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`

Step-by-step 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{(GM_E)/(r) }`

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

`v = \sqrt{(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{(6.67*10^(-11)*5.89*10^(24))/(6.37*10^6+80*10^3) }`

v =7804.42

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