The orbital speed of an artificial satellite very close to the surface of the earth is vo . Then the orbital speed of another artificial satellite at a height equal to the three times the radius of the earth is:

Question

The orbital speed of an artificial satellite very close to the surface of the earth is vo . Then the orbital speed of another artificial satellite at a height equal to the three times the radius of the earth is: (A)  4 vo  (B)  2 vo  (C)  0.5 vo  (D)  vo

Tardigrade Admin · Accepted Answer

vo=√(GM/R) vo=√(GM/R+3R)=√(GM/4R) ⇒ vo=(1/2)vo=0.5 vo

Q. The orbital speed of an artificial satellite very close to the surface of the earth is $v_{o}$ . Then the orbital speed of another artificial satellite at a height equal to the three times the radius of the earth is:

$4 v_{o}$

$2 v_{o}$

$0.5 v_{o}$

$v_{o}$

$2/3 v_{o}$

$v_{o} = \frac{GM}{R}$
$v_{o} = \frac{GM}{R + 3 R} = \frac{GM}{4 R}$
$\Rightarrow$ $v_{o} = \frac{1}{2} v_{o} = 0.5 v_{o}$

Q. The orbital speed of an artificial satellite very close to the surface of the earth is vo​ . Then the orbital speed of another artificial satellite at a height equal to the three times the radius of the earth is:

4vo​

2vo​

0.5vo​

vo​

2/3vo​

vo​=RGM​​ vo​=R+3RGM​​=4RGM​​ ⇒ vo​=21​vo​=0.5vo​