Orbital Velocity

Earth’s orbit constitutes several satellites that hover for miles around the planet’s surface in a constant motion. How’s that possible? That’s where you derive the orbital velocity importance and how it protonates the motion with proper velocity. Everything moving against the gravitational fields needs power, or it might crash down to the ground in seconds.

The orbital velocity is the required force that helps any projectile retain the constant motion while gravity tries to defy it hard. The elliptical or orbital path around the planet defines the exact point that creates a balance between gravity and inertia. 

Orbital velocity retaliates the power of gravity and weakens it when applied at a particular distance and altitude. Please keep reading to know more about it.

What is Orbital Velocity?

The pace (speed) required by any celestial object like the satellite, star, or the planet to revolve around the earth’s orbit is known as the orbital velocity. It is calculated to acquire the sustained speed which:

• Falls on a similar line as that of the projectile’s rotational velocity.
• Has enough power to pull the object with the force of gravity towards the body’s surface.

The best example to understand the orbital velocity importance is the pace at which an aeroplane travels to the sky and that of a satellite. The aeroplane flies high due to its engine and does not have enough velocity to sustain the gravitational force after the engine turns off.

On the contrary, the satellite does not need additional power to remain around the earth’s orbit. It surpasses the gravitational force and retains an accurate orbital velocity to function effectively. The orbital velocity of any object is directly proportional to the distance at which it rotates around the planet in space.  

Factors affecting Orbital Velocity

Orbital or the circular motion of an object around the planet or any other celestial body results in the orbital velocity. The object follows the straight path through the curvature, which prevents it from falling. Perhaps, this is possible only when the object retains a specific speed.

As the principle of inertia is applicable in space, the probability of objects maintaining a constant speed increases here. As per Sir Isaac Newton’s Laws of Inertia, an object in motion stays in motion unless acted through an outside force. Inside the earth’s atmosphere, the flying object might counter several air molecules that slow down the object’s speed moving through the sky.

Orbital Velocity Equation

Here is the equation for orbital velocity given by:

In this equation,

vo= GMr

G is denoted for gravitational constant,

M is denoted for the body mass in the centre,

And r is denoted for the radius of the central object.

This equation helps determine the orbital velocity of the planet when you have the details about M (mass) and R (radius).

The dedicated unit for orbital velocity expression is m/s.

How to Get the Expression for Orbital Velocity?

To know the exact value of orbital velocity, learning about the centripetal force and the gravitational force is imperative. This is the actual force that results in orbiting. The planet’s gravitational force helps the projectile retain the exact force that allows it to revolve in orbit. And the centripetal force leads to the circular motion of the objects in orbit.

FC=mvo22

For the formula derivation, pick a mass satellite that rotates around the earth in orbit with r as the radius and has the height from the planet’s surface. 

Hence, we derive:

r=R+h

Now, the centripetal force is necessary for the motion of a satellite that is furnished through the gravitational force. It is the applicable force amongst the planet and the projectile. 

Fg=GmMr2

FC=Fg

mvo22=GmMr2

vo2=GMr

vo=GMr= GMR+h

Since g is the acceleration due to gravity, there its value will be: 

mg= GMmR2 

g= GMR2

GM=gR2

On substituting the value of g in the above (i) equation, we get: 

vo=gR2R+h

If the satellite is very close to the earth, then  R+h ≈ R

vo= gR

Conclusion

Orbital velocity is a critical and scoring chapter of physics. It is the foundation to get a notch on the motion of a satellite around the earth. If you know all about what orbital velocity is, it is also possible to understand and derive the formula for its relationship with the escape velocity. Brush up your concepts to score well ahead.