Question

The table below lists the specifications for three different satellites in their circular orbits around the earth. Rank the satellites according to their orbital speeds, greatest first.

	Mass of Satellite	Radius of Orbital Path
Satellite $1$	$M$	$R$
Satellite $2$	$2M$	$R$
Satellite $3$	$2M$	$2R$

• A. $1,2,3$
• B. $1$ and $2$ tie, $3$
• C. $1,2$ and $3$ tie
• D. $1$ and $3$ tie, $2$
• E. All tie

Answer 1

The correct option is B $1$ and $2$ tie, $3$

Orbital speed of satellite $v=\sqrt{\frac{G{M}_e}{r}}$ where $M_e$ is the mass of earth and $r$ is the orbital radius.

$⟹$ Orbital speed of satellite is independent of mass of satellite.

$\therefore$ $v_1=\sqrt{\frac{G{M}_e}{R}}$ $v_2=\sqrt{\frac{G{M}_e}{R}}$ $v_3=\sqrt{\frac{G{M}_e}{2R}}$

$⟹$ $v_1=v_2>v_3$