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Orbital Velocity

Two artificia...

Question

Two artificial satellites of masses $m_{1}$ and $m_{2}$ are moving with speeds $v_{1}$ and $v_{2}$ in orbits of radii $r_{1}$ and $r_{2}$ respectively. If $r_{1} > r_{2}$ , then which of the following statements is true?

$v_{1} = v_{2}$

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$v_{1} > v_{2}$

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$v_{1} < v_{2}$

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$\frac{v_{1}}{r_{1}} \frac{v_{2}}{r_{2}}$

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Solution

The correct option is C
$v_{1} < v_{2}$

Orbital velocity:
The velocity at which a body of an entity revolves around the other one in an orbit is called orbital velocity.
Orbital velocity is expressed in $meter per second (m / s)$ .
An object throughout orbit is one that moves in a regular circular motion around the Earth. This same velocity of this orbit is determined by the distance seen between the object and the middle of the Earth.
Mathematically, orbital velocity can be represented as:
$v = \sqrt{\frac{GM}{r}}$
Here,
G is the gravitational constant.
M is the center body's mass.
r is the radius of the orbit.
and,
mass is constant.
Now,
$v \propto \frac{1}{r}$
Thus,
$r_{1} > r_{2} \Rightarrow v_{2} > v_{1}$
Therefore, option C is correct.

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