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Escape Velocity Calculator

Select the physical parameter (escape velocity, planet mass, or planet radius) and the calculator will employ the physical escape velocity equation to find its value

I want to calculate

Planet Mass

The Planet (M)

kg ▾

Orbit Radius (r)

m ▾

The Planet (R)

Sun's mass (Mc)

Radius G

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Use this free escape velocity calculator to estimate the minimum speed an object must achieve to break free from a planet's gravitational pull. This guide will help you understand the concept and calculations behind escape velocity.

What Is Escape Velocity?

In physics:

"Escape velocity is the lowest speed an object must reach to move away from a celestial body without further propulsion."

Escape Velocity Illustration

Earth’s Escape Velocity

The escape velocity for Earth is:

11.2 km/s
6.96 miles/s

Escape Velocity Formula

Given a planet's mass and radius, escape velocity is calculated using:

V_e = √(2GM / R)

Where:

M = Mass of the planet
R = Radius of the planet
G = Gravitational constant = 6.67 × 10^-11 N·m²/kg²

It is also known as the second cosmic velocity.

Launch Energy

An object launched into space possesses both kinetic and potential energy. The total energy is:

Kinetic Energy + Potential Energy = ½ mv² - GMm/R

When the object escapes the gravitational field:

Potential energy → 0
Kinetic energy → 0 (ideally)

Thus, total energy at escape: 0 + 0 = 0

Escape Velocity of Solar System Bodies

Location	Relative To	V_e (km/s)
Sun	Sun's gravity	617.5
Mercury	Mercury's gravity	4.25
Venus	Venus's gravity	10.36
Earth	Earth's gravity	11.19
Moon	Moon's gravity	2.38
Mars	Mars' gravity	5.03
Jupiter	Jupiter's gravity	60.20
Saturn	Saturn's gravity	36.09
Uranus	Uranus' gravity	21.38
Neptune	Neptune's gravity	23.56
Pluto	Pluto's gravity	1.23

Our calculator automatically selects escape velocity for your chosen planet or star.

Example Calculation

Find the escape velocity for a satellite orbiting Neptune.

Given:

Mass of Neptune: M = 1.024 × 10²⁶ kg
Radius of Neptune: R = 24,622 km = 24,622,000 m

Solution:

V_e = √(2GM / R)

Substitute values:

V_e = √(2 × 6.67 × 10^-11 × 1.024 × 10²⁶ / 24,622,000)

Step 1: Multiply numerator:

2 × 6.67 × 10^-11 × 1.024 × 10²⁶ = 1.364 × 10¹⁶

Step 2: Divide by radius:

1.364 × 10¹⁶ / 24,622,000 ≈ 5.54 × 10¹¹

Step 3: Square root:

V_e ≈ √(5.54 × 10¹¹) ≈ 744,000 m/s ≈ 0.744 km/s

💡 Use the escape velocity calculator for instant results!

How the Calculator Works

Input:

Choose to calculate Escape Velocity, Planet Mass, or Planet Radius
Select the planet or star
Enter the required parameters
Click Calculate

Output:

Escape velocity
First cosmic velocity
Orbital speed
Third cosmic velocity
Orbital period

FAQs

Is Earth's gravity zero at some height?

Gravity never completely disappears. Its effect weakens with distance but is always present.

Acceleration due to gravity on Earth?

Standard value: 9.8 m/s² at sea level.

How massive is the Sun?

Approximately 1.989 × 10³⁰ kg.

Why is escape velocity “minimum”?

It’s the least speed needed to leave a planet's gravity without extra propulsion.

Does zero gravity exist?

No, gravity is everywhere. Weightlessness is due to free-fall conditions in orbit.

How massive is a black hole?

Stellar black holes: ~10 solar masses. Supermassive black holes: millions/billions of solar masses. Escape velocity can be calculated near black holes.

Conclusion

Escape velocity is essential for launching satellites and spacecraft safely. This calculator simplifies determining the minimum speed needed to overcome a planet or star's gravity.

References

From Wikipedia: Escape velocity
From Khan Academy: Gravity and Orbits
From Lumen Learning: Black Holes

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