Escape Velocity Formula| Easy Explanation

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Escape speed is defined as the minimum speed or velocity necessary for a mass to be pushed from the earth’s surface in order to escape the planet’s gravitational attraction. In simple words, this is the speed at which an object must travel to escape the gravitational attraction exerted by our planet. The unit of escape speed or velocity is a meter per second (m.s^-1).

Escape velocity Formula- Derivation

Escape velocity (v_esc) is the velocity that a space shuttle must accomplish in order to escape the velocity of celestial bodies such as planets.

The kinetic energy (K.E) of the body on the earth’s surface when it is thrown vertically upward with escape velocity is given as:

K.E = 0.5 mv²_esc

Since the object is thrown with escape velocity will just reach to point where g=zero (at infinity). At that point, the absolute potential energy is zero and the body comes to rest. So increase in potential energy is the difference between potential energy at infinity (Infinity) and gravitational potential energy at the surface of the earth.

Increase in P.E = P.E at the surface of the earth – P.E at an infinite distance from the surface of the earth

Increase in P.E = 0 -(-GmM/R ) = GmM/R (from law of gravitation)

Similarly, From the law of conservation of energy, a loss in kinetic energy is equal to an increase in kinetic energy.

1/2mv_e² =GmM/R
v_e²=2GM/R
v_e=(2GM/R)^1/2 (Escape velocity formula) — (1)

Where:

• v_e is escape velocity
• G is the universal gravitational constant
• M is the mass of the body to be escaped from
• R is the distance from the centre of the mass

F=GMm/R² (Law of gravitation)
mg=GMm/R²
g=GM/R² — using the value of g in equation 1
v_e=(2gR)^1/2 (A simplified form of escape velocity formula)
v_esc=(2×9.8×6.4 x 10⁶) = 11km/sec
Note: The escape velocity for different planets in different

Factor affecting escape velocity

• Mass of a planet: Planets with greater mass are more difficult to escape than planets with less mass. This is due to the fact that the more mass a planet has, the stronger its gravitational pull.
• Radius: the distance between the centre of the planet and the object that is trying to escape.
• Newton’s universal constant of gravity (G): G is approximately equal to 6.67 × 10^–11 metres³/(kg)(second)².

Escape Velocity in Simple Terms

Escape velocity is the minimum speed that an object needs to reach in order to break free from the gravitational pull of a planet or other celestial body. In simple terms, it is the speed that an object must achieve to escape the gravity of a planet and continue moving away from it without falling back. The value of the escape velocity depends on the mass and radius of the planet, and it is typically higher for larger and more massive planets. To escape the Earth’s gravity, for example, an object needs to reach a speed of approximately 11.2 km/s (25,000 miles per hour).

Summary

• Escape velocity is defined as the minimum velocity required to drive a mass away from the Earth’s surface in order to escape the planet’s gravitational attraction.
• The unit of escape r velocity is a meter per second (m.s^-1).
• The escape velocity formula is given as v_e=(2GM/R)^1/2
• The escape velocity for the planet earth is 11 km/sec.

Frequently Asked Questions

1. What is the Gravitational field?

The space around the earth in which its gravitational force acts on a body is called the gravitational field. When an object is moved by the gravitational field, the work is done by the gravitational force. If the displacement is in the direction of gravitational force, the work is positive. If the displacement is against the gravitational force, the work is negative.

2. What is Elastic potential energy?

the energy stored in a compressed spring is the potential energy possessed by the spring due to its compressed state. This form of energy is Elastic potential energy.

3. What is escape velocity and how is it calculated?

Escape velocity is the minimum speed that an object needs to achieve in order to break free from the gravitational pull of a planet or other celestial body. It is calculated using the mass and radius of the planet and the gravitational constant. Refer full article details to find the formula of escape velocity.

4. How does the escape velocity of a planet depend on its mass and radius?

The escape velocity of a planet is directly proportional to the square root of its mass and inversely proportional to the square root of its radius.

5. What is the escape velocity of Earth and how was it determined?

The escape velocity of Earth is approximately 11.2 km/s, and it was determined by considering the energy required to move an object from Earth’s surface to an infinite distance away from it.

6. Can an object with a velocity below the escape velocity still leave the gravitational influence of a planet? If so, how?

The speed of an object in orbit is directly related to the escape velocity of a planet; if the object’s speed is less than the escape velocity, it will remain in orbit, while if it exceeds the escape velocity, it will escape the planet’s gravity.

7. What is the relationship between escape velocity and the kinetic energy of an object?

The kinetic energy of an object is directly proportional to the square of its velocity, so increasing the velocity of an object increases its kinetic energy and therefore its ability to escape a planet’s gravi

8. How does the escape velocity of the Moon compare to that of Earth?

The escape velocity of the Moon is much lower than that of Earth, at approximately 2.4 km/s.

9. How does the escape velocity of a planet affect the ability of spacecraft to enter and leave its orbit?

The higher the escape velocity of a planet, the more difficult it is for its atmosphere to retain gases, as they require more energy to remain bound to the planet.

The escape velocity of a planet affects the ability of spacecraft to enter and leave its orbit, as they must achieve a speed greater than the escape velocity to escape the planet’s gravity and travel to other locations in space.

10. Can the escape velocity of a planet be exceeded, and if so, what would happen?

If the escape velocity of a planet is exceeded, the object would leave the planet’s gravity and continue moving away from it.

More Links

Velocity Formula & Definition

Velocity Time Graph

How to Find Instantaneous Velocity

Can Velocity be Negative?

Critical Velocity| Fluids

Angular Momentum| Rotational Momentum

The Spring Constant & Spring Force Concept

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