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Home > News & Articles > Orbital Velocity Formula: Definitions, Examples, Derivations, Calculations, Transverse, Space Exploration, and Sample Questions
Updated on 26th October, 2023 , 4 min read
The orbital velocity formula is the speed that enables a satellite, whether natural or manufactured, to stay in orbit. The formula used to determine a body's velocity as it orbits another body is known as the orbital velocity formula. Artificial satellites use orbital velocity to help them rotate around a certain planet. Any planet's orbital velocity may be computed using its known mass M and radius R. Metres per second (m/s) is the unit of measurement.
The speed at which an object's location changes in relation to time and a frame of reference. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction. It has a meter per second (msâ»Â¹) SI unit. A body is considered to be accelerating if its velocity changes, either in magnitude or direction.
The orbital velocity of a body is the apparent rate of rotation around another body. An object's regular, circular travel around the Earth is referred to as an orbit. The orbital velocity increases with the mass of the body in the center of attraction for a given height or distance. Orbital velocity is defined as the speed required to keep a satellite in orbit, whether it is man-made or natural. It is frequently used by space organizations to plan satellite launches. It helps scientists figure out the velocities at which satellites should orbit a planet or other celestial body to avoid colliding with it.
If the muzzle velocity of a cannon shot from a hilltop is increased, the bullet will go farther. It is possible to imagine the Earth's surface bending away from the projectile or satellite at the same rate as it is falling in its direction. The orbital velocity is inversely proportional to the body's radius and directly proportional to the mass of the body for which it is being computed.
The height of a satellite in orbit around the Earth affects its orbital velocity. The closer a satellite is to the Earth, the higher its orbital velocity. It is equal to the square root of the ratio of the orbital radius divided by the product of the gravitational constant and the body's mass. The Orbital velocity formula is as follows-
The ideas of gravitational force and centripetal force are used to obtain the formula for orbital velocity. Assume a satellite with a mass of m and a radius of r is circling the planet Earth in a circle at a height of h above the surface. Let's imagine that the Earth has a mass of M and a radius of R. This suggests that,
We now understand that a centripetal force of mV²/r is necessary to cause the satellite to rotate inside its orbit. The gravitational pull that exists between the satellite and the earth provides this force.
So, we have
mV²/r = GMm/r²
V² = GM/r
Using (1), we have
V² = GM/(R + h)
As (R + h) ≈ R, we get,
This yields the equation for an object's or satellite's orbital velocity around a planet.
The transverse orbital velocity is proportional to the separation from the central body due to Kepler's second law, often known as the law of conservation of angular momentum. No matter what section of the body's orbit it marks over a set length of time, the line from the core to the body sweeps a constant area of the orbital plane as the body goes around its orbit.
In space exploration, orbital velocity is a crucial topic. Space authorities heavily rely on it to understand how to launch satellites. It aids scientists in figuring out the velocities at which satellites must orbit a planet or other celestial body to prevent collapsing into it. The two most crucial parameters required to design a satellite or space mission are orbital velocity and escape velocity. These two things are frequently used to solve problems in competitive exams.
Solution: Earth's radial distance, planetary mass, and satellite separation from Earth's surface are the following factors that influence orbital velocity.
Solution: The mass is observed to not be impacted by orbital velocity when considering the mass of a satellite (not the mass of the body that orbits).
Must Read: Value of e.
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By - Nikita Parmar 2023-08-25 09:48:44 , 11 min readAns. A satellite’s orbital speed can be used to determine its orbit.
Ans. By taking into account the gravitational force, which supplies the centripetal force necessary to maintain the orbit, the formula for orbital speed is obtained.
Ans. The Earth orbits at a speed of 30 km/s.
Ans. The radius of the plane, the satellite’s distance from the Earth’s surface, and the planetary mass all affect the orbital velocity.
Ans. A body’s minimal velocity need to sustain an orbit around the planet may be calculated using the straightforward formula Derivation of Orbital Velocity.
Ans. The velocity needed for a natural or manufactured satellite to stay in its specific orbit is known as the orbital velocity.
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