The minimal velocity needed for an object to leave a celestial body like a planet or moon and travel into space without being drawn back is known as its escape velocity. It's a fundamental concept for space travel and understanding the motions of celestial bodies.

The mass and radius of the celestial body affect the escape velocity. Larger bodies with the greater mass will require higher escape velocities. The concept is essential to spacecraft design and mission planning because it gives them the necessary speed to overcome gravity and explore depth of the space.

Escape Velocity Formula :

Mathematically, escape velocity is calculated using the formula :

ve = √2GM / r
Where :
  • ve is Escape Velocity
  • G is the Gravitational Constant
  • M is the mass of the Celestial Body
  • r is the distance from the center of the body to the object

Escape Velocity Derivation :

The escape velocity, denoted as ve can be derived using the principles of conservation of energy. The derivation involves setting the initial kinetic energy of the object equal to the negative of its potential energy at the point of launch.

1. Kinetic Energy (KE) at launch:

The kinetic energy of an object with mass m and velocity v is given by :

KE = ½ mv2

2. Potential Energy (PE) at the surface of the celestial body:

The potential energy of an object of mass m at a distance r from the center of a celestial body with mass M is given by :

PE = - GMm / r
where G is the gravitational constant.

3. Conservation of Energy:

At launch, the total mechanical energy (sum of kinetic and potential energy) is conserved. Therefore:

KE + PE = 0
By substituting KE and PE values from above formula :
½ mve2 - GMm / r = 0
½ mve2 = GMm / r
Multiply both sides by 2/m :
ve2 = 2GM / r
Take the square root of both sides to solve for :
ve = √2GM / r

This is the escape velocity formula. It shows that the escape velocity (ve) is equal to the square root of 2GM/r, G is gravitational constant, M is mass of the celestial body, and r is the distance from the center of the celestial body to the object.

Units of Escape Velocity :

Escape velocity is typically measured in units of speed, such as :
  • meters per second (m/s)
  • kilometers per seconds (km/s)
  • kilometers per hour (km/h)
  • centmeters per second (cm/s)
  • miles per hour (mi/h)
  • feet per second (ft/s)
  • yards per second(yd/s)

Escape Velocity of Planets :

Escape Velocities of Planets
Escape Velocity of Earth :

According to calculations made at the Earth's surface, the escape velocity of Earth is roughly 11.2 km/s, or 6.95 mi/s. This means that in order for an object to overcome Earth's gravitational pull and escape into space, it must achieve a speed of at least 11.2 km/s relative to Earth's surface.

Escape Velocity of Moon :

The escape velocity of the Moon is about 2.38 kilometers per second (km/s), or roughly 1.48 miles per second (mi/s). This means that in order for an object to leave the Moon's gravitational influence and travel into space, it needs to have a minimum speed of 2.38 km/s relative to the Moon's surface.

Escape Velocity of Mercury :

The escape velocity of Mercury which is the the closest planet to the Sun in the solar system, is approximately 4.25 kilometers per second (km/s), or roughly 2.64 miles per second (mi/s). This value represents the minimum speed required for an object to break free from Mercury's gravitational pull and travel into space.

Escape Velocity of Venus :

The escape velocity of Venus which is the second planet from the Sun in the solar system, is approximately 10.36 kilometers per second (km/s), or 6.44 miles per second (mi/s). This escape velocity represents the minimum speed required for an object to overcome Venus' gravitational pull and leave its surface without being drawn back.
Due to Venus having a mass and radius similar to Earth's, its escape velocity is also relatively close to Earth's.

Escape Velocity of Mars :

The escape velocity of Mars which is the fourth planet from the Sun in our solar system, is approximately 5.03 kilometers per second (km/s), or roughly 3.13 miles per second (mi/s). This value denotes the minimum speed needed for an object to break free from Mars' gravitational pull and move into space without being pulled back.

Escape Velocity of Jupiter :

The escape velocity of Jupiter, the largest planet in our solar system, is approximately 59.5 kilometers per second (km/s), or about 37 miles per second (mi/s). This value represents the minimum speed required for an object to break free from Jupiter's immense gravitational pull and travel into space without being drawn back.

Escape Velocity of Saturn :

The escape velocity of Saturn, the sixth planet from the Sun in our solar system, is approximately 36.09 kilometers per second (km/s), or about 22.4 miles per second (mi/s). This value signifies the minimum speed required for an object to overcome Saturn's gravitational pull and travel into space without being pulled back.

Escape Velocity of Uranus :

The escape velocity of Uranus, which is the seventh planet from the Sun in our solar system, is approximately 21.3 kilometers per second (km/s), or about 13.3 miles per second (mi/s). This value represents the minimum speed required for an object to break free from Uranus' gravitational pull and travel into space without being drawn back.
Uranus' escape velocity is determine by its mass and size, which are smaller than those of gas giants like Jupiter and Saturn but still substantial enough to require significant velocity for escape.

Escape Velocity of Neptune :

The escape velocity of Neptune which is the eighth and outermost planet in our solar system, is approximately 23.5 kilometers per second (km/s), or about 14.6 miles per second (mi/s). This figure denotes the minimum speed required for an object to overcome Neptune's gravitational pull and venture into space without being pulled back.

Escape Velocity of Pluto :

The escape velocity of Pluto, which once considered the ninth planet in our solar system but now classified as a dwarf planet, is approximately 1.2 kilometers per second (km/s), or about 0.75 miles per second (mi/s). This value represents the minimum speed required for an object to break free from Pluto's gravitational pull and travel into space without being pulled back.

Why to use our Escape Velocity Calculator?

Our Escape Velocity Calculator is a valuable tool for anyone interested in understanding the dynamics of space travel and celestial bodies. By using this calculator, you can quickly and accurately determine the escape velocity of various celestial objects, including planets, moons, and dwarf planets. Whether you're a student exploring the principles of physics and astronomy, an engineer designing spacecraft missions, or an enthusiast curious about space exploration, our Escape Velocity Calculator provides instant access to essential information. With just a few inputs, you can calculate the minimum speed required for objects to break free from the gravitational pull of celestial bodies, aiding in mission planning, spacecraft design, and scientific exploration. Accessible and user-friendly, our calculator empowers individuals to explore the fascinating realm of space and deepen their understanding of the universe's dynamics.