Question

please include steps and reasoning

A 1 034-kg satellite orbits the Earth at a constant altitude of 105-km.

(a) How much energy must be added to the system to move the satellite into a circular orbit with altitude 196 km?

=______MJ

(b) What is the change in the system's kinetic energy?

=______ MJ

(c) What is the change in the system's potential energy?

=_______MJ

Answer 1

a)
given

m = 1034 kg
h1 = 105 km
h2 = 196 km

we know,
Re = 6.37*10^6 m
Me = 5.98*10^24 kg

so,

r1 = Re + h1 = 6.37*10^6 + 0.105*10^6 = 6.475*10^6 m
r2 = Re + h2 = 6.37*10^6 + 0.196*10^6 = 6.566*10^6 m

we know total energy of saceship, E1 = -G*Me*m/(2*r)

Energy must be added, E = E2 - E1

= -G*Me*m/(2*r2) - ( -G*Me*m/(2*r1))

= G*Me*m*(1/r1 - 1/r2)

= 6.67*10^-11*5.98*10^24*1034*(1/(6.475*10^6) - 1/(6.566*10^6) )/2

= 4.42*10^8 J

= 442 MJ

b) change in kinetic energy = (1/2)*m*v2^2 - (1/2)*m*v1^2

= G*Me*m*(1/r2 - 1/r1)/2

= 6.67*10^-11*5.98*10^24*1034*( 1/(6.566*10^6) -1/(6.475*10^6))/2

= -442 MJ

c) change in potential energy = 884 MJ