Question

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.)

Answer 1

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) $7.730*10^3m/s$

b) $7.80*10^3m/s$

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 = $6.67 *10^{-11}m^3kg^{-1}s^{-2}$

mass of the earth = $5.98*10^{24}kg$

radius of the earth = $6.37 *10^{6}m$

The original speed for both circular orbit is given as:

$v = \sqrt{\frac{GM_E}{r} }$

(a) Calculate the satellite's initial speed m/s

$v = \sqrt{\frac{6.67*10^{-11}*5.89*10^{24}}{6.37*10^6+205*10^3} }$

v = 7729.88

v = $7.730*10^3m/s$

b) Calculate its final speed in this process m/s

$v = \sqrt{\frac{6.67*10^{-11}*5.89*10^{24}}{6.37*10^6+80*10^3} }$

v =7804.42

$v =7.80*10^3m/s$