Question

Two satellites A and B of the same mass are orbiting Earth in concentric orbits. The distance of satellite B from Earth’s center is twice that of satellite A. What is the ratio of the tangential speed of B to that of A?

Answer 1

Answer:

ratio of tangential velocity of satellite b and a will be 0.707

Explanation:

We have given distance of satellite B from satellite A is twice

So $r_b=2r_a$

Tangential speed of the satellite is given by

$v=\sqrt{\frac{GM}{r}}$, G is gravitational constant. M is mass of satellite and r is distance from the earth

We have to find the ratio of tangential velocities of b and a

From the relation we can see that tangential velocity is inversely proportional to square root of distance from earth

So $\frac{v_b}{v_a}=\sqrt{\frac{r_a}{r_b}}$

$\frac{v_b}{v_a}=\sqrt{\frac{r_a}{2r_a}}$

$\frac{v_b}{v_a}=\sqrt{\frac{1}{2}}$

$\frac{v_b}{v_a}=0.707$

So ratio of tangential velocity of satellite b and a will be 0.707

Answer 2

The ratio of tangential velocity of satellite B to satellite A is 0.707.

Tangential Speed of Satellite

The Tangential velocity is the linear speed of any object moving along a circular path. The tangential speed of the satellite is given below.

$v = \sqrt{\dfrac{Gm}{r}}$

Where v is the velocity, m is the mass and r is the circular distance. G is the gravitational constant.

Given that mass of both the satellite is the same. Let us consider the mass of both satellites as m. The distance of satellite B from Earth’s center is twice that of satellite A.

Let us consider that the distance of satellite A from the center of the earth is r. The distance of satellite B from the center of the earth is 2r.

The tangential speed of satellite A is,

$v_a = \sqrt{\dfrac {Gm}{r}}$

The tangential speed of satellite B is,

$v_b = \sqrt{\dfrac {Gm}{2r}}$

In the ratio form, the tangential speed of both satellites is given below.

$\dfrac {v_b}{v_a} = \dfrac {\sqrt{\dfrac {GM}{2r}} }{\sqrt{\dfrac {Gm}{r}} }$

$\dfrac {v_b}{v_a} = \sqrt{\dfrac{1}{2}}$

$\dfrac {v_b}{v_a} = 0.707$

Hence we can conclude that the ratio of tangential velocity of satellite B to satellite A is 0.707.

To know more about the tangential speed of satellites, follow the link given below.

https://brainly.com/question/21322214.