Question

Two satellites orbit the Earth in circular orbits of the same radius. One satellite is twice as massive as the other. Which statement is true about the speeds of these satellites? A) The heavier satellite moves twice as fast as the lighter one. B) The two satellites have the same speed. C) The lighter satellite moves twice as fast as the heavier one. D) The ratio of their speeds depends on the orbital radius.

Answer 1

To solve this problem it is necessary to apply the concepts related to the orbital velocity of a satellite on earth.

This concept is expressed in the equation,

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

Where,

G = Universal Gravitational constant

$m_E =$ Mass of the Earth

Therefore the ratio of the velocity from two satellites is,

$\frac{v_1}{v_2} = \sqrt{\frac{r_2}{r_1}}$

The ratio between the two satellites is the same, then

$\frac{v_1}{v_2} = \sqrt{\frac{r}{r}}$

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

$v_1 =v_2$

Therefore the correct option is B.