperlearning User | 20th Sep, 2016, 01:32: PM

Expert Answer:

begin mathsize 12px style Given colon space Satellite apostrophe straight s space radius space of space orbit comma space straight r equals 44 comma 400 space km equals 444 space cross times space 10 to the power of 5
space space space space space space space space space space space Mass space of space the space Earth comma space straight M subscript straight e equals 6 cross times 10 to the power of 24 space kg comma space
space space space space space space space space space space space Gravitational space constant comma space straight G equals 6.67 cross times space 10 to the power of negative 11 end exponent space Nm squared divided by kg squared right parenthesis
Acceleration space of space the space satellite comma space straight a equals GM subscript straight e over straight r squared
Substituting space the space values comma space we space get
space straight a equals fraction numerator 6.67 cross times space 10 to the power of negative 11 end exponent cross times 6 cross times 10 to the power of 24 over denominator open parentheses 444 space cross times space 10 to the power of 5 close parentheses squared end fraction
space straight a equals 2.03 cross times 10 cubed space straight m divided by straight s squared
or space space straight a equals 0.20 space straight m divided by straight s squared

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space end style

Answered by  | 20th Sep, 2016, 03:32: PM