1. Speed of a satellite in a circular orbit

For a satellite revolving around a planet in a circular orbit, the orbital speed is

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

where:

• $G$ = gravitational constant
• $M$ = mass of the planet
• $r$ = radius of the orbit from the center of the planet

2. Apply to the two satellites

For satellite $S_1$:

$v_1 = \sqrt{\frac{GM}{R_1}}$

For satellite $S_2$:

$v_2 = \sqrt{\frac{GM}{R_2}}$

3. Take the ratio

$\frac{v_1}{v_2} = \sqrt{\frac{GM/R_1}{GM/R_2}} = \sqrt{\frac{R_2}{R_1}}$

Given:

$R_1 = 3200\text{ km}, \quad R_2 = 800\text{ km}$

So,

$\frac{v_1}{v_2} = \sqrt{\frac{800}{3200}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$

4. Compare with the form given

It is given that

$\frac{v_1}{v_2} = \frac{1}{x}$

Thus,

$\frac{1}{x} = \frac{1}{2} \implies x = 2$

Final Answer

$x = 2$