Before we go into orbit, let's discuss an important difference in physics. The difference between weight and mass.
(행성)궤도를 논하기 전에 먼저 질량(mass)과 중량(weight)의 차이를 살펴보자.
Mass is a property of an object that can describe as the ability for that object to resist acceleration. Weight on the other hand, depends on the local gravitational field.
Mass always stays the same. If my mass is 75 kilograms, I'll be 75 kilograms whether I'm here on Earth, on the Moon, or somewhere in deep space. But weight is actually a measurement of the force felt by an object within a gravitational field. Which means that weight can change in different gravities. It's a product of the mass and the local gravitational field. So, weight is equal to m times g, in multiples of one Earth gravity.
'질량'은 변함없는 '무게'다. 지구에 있든, 달에 있든 심지어 저 먼 심우주에 있든 같다. 반면 '중량'은 물체가 중력장에서 끌림으로 측정되는 값이다. 다른 중력장에서 중량의 값은 변한다. 중량은 질량에 중력 가속도를 곱한 값이다.
On the moon where gravity is roughly one-sixth of Earth's gravity, my mass is still 75 kilograms, but my weight is reduced by a factor of six. That means that on the moon, my weight would be 12.5 kilograms even though my mass is still 75 kilograms. What does it mean to be weightless if weight depends on the local gravity?
지구 중력가속도의 6분의 1에 해당하는 달에서 중량 75킬로그램은 12.5 킬로그램이 된다. 중량은 물체가 놓인 중력장(local gravitational field)에 따라 측정값이 달라진다.
Well imagine a region of space so far from stars and planets that the local gravitational field is very close to zero. What would someone with a mass of 75 kilograms feel when there is zero gravitational force on them. They would feel a weight of zero kilograms. So, when an astronaut is floating freely in space, are they weightless?
저멀리 별이나 행성의 중력이 미치지 않는(중력가속도가 0인) 깊은 우주로 나갔다고 상상해보자. 지구에서 중량 75킬로그램인 우주인이 자유롭게 떠 있으면 무게가 없어진다는 뜻인가?
No, it's a common misconception that astronauts experience weightlessness when they are above Earth's atmosphere where gravity is weak. In fact, there's still enough gravity in the environment around Earth that they have a measurable weight. However, this is different from experiencing free fall acceleration in a gravitational field that is not restricted by any other forces. Astronauts feel weightless because both the spacecraft that they're in and the astronauts themselves, are in a state of free fall above the earth. Astronauts feel weightless because both the spacecraft that they're in and the astronauts themselves, are in a state of free fall above the earth. A body is in free fall whenever gravity is the only force acting upon it.
그렇지 않다. 지구의 대기권 밖, 중력이 약한 곳으로 나간 우주인이 무게를 느끼지 못한다는 의미를 잘못 이해해서 생긴 오해다. [어째듯 둥둥 떠있는 모습을 보면 지표면 가까운 높이에서 자유낙하 하는 경우와는 다르긴하다.] 우주인뿐만 아니라 우주선도 지구상에서 자유낙하의 조건하에 있기는 매한가지다.
If I release a ball either here or from up high in space, the only force acting on the ball while it's moving is gravity. When it's moving it's in a state of free fall and experiences weightlessness. Since the force of gravity acts on it, the ball accelerates and moves towards the earth until it hits the Earth's surface.
만일 지금 선자리에서건 저높이 우주에서건 공을 놨다고 해보자. 공에 작용하는 힘은 오직 중력뿐이라면 공은 지구 표면으로 '자유낙하' 하며 떨어진다. [자유낙하: 지구 중심을 향해 지표면에 수직으로 떨어진다]
What do you think would happen when the ball is thrown horizontally?
만일 공을 수평으로 던지면 어떻게 될까?
Newton was the first to imagine what would happen if you climbed a tall mountain in order to fire a cannonball horizontally. Newton reason that the cannonball would curve towards the Earth due to gravity. If the cannonball was fired at a faster speed, it would go a longer distance. Eventually, if the cannonball could be fired fast enough, it would fall towards the ground on a curved trajectory that matches the curvature of Earth's surface. This was the first time someone had reckoned about orbital motion. This is very similar to how flying is described in Douglas Adams' A Hitchhiker's Guide to the Galaxy. Where it is stated, "There's an art to flying or rather a knack. The knack lies on learning how to throw yourself at the ground and miss."
뉴턴의 생각은 산정상에 올라가 대포를 수평방향으로 쏴보는 것이다. 지구 중력에 이끌려 포물선을 그리며 떨어질 것이다. 좀더 빠른 속도로 쏘면 더 멀리 가서 떨어진다. 아예 궤도를 도는 속도로 쏠 수도 있을 것이다.
When an astronaut orbits the Earth in the International Space Station, the only force acting on the astronaut is gravity. The astronaut is travelling in a stable orbit around the Earth. So although gravity is pulling on the astronaut towards the earth, the circular motion makes it possible for the astronaut to miss the Earth.
One way to experience weightlessness without being in orbit or at a vast distance from the earth, is to fly in an airplane on a parabolic trajectory. Special aircraft that can withstand many times the force of gravity navigate to a high altitude before climbing into an inverted parabolic flight path. During the arc of the parabola the airplane and the occupants within it only experienced the force of gravity and therefore they feel weightless. These moments feel like zero gravity but they only last about 20 seconds. The airplane can't stay in free fall for very long, for obvious reasons.
"T minus 15 second. Guidance is internal. 12, 11, 10, 9, ignition sequence starts. 6, 5, 4, 3, 2, 1, 0. All engines (are) in running. Lift-off. We have a lift-off. 32 minutes. . . . . Lift-off on the Apollo 11."
Rockets like the Saturn V, that carried the crew of the Apollo 11 mission to the Moon must expend energy to climb through Earth's gravitational field. The speed of a spacecraft dictates how high it will go in a given scenario. So just how much energy is required for a rocket to escape from a planet entirely.
인간을 달로 보낸 새턴 V 로켓은 지구 중력을 벗어나기 위해 얼마나 많은 에너지가 필요할까?
Let's consider an example of a rocket escaping from Earth. Kinetic Energy is the energy associated with the speed of an object, which is supplied to a rocket by burning fuel and expelling it from the rocket's nozzles. The energy required to break the gravitational grasp of a planet like Earth, depends on the mass of the planet as well as its size. When a speed is associated with kinetic energy of a departing rocket, we call it the Escape Velocity.
Earth has an escape velocity which is roughly 11.2 kilometers per second, which is more than 40,000 kilometers per hour. But let's not get too carried away, getting to space is much more complicated than merely getting a vehicle to the right speeds. This calculation considers the pure physics involved in climbing out of the gravitational potential well. So, we ignore otherwise important factors like air resistance. 11.2 kilometers per second is the instantaneous velocity you'd need traveling directly upwards from earth's surface in order to escape earth's gravitational well. At sea level,11.2 kilometers per second is equivalent to Mach 33, which is fast enough to make the air around the spaceship into a boiling plasma, so instead, rockets accelerate out of our atmosphere starting from a standstill.
Although we used Apollo 11 to introduce you to the concept of escape velocity, it's worth pointing out that in order to reach the moon, the astronauts never exceeded Earth's escape velocity at all. The moon is gravitationally bound to Earth and a voyage there hasn't escaped from Earth's gravitational sphere of influence. The moon itself is also trapped within Earth's gravitational well. Out of all the spacecraft launched by humanity, only a few have achieved Earth's escape velocity. Those spacecraft which traveled to other planets in our solar system. But a small subset of spacecraft have voyaged well beyond the earth's grasp and escaped from the gravitational pull of the entire solar system.
One such spacecraft Voyager 2, launched in 1977 and is now considered to be an interstellar traveler. The red line in this graph represents the changes in speed experienced by Voyager 2, from 1977 to 1989 on its journey past the outer planets.
In order for Voyager 2 to achieve escape velocity from our solar system, it needed a gravity assist from the planet Jupiter. A gravity assist is a way for a space probe to boost its kinetic energy by stealing the orbital energy from a heavy body like Jupiter. Over the course of Voyager 2's transit through the solar system, it was repeatedly boosted by encounters with planets, Saturn, Uranus and Neptune. At present, Voyager 2 is traveling at 15.4 kilometers per second on its way to the outermost edge of our solar system.
By contrast, the fastest humans have ever traveled was accomplished by the crew of Apollo 10 in 1969, achieving a top speed of nearly 11.08 kilometers per second. However, their speed record was on their way back through Earth's atmosphere and not on the way out. But even faster than the Voyager spacecraft, the current speed record held by a human object is the New Horizons probe, which took pictures of Pluto in a Flyby in 2015. New Horizons accelerated away from Earth achieving a whopping 16.26 kilometers per second, making it the fastest spacecraft ever launched.
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Deriving the formula for escape velocity is relatively straightforward. It involves setting the gravitational potential energy equation of an object on the surface of a body which is GMm over r, equal to its kinetic energy which is equal to one-half m v squared.
Since the little m mass, which represents the mass of the object you want to move, appears on both sides of the equation, we can eliminate those from the equation altogether. This means that the escape velocity of an object does not depend on its own mass.
We can finally rearrange the terms of this equation solving for v_e the escape velocity. So, escape velocity v_e, can be calculated by multiplying two times the universal gravitational constant G, times the mass of the body capital M and dividing by the radius of the body's surface r, all taken underneath a square root sign. So, increasing the mass of a body will increase its escape velocity and decreasing the radius of a body, will also increase its escape velocity.
위에서 얻은 탈출속도 공식을 살펴보면, 탈출속도는 운동하는 물체의 질량 m 과는 상관없이 끌어당기는 물체의 질량 M 에 비례하고 거리 r 에 반비례 한다. 질량 M이 무거울 수록 탈출 속도는 높아야 하며 멀어질 수록 탈출 속도는 낮아진다.
In order for spacecraft to escape from Earth, escape velocity is required to ensure the gravitational potential well can be climbed. In fact, if you'd like to explore these ideas further, we've created an escape velocity calculator that you can use to plan a mission across the Solar System.
우주선이 지구를 벗어나려면 탈출속도는 지구중력 포텐셜 우물을 넘어서야 한다. 태양계를 벗어나려는 우주선의 탈출 속도는 얼마가 되어야 하는지 계산해 볼 수도 있다.
* 지구로부터 탈출하기 위해서는 11.2 km/s의 속도면 되지만, 태양으로부터 탈출하기 위해서는 617.5 km/s의 속도가 필요하다. 지구에서 탈출하기 위해 단숨에 탈출속도에 도달하기는 어렵다. 질량 M 에서 멀어지면서 서서히 속도를 증가시키다 어느 순간 탈출 속도에 도달하면 지구 중력을 벗어날 수 있다. 실제로 거대한 로켓이 지구에서 발사되면 서서히 가속되면서 마침내 탈출속도에 이를 수 있다. 보이져 우주 탐사선의 경우 1977년에 발사되어 43년이 지난 현재 태양계 최외곽을 벗어나는 중이다. 자체 추진력으로 태양계 탈출속도에 이를 만큼의 자체 추진력을 가지고 있지 않다. 긴 시간 동안 목성과 토성등 거대한 행성의 인력에 도움을 받아(gravity assist) 가속되었다.
오늘날 대부분 심우주 우주 탐사선들은 태양의 인력을 벗어나기 위해 행성의 중력을 이용한다. 혜성 탐사선 로제타의 경우 소형 탐사선으로 자체 추진력은 없이 12년간 지구를 세번씩 접근하면서 가속되었다. 비행 궤도는 지구뿐만 아니라 화성, 심지어 대형 소행성의 중력을 이용한 비행이었다.
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What could escape velocity possibly have to do with black holes? Well, chew on this for a minute. What if we calculated the density of an object for which the speed of light is equal to the object's escape velocity? The answer is something sinister, something dark.
그렇다면 빛조차 끌어들인다는 블랙홀에서 탈출할 수 있는 속도는 얼마나 될까? 탈출속도가 빛의 속도와 같은 물체의 밀도를 계산 할 수 있을까? [탈출 속도는 움직이는 물체의 질량과 무관 하다 해도 질량이 없는 광자와 거대질량의 블랙홀 사이의 인력은 합당하지도 않다.] 이에 대한 답을 뉴튼역학(고전역학)으로 구하기는 모순되는 점이 많다.
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