When you throw a ball up into the air, why doesn’t it fly through the atmosphere and escape into outer space? This is because gravity pulls it back down. Then how does a rocket fly into outer space? It can fly into outer space because it is travelling at a very high velocity. This velocity is called escape velocity. The escape velocity of celestial bodies like planets and their natural satellites (the moon for us) is the minimum velocity that has to be achieved by an object, to escape the gravitational sphere of influence (pull or force or attraction) of the celestial body. At this velocity, the sum of the gravitational potential energy and kinetic energy of the system will be equal to zero.
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What is Escape Velocity?
Escape velocity is defined as the speed at which an object travels to break free from either the planet’s or moon’s gravity and leave without any development of propulsion.
Escape Velocity Equation
The escape velocity equation is obtained by equating the kinetic energy of an object with mass m and travelling with a velocity of v and gravitational potential energy of the same object.
\(\begin{array}{l} v_c = \sqrt {\frac {2GM}{r}}\end{array} \) |
where,
- vc is the escape velocity
- G is the universal gravitational constant
- M is the mass of the celestial object whose gravitational pull has to be superseded
- r is the distance from the object to the centre of mass of the body to be escaped
From this relation, it is obvious that escape velocities for larger planets (or celestial bodies) is greater since it will have a larger mass compared to smaller planets with a lower mass (having less gravity in comparison).
This video helps you understand the concept of escape velocity clearly.
Escape Velocity of Earth
For earth, the acceleration due to gravity, g = 9.8 m/s2
The radius of the earth, R = 6.4 × 106 m
The escape velocity of the earth, ve = √2 × 9.8 × 6.4 × 106
Therefore, ve = 11.2 × 103 m/s = 11.2 km/s
Escape Velocity of Different Objects
The following is the table with an escape velocity of different celestial bodies:
| Body | Escape Velocity in km/s |
| Sun | 618 km/s |
| Moon | 2.38 km/s |
| Earth | 11.2 km/s |
| Jupiter | 59.5 km/s |
| Ceres | 0.64 km/s |
Frequently Asked Questions – FAQs
What does escape velocity depend on?
Escape velocity depends on the mass and radius of the celestial body.
What is the difference between orbital velocity and escape velocity?
The difference between orbital velocity and escape velocity is that orbital velocity is the speed that is required to reach the orbit of a planet or star whereas escape velocity is the speed that is required to leave the orbit.
How is escape velocity and orbital velocity related?
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.
In our solar system, which planet has the highest escape velocity.
In our solar system, Jupiter has the highest escape velocity. The escape velocity of Saturn is 60.20 km/s.
In our solar system, which planet has the lowest escape velocity.
In our solar system, Mercury has the lowest escape velocity. The escape velocity of Mercury is 4.25 km/s.
Thanks it help me a lot.