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Introduction
Orbital Velocity can be defined as the speed at which a celestial body, mainly a satellite, revolves around the orbit of another celestial body. The satellite revolves around a celestial body always greater in mass than the satellite.
The Formula:
The orbital velocity formula for any revolving object is given by, Where,
Vorbit=GMR
G is the gravitational constant, and its value is 6.67310-11 Nm2/kg2.
M denotes the mass of the body at its centre.
R denotes the orbit’s radius.
Orbital velocity
The motion of an object in the earth’s orbit is known as orbital motion. Orbital velocity is the rate at which an object moves around the earth’s orbit. It is constant in the gravitational field.
The earth, along with some other planets, orbits the sun in a nearly circular path. Human-launched artificial satellites follow a nearly circular path around the earth as well. Orbital motion is the name for this type of movement. This velocity can be calculated by the formula:
Vorbit = GMR
Where,
G denotes the gravitational constant
M denotes the mass of the body at the centre
And, R denotes the radius of the orbit
Relationship Between Escape And Orbital Velocity
The smallest velocity required for an object to escape the gravitational force of a planet or object is its escape velocity. Ve = 2Vo, where Ve is the escape velocity, and Vo is the orbital velocity, defines the relationship between the escape velocity and the orbital velocity. And the escape velocity is two times the orbit velocity divided by two.
In rocket science and space travel, escape velocity is the velocity required for an object (such as a rocket) to escape the gravitational orbit of a celestial body (such as a planet or a star). In kinematics, we discovered that the range of a projectile is determined by its initial velocity. Rmax= u2/2g, which means that the particle flies away from the gravitational impact of the earth at a given initial velocity.
The velocity of escape is the smallest amount of velocity with which a particle can escape the planet’s gravitational sphere of influence (ve). When a body is given an escape velocity, it theoretically travels to infinity. Because gravitational force is a conservative force, the energy conservation law holds true. Applying the law of energy conservation for a particle with the required minimum velocity to infinity
Ui + Ki = Uf + Kf
The particles have no interaction at infinity, so the final potential energy is zero. And we know that the final velocity of the body is zero after reaching its maximum height, so we can deduce the particle’s final kinetic energy is also zero.
Then,
Ui + Ki = 0 and we know that, Ui = −GMm / R , Ki= (½)mve2
We get,
(1/2)mve2+ ( −GMm/ R ) = 0
⇒ (1/2)mve2= GMm / R
That implies,
ve= √ 2GM / R ……………(1)
The above formula clearly shows that the escape velocity is independent of the test mass (m). If the source mass is the earth, the escape velocity is 11.2 km/s. When v = ve, the body leaves the gravitational field or control of the planets; when 0≤ v< ve, the body either falls to Earth or continues to orbit the Earth within its sphere of influence.
Orbital Velocity of a Satellite
It basically refers to the amount of velocity required by a satellite to be launched into the orbit of a planetary system.
We have also cleared the concept of the orbital speed of a satellite. To put it in simple terms, the amount of speed required by a satellite to orbit around a planetary system without losing its momentum is known as orbital speed.
For your better understanding, we have also discussed the formula by which you can calculate the orbit speed of a satellite.
The orbital velocity of a satellite is the velocity required by the satellite to balance the gravitational pull and the inertia of the satellite’s motion. This concept can be further explained with the following example:
- Take, for instance, that we use a device to launch a certain object horizontally across the earth’s surface.
- At some point in time, the object would orbit across the earth’s surface for a certain distance and eventually fall on the earth’s surface.
- If we consider using a device that can create a velocity or speed of the exact amount that can launch the object into the earth’s orbit, the object would get stuck in the earth’s orbit and would not return to the surface.
- This velocity is known as the orbital velocity, and this same concept is used in space physics to launch satellites into the earth’s surface.
Hence, this velocity required for a satellite to find a balance between the gravitational pull of the earth and the inertia of its motion is known as the orbital velocity of a satellite.
Speed of satellite
The formula for centripetal force and gravitation is used to derive the equation for calculating the speed for the orbital velocity of a satellite.
To circle an orbit of the earth, which is almost 35,786 km far from the earth’s surface, the satellite would have to maintain a velocity of about 11,300 km/h. This orbital speed and distance allow the satellite to revolve around the earth in 24 hours.
Conclusion:
The orbital velocity is the speed required by a satellite to maintain a balance between the gravitational pull of the celestial body or planet it is orbiting and the inertia of its motion.
In simple terms, orbital velocity can be defined as the speed or velocity required by a satellite to keep orbiting a celestial body without losing velocity. Also, the satellite revolves around a celestial body that is always greater in mass than the satellite.
