Question

Two satellites are in circular orbits around Earth. Satellite A has speed vA. Satellite B has an orbital radius nine times that of satellite A. What is the speed of Satellite B?

A. vA.9
B. vA/3
C. 3vA
D. 9vA

Answer 1

Answer:

option B

Explanation:

given,

Satellite B has an orbital radius nine times that of satellite A.

R' = 9 R

now, orbital velocity of the satellite A

$v_a =\sqrt{\dfrac{GM}{R}}$........(1)

now, orbital velocity of satellite B

$v_b=\sqrt{\dfrac{GM}{R'}}$

$v_b=\sqrt{\dfrac{GM}{9R}}$

$v_b=\dfrac{1}{3}\sqrt{\dfrac{GM}{R}}$

from equation 1

$v_b=\dfrac{v_a}{3}$

hence, the correct answer is option B

Answer 2

The speed of satellite B will be "$\frac{V_A}{3}$".

According to the question,

The orbital speed of satellite A will be:

→ $V_A = \sqrt{\frac{9M}{R_A} }$

if,

• $R_B = 9R_A$

then,

Speed of satellite B will be:

→ $V_B = \sqrt{\frac{9M}{9R_A} }$

        $= \frac{1}{3} V_A$

        $= \frac{V_A}{3}$

Thus the above answer i.e., "option B" is right.

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