Table of Contents

**Introduction:**

The escape velocity of the Earth is substantially higher than that necessary to put an Earth satellite into orbit. The goal of satellites is to balance Earth’s gravity, not to escape it. The orbital velocity required to achieve a balance between gravity’s pull on the satellite and the inertia of the satellite’s motion (the satellite’s tendency to keep going) is known as orbital velocity. At an altitude of 150 miles, this is roughly 17,000 mph (27,359 kph) (242 kilometers).

In order to orbit the earth, satellites are launched from its surface. A number of rockets are launched from the satellite at the appropriate time to place it in the intended orbit. Once the satellite has been placed in the desired orbit at the precise speed, it will continue to move in that orbit due to the earth’s gravitational attraction.

The speed at which one body spins around another is known as the orbital velocity of a body or the orbital velocity of a satellite. Objects in orbit are those that travel in a consistent circular motion around the Earth. The distance between the object and the earth’s center determines the orbit’s velocity.

This velocity is frequently assigned to artificial satellites in order for them to rotate around a specific planet.

Let us assume the orbit’s radius be a and the planet’s speed in the orbit be u. The force on the planet equals its mass times the acceleration, according to Newton’s second law.

**⇒GMm/r²=m(v²/a)**

**v=√GM/a**

Hence the orbital velocity is given by the above-derived expression, where G = gravitational constant, M = mass of the body at center & R = radius of the orbit.

Note: If mass M and radius R are known, the orbital velocity formula can be used to compute the orbital velocity of any planet.

**Geostationary Satellite:**

The earth revolves once every 24 hours around its own axis (the line connecting the north and south poles). Assume a satellite is launched into orbit in the equatorial plane. Assume the satellite’s height is such that its time period is 24 hours and it moves in the same direction as the earth. The satellite will always be visible from a specific point on the equator. This satellite will appear to be stationary from Earth’s perspective. Geostationary satellites are one type of satellite. Satellites of this type are used for telecommunications, weather forecasting, and other purposes.

**Escape Velocity:**

In astronomy and space research, escape velocity is the velocity at which a body can escape from a gravitational center of attraction without further acceleration.

**Escape Velocity Derivation:**

When a stone is hurled up, it rises to its greatest height and then falls back down. The gravitational potential energy of the particle grows as it rises, whereas the kinetic energy of the particle decreases. The particle will continue to rise until its kinetic energy reaches zero, at which point it will return.

Let u be the initial velocity of the particle. Then kinetic energy can be written as,

**k=½mv²**

Gravitational potential energy,

**U=-GMm/R**

When the particles attain a height h above the earth surface, let’s say its speed becomes v,

So,

**The new kinetic energy =½mv²**

and

**The gravitational potential energy =-GMm/R+h**

By conservation of energy

**½mu²-GM m/R=1/2 m v²-GM m/R+h**

**½ m v²=[1/2 m u²-G M m/R]+GM m/R+h**

The particle will reach maximum height when v becomes zero (v=0)

Let say if

**1/2 mu²-G Mm/R≥0**

Thus 1/2mv² never becomes zero, so the particle will further keep on traveling away from the earth if

**1/2 mu²-GMm/R≥0**

Thus,

**u ≥ √2 G M/ R**

The above expression is known as the escape velocity.

**g=Gm / R²⇒ V _{escape }=√2gR**

**Escape and Orbital Velocity :**

Escape velocity is the speed at which a body must travel to escape the gravitational field of the earth. It has a speed of 11 km/s. The velocity necessary for a satellite to move in Earth’s orbit is known as orbital velocity. Its speed is 8 kilometers per second or 29000 kilometers per hour.

**Relationship between Escape and Orbital velocity:**

The relationship between escape velocity and orbital velocity in astrophysics can be stated mathematically as-

**V _{o}=V _{e }(2)^{1/2} or V _{e}=√2 V _{o}**

**Time Period of a Satellite:**

A satellite’s period is the amount of time it takes to complete one full orbit around an object. One year is the period of the Earth’s orbit around the sun. You can calculate the period of a satellite if you know its speed and the radius at which it orbits.

**T=2πa / v**

**⇒2π a (GM / a) ^{1/2 }=2π (GM)^{1/2 }a ^{3/2}**

Or

**T ^{2}=(4 π^{2 }/ GM) a ^{3}**

Newton’s laws control the movement of objects. The same fundamental laws that control the motion of objects on Earth apply to the motion of planets, moons, and other satellites in the skies. The mathematics used to describe the motion of a satellite is the same as that used to describe circular motion. We learned about Orbital Velocity, Orbital Velocity of a Satellite, Escape and Orbital Velocity and their link, Time Period of a Satellite, and other FAQs in this post. In subsequent portions of the Gravitation chapter, we’ll go over a few more theoretical and statistical ideas.I hope you find our work both educational and enjoyable to read.

Also read: **Brain Exercises for Better Thinking**

**Frequently Asked Questions (FAQs):**

**Question 1: How do you define Escape Velocity?**

**Answer:** “The speed at which a body must travel to escape the gravitational field of the earth.” It is common knowledge that an object pushed upward returns to the ground after reaching a certain height. This is owing to the downward force of gravity. The item soars to a larger height with enhanced initial velocity before returning. If we keep raising the object’s starting velocity, it will eventually stop returning to the ground. It will be able to break free from gravity’s grip. The initial velocity at which an object exits the earth’s gravitational field is referred to as E.V.

**Question 2: How do you define Orbital Velocity?**

**Answer:** 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. Gravitational fields prevent it from changing.

The earth, along with some other planets, orbits the sun in a nearly round course. Human-launched artificial satellites follow a nearly circular path around the globe as well. Orbital motion is the name for this type of movement.

**Question 3: How do rockets defy gravity on Earth?**

**Answer:** Any object traveling against the gravitational force requires escape velocity, as we know. The escape velocity from the earth is now known to be 11 km/s. To send rockets or anything into space, the escape velocity of the rocket or item must be greater than the escape velocity.