Throw the disc at the sun too slowly and gravity reels it in; throw it fast enough and it slings past and never returns. The exact threshold between captured and free is escape velocity — and it depends only on the sun, not the disc.
Same sun, same start — only the launch speed differs. Below escape velocity gravity wins and the path closes into a loop; above it, the disc bends once and flies free. The dividing line is a single speed: √(2GM/r).
Escape velocity is the smallest speed an object needs to break free of a massive body's gravity and never fall back — with no engine, no further push. From Earth's surface it is about 11.2 km/s. The remarkable part: it depends only on the pulling body's mass and your distance from its centre, not on the mass of the thing escaping. A pebble and a rocket need the exact same speed.
Gravity pulls harder the closer you are and fades with distance, but never quite reaches zero. To escape, your outward kinetic energy must at least match the depth of the gravitational well — the work gravity would do dragging you back. Set ½mv² equal to GMm/r and solve: v = √(2GM/r). The escaping mass m cancels out, which is exactly why the answer is the same for everything — and it is √2 times the circular orbital speed at that height.
In The Field a sun sits at the centre and tugs the disc inward every frame. Launch it slowly and that pull curves the path into a closed, bound loop — the sun has captured it. Launch it past the threshold and gravity can bend the path only once before the disc outruns the pull and leaves for good. Start closer to the sun and the well is deeper, so the speed you need climbs — just as the formula promises.
Escape velocity is easiest to believe when you can dial the launch speed yourself and watch the path either close into a loop or fly off the screen. Launch the disc, nudge the speed up and down, and find the exact threshold for yourself.
The escape speed here is fixed by the sun and the launch distance. Below it gravity always wins and the loop closes; reach it and the disc never comes back.
To break free of Earth a launch must reach about 11.2 km/s — over thirty times the speed of sound. That single number is why a rocket is mostly fuel: nearly all its mass is spent buying that one speed.
The Moon's escape velocity is only about 2.4 km/s — too low to hold onto fast-moving gas molecules. Over billions of years they drifted away, which is why the Moon has almost no atmosphere.
Squeeze enough mass into a small enough space and the escape velocity climbs past the speed of light itself. At that boundary — the event horizon — not even light can leave, which is exactly what makes a black hole black.
Escape velocity is the single speed that separates "captured forever" from "gone for good". This FAQ travels from launchpads to airless moons, comets, and black holes — and the energy bookkeeping that ties them all together.
Escape velocity is the smallest speed an object needs, with no further push, to break free of a body's gravity and never fall back. Below it, gravity always wins and curves the path back down. Reach it, and the object coasts away forever, slowing but never stopping. From Earth's surface that speed is about 11.2 km/s — roughly thirty-three times the speed of sound.
The escape velocity is v = √(2GM/r). Here G is the gravitational constant (6.674×10⁻¹¹), M is the mass of the body you are leaving, and r is your distance from its centre. Bigger mass means a deeper gravity well and a higher escape speed; greater distance means a shallower well and a lower one. The mass of the escaping object never appears — which is why it cancels out completely.
No — escape velocity is the same for a feather and a freight rocket leaving the same place. In the energy balance ½mv² = GMm/r, the escaping mass m sits on both sides and cancels, so it drops out of the answer. A heavier craft does need more fuel and thrust to reach that speed, but the target speed itself is identical. This is the same reason all objects fall at the same rate in a vacuum.
| Property | Orbital velocity | Escape velocity |
|---|---|---|
| What it does | Holds a circular orbit | Breaks free forever |
| Formula | √(GM/r) | √(2GM/r) |
| Relationship | — | √2 × orbital (≈ 1.41×) |
| At Earth's surface | ≈ 7.9 km/s | ≈ 11.2 km/s |
| Resulting path | Closed loop | Open, never returns |
Plug Earth's numbers into v = √(2GM/r): a mass of about 5.97×10²⁴ kg and a radius of about 6.37×10⁶ m. The arithmetic gives roughly 11,200 m/s, or 11.2 km/s. That figure is set entirely by how much mass Earth has and how big it is. A more massive or more compact planet would demand a higher speed; a smaller one, less.
No — escape velocity is about speed, not direction. Whether you fire straight up or at a shallow angle, the minimum speed to escape is the same, because it depends only on energy, and kinetic energy ignores direction. In practice, launching eastward lets rockets borrow Earth's rotation, and a steeper path spends less time fighting air, but the underlying escape speed never changes with aim.
The Moon's escape velocity is only about 2.4 km/s — far lower than Earth's. Gas molecules at the Moon's temperature move fast enough that many exceed this speed, so over billions of years they have simply leaked away into space. A world can only hold an atmosphere if its escape velocity comfortably beats the typical speed of its gas molecules, which is why small, low-gravity bodies tend to be airless.
At a black hole's event horizon, the escape velocity reaches the speed of light, about 300,000 km/s. Since nothing can travel faster than light, nothing — not even light itself — can escape from inside that boundary. The same formula v = √(2GM/r) still applies: pack enough mass M into a small enough radius r and the required speed climbs past light speed. That limit is precisely what defines the edge of a black hole.
Escape velocity falls off as 1/√r — the farther out you start, the less you need. Because r sits under the square root, doubling your distance from the centre lowers the escape speed by a factor of √2, not 2. This is why launching from a high mountain or, better, from orbit already part-way out of the gravity well takes less speed to finish the escape than launching from the ground.
Yes — escape velocity is the speed needed for a single push with the engine then switched off. If a craft keeps its engine firing, it can climb away slowly and steadily at any speed, because it is constantly adding energy rather than coasting. A space elevator would carry cargo up at walking pace. Escape velocity only sets the bar for the "throw it and let go" case, like a cannonball or a coasting probe.
At exactly escape velocity the object follows a parabolic path: it slows steadily as it climbs but never quite stops, arriving at infinite distance with precisely zero speed left over. Just below that speed, the path is a closed ellipse and the object falls back. Just above it, the path is an open hyperbola and the object reaches the far distance still moving. Escape velocity is the knife-edge between these two families of paths.
Escape is an energy balance. The depth of the gravity well is the gravitational potential energy GMm/r, and motion carries kinetic energy ½mv². Setting the two equal — ½mv² = GMm/r — and solving for v gives √(2GM/r). To escape, your kinetic energy must at least pay off the whole well, leaving you with just enough to coast to infinity. This energy view is why escape velocity ignores both direction and the escaping mass.
Real rockets accelerate gradually because hitting 11.2 km/s in the thick lower atmosphere would create ruinous air drag and heating. Instead they climb steadily, building speed as the air thins, and often reach orbit first. Escape velocity is the figure for an unpowered object thrown once and left alone — a continuously thrusting rocket reaches escape on its own schedule, spending extra fuel to fight gravity and drag along the way.
No — every mass has an escape velocity, from a pebble to a galaxy. The formula v = √(2GM/r) works for moons (the Moon: 2.4 km/s), stars (the Sun's surface: about 618 km/s), asteroids (often just metres per second), and black holes (the speed of light). Wherever there is gravity, there is a speed that breaks free of it. The idea is completely general, not special to planets.
Isaac Newton imagined a cannon on a very tall mountain firing horizontally. Fire it gently and the ball arcs to the ground; fire it harder and it curves around farther; fire it hard enough and it falls "around" the Earth into orbit; harder still and it never comes back. That thought experiment, paired with his law of gravitation, contains escape velocity in seed form. The same logic now guides every interplanetary mission, from Voyager to the probes leaving the Solar System today.
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