Gravitation-Variations in g-Orbital Speed of Satellite

A satellite moves around the Earth in a circular motion. When a satellite is sent into orbit, gravity is the single factor that determines its motion. Artificial satellites and natural satellites are the two types of satellites. Natural satellites, such as the moon, orbit the earth naturally, whereas artificial satellites are constructed on purpose to provide a specific role for us.

What Is Orbital Velocity?

The speed at which the orbital speed of the body, which is usually a planet or natural satellite, is defined as the rate at which it circles around the system’s centre. The system usually revolves in orbit around a large body. The speed of the orbit of Earth around the sun’s orbit is 108,000 kilometres per hour. With the help of the formula presented, it is linking the mass of a certain planet to the radius and gravitational constant. The formula for orbital speed includes an integral constant, G  which is known as the “universal gravitational constant.”

So, we can formulate it as: 

6.673 x 10-11 N m² kg-²

Here, the value of the radius is 6.38 x 106 m.

The objects that travel in a continuous round motion about the Earth are considered to be “in orbital motion.” The speed of the orbit is determined by the distance of your object’s centre to Earth. The velocity must be such that the distance from Earth’s centre remains constant. This is why calculating orbital speed is so important.

At an altitude of 242 km, the orbital speed is 27,359 km per hour. If there is no gravity, it will be carried off in space with the inertia of the satellite.

Let us check out the orbital speed of satellite definition and orbital speed of satellite formula.

The orbital velocity or orbital speed of satellite is described by:

Vorbit = √GM/R

In the equation above, G stands for Gravitational Constant, M represents the object’s weight in the centre, and R represents the radius of the orbit.

The Orbital Velocity Equation is used to calculate how fast the orbital motion of a star is if the radius and mass of M are established.

This unit to describe Orbital Velocity is metres per second (m/s).

Variations in Satellite G-Orbital Speed

Because determining the orbital speed of a satellite and period is significantly easier in circular orbits, we use that assumption in the following derivation. 

An object with negative total energy is gravitationally bound and so revolves in an orbit. This will be confirmed by our calculations for the particular case of circular orbits. We focus on objects circling the Earth, but our findings may be applied to other situations too.

Consider a mass m satellite in a circular orbit around Earth at a distance R from the planet’s centre. It moves with a centripetal acceleration toward the Earth’s centre. The sole force at work is the Earth’s gravity.

We solve for the speed of the orbit, noting that M cancels, to get the orbital speed

Vorbit = √GM/R

The orbital speed, the escape velocity and the value of G are not influenced by the object mass that is being acted upon but the distance of the planet from its centre.

Notice the similarity in the equations for Vorbit and Vesc. 

The escape velocity is exactly √2 times greater, about 40%, than the orbital velocity. It is true for a satellite at any radius.

Ve = √2GM/r

The escape velocity of Earth is much greater than the velocity required to place an Earth satellite in orbit. Orbital speed refers to the speed required to maintain the balance between gravity’s pull on the satellite as well as the inertia that the satellite experiences due to its movement. It is about 27,359 km/h at an altitude of 242 kilometres.

In the absence of gravitational force, inertia and momentum of the satellite will propel it away into space. However, even with gravity, the satellite is too fast, and, eventually, it will go off in a whirlwind. If the satellite travels too slowly, gravity will pull it back towards Earth. Therefore, when the satellite is at the correct pace of its orbit, gravity compensates for that satellite’s inertia.

Now, to find the period of a circular orbit, we note that the satellite travels the circumference of the orbit 2πr in one period T. Using the definition of speed, we have vorbit = 2πr/T

We substitute this in the equation and rearrange it to get

T = 2π√R³/GM

The velocity of all trajectories that impact the Earth’s surface is less than orbital velocity. The astronauts would feel weightless as they accelerated toward Earth along the noncircular trajectories illustrated. Astronauts prepare for life in orbit by free falling for 30 seconds at a time in an aircraft. However, if their orbital velocity is accurate, the Earth’s surface bends away from them at the same pace as they fall toward Earth. The objective of a circular orbit, of course, is to maintain the same distance from the surface.

Conclusion

A body’s orbital velocity is the speed at which it circles around another body. An orbit is known as the path of an object going around the Earth in a regular circular motion. The velocity of this orbit is determined by the distance between the item in question and the earth’s centre. Because manmade satellites may rotate around any planet, this velocity is commonly connected with them. If you know an object’s mass and radius, you can use the Orbital Velocity Formula to compute its orbital velocity.