Newton\'s Law of Gravitation states that two bodies with masses M and N attract
ID: 2000899 • Letter: N
Question
Newton's Law of Gravitation states that two bodies with masses M and N attract each other with a force F=GMN/r2, 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 5.98×10^24kg and is concentrated at its center. Take the radius of the Earth to be 6.37×10^6m and G=6.67×10^11Nm2/kg2. (Is the answer 6.2*10^10 j ? or its wrong?)
Explanation / Answer
given
earth mass is M = 5.98 X 1024 kg
earth radius r = 6.37 X 106m
and satellite mass is m = 1000 kg
heiight is h = 1000 km
the G value G = 6.67 X 10-11Nm2 / kg2
= change in energy is dE
then total work is dE + w = 0
then we have equations for dE = - G M m / r + G M m / ( r + h )
-GMm/r + GMm/(r + h) + w = 0
- ( 6.67 X 10-11 ) X ( 5.98 X 1024 ) ( 1000 ) / ( 6.37 X 106 )
+ ( 6.67 X 10-11 ) ( 5.98 X 1024 ) ( 1000 ) / ( 6.37 X 106 + 1000 X 103 ) + w = 0
- ( 3.98 X 1017 / ( 6.37 X 106 ) ) + ( 3.98 X 1017 / 7.37 X 106 ) + w = 0
- 6.24 X 1010 + 5.40 X 1010 + w = 0
w - 0.84 X 1010 = 0
w = 0.84 X 1010
w = 8.4 X 109 J
the work (in J) required to launch a satellite is w = 8.4 X 109 J and
but not 6.2 X 1010 J