Newton\'s Law of Gravitation states that two bodies with masses M and jV attract
ID: 1438469 • Letter: N
Question
Newton's Law of Gravitation states that two bodies with masses M and jV attract each other with a force F = G MN/r^2 where r is the distance between the bodies and G is the gravitational constant. Use Newton's Law of Gravitation to compute the work (in J) required to launch a 1000-kg satellite vertically to an orbit 1000 km high. You may assume that Earth's mass is 5.98 Times 10^24 kg and is concentrated at its center. Take the radius of the Earth to be 6.37 Times 10^6 m and G = 6.67 Times 10^-11 N m^2 jkg^2. Work done = JExplanation / Answer
W = change in gravitational potential energy
=G*M*N/r2- G*M/r1
=G*M*N (1/r2 - 1/r1)
r2 = 6.37*10^6 m
r1 = 6.37*10^6 + 1*10^6 = 7.37*10^6 m
W = G*M*N (1/r2 - 1/r1)
= (6.673*10^-11)*(5.98*10^24)*(1000)* (1/(6.37*10^6) - 1/(7.37*10^6))
= 3.99*10^17 * (2.13*10^-8 )
=8.5*10^9 J
Answer: 8.5*10^9 J