Many people assume air resistance acting on a moving object will always make the object slow down. It can, however, actually be responsible for making the object speed up. Consider a 180-kg Earth satellite in a circular orbit at an altitude of 205 km. A small force of air resistance makes the satellite drop into a circular orbit with an altitude of 80 km. (Use the following values: G = 6.67 10-11 m3 kg−1 s−2, mass of the Earth 5.98 1024 kg, radius of the Earth 6.37 106 m.)
(a) Calculate the satellite's initial speed. m/s
(b) Calculate its final speed in this process. m/s
Answer:
a) [tex]7.730*10^3m/s[/tex]
b) [tex]7.80*10^3m/s[/tex]
Explanation:
Given that;
The Earth satellite = 180-kg
altitude (radius r ) = 205 km
After the satellite drop into a circular orbit; the final altitude (r) = 80 km
G = [tex]6.67 *10^{-11}m^3kg^{-1}s^{-2}[/tex]
mass of the earth = [tex]5.98*10^{24}kg[/tex]
radius of the earth = [tex]6.37 *10^{6}m[/tex]
The original speed for both circular orbit is given as:
[tex]v = \sqrt{\frac{GM_E}{r} }[/tex]
(a) Calculate the satellite's initial speed m/s
[tex]v = \sqrt{\frac{6.67*10^{-11}*5.89*10^{24}}{6.37*10^6+205*10^3} }[/tex]
v = 7729.88
v = [tex]7.730*10^3m/s[/tex]
b) Calculate its final speed in this process m/s
[tex]v = \sqrt{\frac{6.67*10^{-11}*5.89*10^{24}}{6.37*10^6+80*10^3} }[/tex]
v =7804.42
[tex]v =7.80*10^3m/s[/tex]
