Respuesta :
Answer:
Explanation:
Given
Satellite A has a mass of 7 m and at a radius of 5 r
Satellite B has a mass of 8 m and at a radius of 8 r
Orbital velocity is the velocity required by a satellite to remain in its orbit
Orbital velocity can be find by equating centripetal force on satellite and Force of gravitation between satellite and Planet
[tex]\frac{1}{2}mv^2=\frac{GMm}{r^2}[/tex]
[tex]v_{orbit}=\sqrt{\frac{GM}{r}}[/tex]
where M=mass of Planet
m=mass of body
r=distance from center of Planet
We can say that orbital velocity is independent of mass of satellite
For satellite A
[tex]v_{a}=\sqrt{\frac{GM}{5r}}----1[/tex]
For satellite B
[tex]v_{b}=\sqrt{\frac{GM}{8r}}----2[/tex]
divide 1 and 2 we get
[tex]\frac{v_b}{v_a}=\frac{\sqrt{\frac{GM}{8r}}}{\sqrt{\frac{GM}{5r}}}[/tex]
[tex]\frac{v_b}{v_a}=\sqrt{\frac{5}{8}}[/tex]
The ratio of the orbital velocity of satellite B to satellite A is [tex]\sqrt{\dfrac {5}{7}[/tex].
Option 2 is the correct answer.
Orbital Velocity
A velocity of a satellite is required to place or maintain that satellite in a given orbit is called the orbital velocity of the satellite.
The orbital speed of the satellite can be calculated by the formula given below.
[tex]v = \sqrt{\dfrac {Gm}{R}}[/tex]
Where v is the orbital velocity, M is the mass and R is the radius of the satellite. G is the gravitational constant.
Given that, there are two satellites A and B orbit the Earth in the same plane. For satellite A, mass m1 is 7m and radii r1 is 5r. For satellite B, mass m2 is 8m and radii r2 is 8r.
The orbital velocity for satellite A is given as,
[tex]v_A = \sqrt{\dfrac {G\times 7m}{5r}}[/tex]
The orbital velocity for satellite B is given as,
[tex]v_B= \sqrt{\dfrac {G\times 8m}{8r}}[/tex]
The ratio of the orbital velocities of both the satellite is,
[tex]\dfrac {v_B}{v_A} = \dfrac {\sqrt{\dfrac {G\times 8m}{8r}}}{ \sqrt{\dfrac {G\times 7m}{5r}}}[/tex]
[tex]\dfrac {v_B}{v_A} = \sqrt{\dfrac {5}{7}}[/tex]
Hence we can conclude that the ratio of the orbital velocity of satellite B to satellite A is [tex]\sqrt{\dfrac {5}{7}[/tex]. Option 2 is the correct answer.
To know more about the orbital velocity, follow the link given below.
https://brainly.com/question/16040381.
