Introduction
Understanding the difference between escape velocity and orbital velocity is essential for exams like JEE, NEET and other competitive exams. This topic is crucial in physics, space science, and celestial mechanics.
Relationship between Escape and Orbital Velocity
Deriving the relation between escape velocity and orbital velocity equation is very important to understand the concept. For any, massive body or planet.
The relationship between escape velocity and orbital velocity can be mathematically represented as:
Escape velocity is given by :
Ve = √2GM/R
Orbital velocity is given by :
Vo = √GM/R
Meanwhile, if we divide the above equations, we get,
\(\begin{array}{l}\frac{{{v}_{e}}}{{{v}_{o}}}=\frac{\sqrt{\frac{2GM}{R}}}{\sqrt{\frac{GM}{R}}}\end{array} \)
\(\begin{array}{l}\Rightarrow \frac{{{v}_{e}}}{{{v}_{o}}}=\sqrt{2}\end{array} \)
It shows that escape velocity is √2 times greater than orbital velocity.
Certain conditions need to be taken into consideration. The main one is that the escape velocity should be a square root of 2 times larger than the orbital velocity to be free.
- When the velocities are the same, the object will be in constant orbit and at the same elevation.
- If escape velocity is less than orbital, then the orbit will diminish, which will result in the object crashing.
- If it is more, then the object will be free in orbit and will likely float into space.
- If orbital velocity increases, the escape velocity will also increase and vise-versa.
- If orbital velocity decreases, the escape velocity will also decrease and vise-versa.
Difference Between Escape Velocity and Orbital Velocity
| Parameter | Escape Velocity | Orbital Velocity |
|---|---|---|
| Definition | The minimum speed needed for an object to escape from a celestial body’s gravitational pull without further propulsion. | The velocity required for an object to stay in a stable orbit around a celestial body. |
| Formula | Ve = √2gR or Ve = √2GM/R | Vo = √GM/R or Vo = √gR |
| Magnitude | Higher than orbital velocity. | Lower than escape velocity. |
| Dependence on Gravity | Depends on the mass and radius of the celestial body. | Also depends on the mass and radius of the celestial body. |
| Application | Used for launching spacecrafts out of Earth’s gravitational field. | Used for satellites to orbit planets. |
| Example | Rockets leaving Earth for deep space missions. | Satellites like GPS, ISS orbiting Earth. |
FAQs on Escape and Orbital Velocity
Q1. Why is escape velocity greater than orbital velocity?
A: Escape velocity must overcome the entire gravitational pull of the celestial body, whereas orbital velocity only needs to balance gravitational attraction.
Q2. What is the escape velocity of Earth?
A: Approximately 11.2 km/s.
Q3. What is the orbital velocity of a satellite around Earth?
A: Around 7.9 km/s at low Earth orbit.
Q4. Can a satellite in orbit achieve escape velocity?
A: Yes, if additional thrust is applied, a satellite can reach escape velocity and leave Earth’s gravitational field.
Q5. What happens if an object moves faster than orbital velocity but less than escape velocity?
A: It will enter an elliptical orbit rather than escaping completely.
Q6. What is escape velocity?
A: Escape velocity is the minimum velocity required to overcome the gravitational potential of a massive body and escape to infinity.
Q7. What is orbital velocity?
A: Orbital velocity is the velocity with which an object revolves around a massive body. The relation between escape velocity and orbital velocity are proportional.
Q8. How escape velocity and orbital velocity are related?
A: Escape velocity is a function of orbital velocity for an object. Escape velocity is derived by considering the product of orbital velocity and the square root of 2. Also, the gravitational field that controls the orbit can be obtained.
Q9. Which planet has the highest escape velocity in our solar system?
A: In our solar system, Jupiter has the highest escape velocity. The escape velocity of Saturn is 60.20 km/s.
MCQs on Escape and Orbital Velocity
Q1. What is the primary difference between escape velocity and orbital velocity?
A) Escape velocity is always lower than orbital velocity.
B) Escape velocity is the speed required to leave the gravitational field, while orbital velocity keeps an object in orbit.
C) Orbital velocity is required for deep space missions.
D) Escape velocity is only needed for satellites.
Answer: B
Explanation: Escape velocity allows an object to leave a gravitational field, whereas orbital velocity allows it to stay in orbit.
Q2. If Earth’s radius were doubled, how would escape velocity change?
A) It would double.
B) It would be halved.
C) It would increase by √2
D) It would decrease by √2
Answer: D
Explanation: Since escape velocity is inversely proportional to the square root of the radius, doubling the radius reduces escape velocity by a factor of √2.
Conclusion
Understanding escape velocity vs. orbital velocity is essential for physics, astronomy, and space exploration. These concepts play a key role in designing satellites, launching rockets, and exploring celestial bodies.
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Written by: Neeraj Anand
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