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Escape Velocity Formula

Educational Resources. This was a fun publicity stunt. But how the Roadster got to space is an even cooler story. The Roadster hitched a ride on the newest SpaceX rocket, the Falcon Heavy , as it made its maiden voyage into space.

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At the time of its launch, the Falcon Heavy was the most powerful operational rocket in the world though not in history. You might be wondering about how hard it is to launch something that large. How fast does it need to go? But why is the escape velocity the same, no matter the mass of the object? The reason is that mass and escape velocity are not related.

For example, say you wanted to drive km in an hour. It would not matter if you were driving a tiny car or a big transport truck. So what exactly is the escape velocity from the surface of the Earth?

It is a whopping At that speed, you could travel from the North Pole to the South Pole in about 21 minutes! Most satellites and spacecraft sent into space do not reach escape velocity! If a rocket goes fast enough and high enough to enter space but does not reach escape velocity, it will enter orbit around the Earth. The International Space Station and many satellites orbit the Earth. Escape velocity depends on a number of factors. Scientists have determined that the escape velocity for any large object such as a planet or star can be calculated from the following equation:.

The M in the equation represents the mass of the planet. Planets with more mass are harder to escape than planets with less mass. This is because the more mass a planet has, the stronger its force of gravity. For example, when you watch footage of astronauts jumping on the Moon, it looks effortless. As of , only 24 humans have ever reached escape velocity.


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They were the crews of the Apollo missions that flew to the Moon between and The r in the equation represents radius , which is the distance between the centre of the planet and the object that is trying to escape. In other words, radius is the distance between the centre of the planet and its surface.

If the object moves far enough away, it feels almost no attraction. When this happens, the escape velocity will basically be zero!

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Finally, the G in the equation is a constant. For the moment, all you need to know is that we need this constant to make the equation work. G is approximately equal to 6. For M, we use the mass of the Earth, which is approximately 5. Escape velocity equals the square roots of 2GM over r which equals the square root of 2 times 6. You can calculate the escape velocity from any body in space as long as you know its radius and its mass. For example, using the above equation, we can calculate the escape velocity of the Moon.

From its equator, the Moon has a radius of 1 km. It also has an estimated mass of 7. That is much less than the In the future, perhaps rockets will be built on and take off from the Moon rather than from Earth! The escape velocity of Mars is 4. The escape velocity of Earth is The escape velocity of Venus is The escape velocity of Mars is 5.

The escape velocity of Saturn is The escape velocity of Uranus is The escape velocity of Neptune is The escape velocity of Jupiter is All we need to do is accelerate the rocket to As the scientists and engineers at SpaceX know well, acceleration and pointing the rockets are the hard part! It was the rocket used to get astronauts to the Moon in the s and s. Is the cost and risk of sending spacecraft beyond Earth orbit justified by the scientific gains? Barnett, A. SpaceX Falcon Heavy: How it stacks up with other massive rockets. You are confusing velocity and acceleration.

If you have a high enough velocity, the effect of de acceleration can not slow you down before you get far enough away from the gravitational source. The problem is that would require constant thrust. The escape velocity is only for objects thrown projected into space , with the initial velocity and they are not powered.

Escape velocity is the speed at which you'll leave the Earth and not return if you don't continue to propel your craft. Below that speed, gravity will pull you back down. XKCD's got one of the more accessible explanations. The key difference is that "escape velocity" is how fast you would have to throw a stone straight up from the Earth's surface ignoring air drag , for it to escape from Earth's gravitational influence. It would be coasting the whole way, always losing speed due to Earth's gravitational pull. If, on the other hand, you have a rocket engine with sufficient fuel, you can just keep rising slowly 1 mph , which is almost a hover, until you've gotten way out into space and Earth's gravity is overwhelmed by the Sun, Jupiter, etc.

You could keep throttling back to maintain the same upward speed gravity decreases with distance, and the rocket carries less fuel if you wanted to, or let the rocket speed up. Unless you are very far away from Earth, if you are only moving away at 1 mph the gravity of Earth will pull you back to Earth assuming you do not have an infinite fuel supply to maintain a 1mph thrust. So you are correct when you say. Is it because the object has to gain a certain speed once it reaches orbit in order to maintain that altitude. Think of a ball tossed in the air, it starts by moving quickly, but as it rises higher it goes slower, than stops and falls back down.

At some point it is moving away from Earth at 1mph, but gravity overcomes that momentum. Air Resistance has some impact on the ball, but you can throw horizontally much farther than you can up. Gravity works pretty much them same on the surface of the Earth as it does a miles up. When you throw something horizontally it falls towards the earth in an arc, attracted by the gravity of the Earth. If it is moving fast enough the curvature of the Earth will match the arc of the falling object, this is called Orbital speed and the object will not hit the earth. If you had a nearly infinite fuel supply, and you kept moving away from Earth at 1 mph, yes you could escape.

You could do this with a solar sail there are a couple of issues using the sail near Earth but assuming you start in a high stable orbit, you could easily expand until your escape. Of note, using a solar sail, as you move farther from Earth your speed would increase unless you lowered the efficiency of the sail. In other words, if you started with a solar sail to get 1 mph thrust, you would need to work to maintain that speed, otherwise you would soon be going faster. Looking at this in another way, consider the concept of gravity wells.

The gravity well of course is not a "real", physical well, but it is a commonly used metaphor to describe how much energy is required to escape from the gravitational effect of a body, and it provides a reasonably straight-forward way of answering your question. Space buffs, bear with me below; this is meant as an explanation, not a university-level physics and astronomy lecture. If you are at or near the bottom of a gravity well say, at the surface of the Earth and want to climb out of that well, you basically have two options. Either climb very fast for a short distance this is the approach taken for getting off the surface of the Earth, for reasons stated in other answers , or climb slowly for a much longer distance this works once you are far enough away from the body forming the gravity well that the predominant gravitational forces acting on you are small or negligible.

Each way of looking at it represents the same thing: you provide some sort of energy input, usually in terms of fuel of some kind, which is used to climb the "side" of the gravity well.

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The energy provided as input becomes potential energy as you climb farther from the surface, and at some point, your potential energy exceeds the gravitational pull at that point of the body that forms the gravity well; you "continue on a tangent" and move straight on from that point forward rather than following the curve of the gravity well. Once that happens, you have reached escape velocity from that body. If you don't climb far enough for your rate of climb at the time you stop actively climbing, then when you stop climbing let's assume you cannot grab hold of anything, because in space there is nothing to hold on to you will fall back toward the body that forms the gravity well you are trying to climb out of; you did not attain escape velocity.

Of course, there are usually multiple gravitational forces to contend with at any one point. However, one of them will project a stronger force on you than the others; that's the concept behind the sphere of influence. Near Earth yes, that most definitely includes low Earth orbit , it's Earth's gravity that dominates; take a trip to Luna and its gravity will exert the greater force once you pass the Earth-Moon system L1 Lagrangian point.

Hence, the depth of Earth's gravity well is approximately Wikipedia gives the escape velocity at 9, km above the Earth's surface as 7. To get outside the hill sphere and into "solar space" rather than being in "Earth Space" , you're looking at years of continuous 1.


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Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site the association bonus does not count. Would you like to answer one of these unanswered questions instead? Home Questions Tags Users Unanswered. Couldn't I escape Earth's gravity traveling only 1 mph 0. Ask Question. Asked 5 years, 5 months ago. Active 11 months ago.

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Viewed k times. What initial speed do you need to reach infinite distance to the planet. It takes infinite time to get there, but the escape velocity has the necessary kinetic energy for infinity. To reach a low or higher orbit, less energy and velocity is needed. Anthony X Anthony X Everyone 7, 21 21 silver badges bronze badges. The waste is so gigantic that this is impossible. By that standard, isn't every orbital calculation an academic exercise?