Escape velocity is one of the most fundamental principles in the universe, but what exactly does it mean? How does it affect your life? To be honest, you probably have the most relevant and important escape velocity in your life right now, and you might not even realize it! This article will explain exactly what escape velocity means and how it affects your life – plus, we’ll show you how to calculate the escape velocity of Earth and other planets, so you can see how close to home the concept of escape velocity really gets! Read on to learn more about orbits and escape velocity!

 

Hyperbolic Orbit

A hyperbolic orbit is an elliptical orbit with one focus at infinity. This means that a satellite in a hyperbolic orbit has its velocity continuously increasing, which means it will eventually leave Earth’s gravitational pull completely; in other words, a satellite in a hyperbolic orbit will escape Earth’s gravity if given enough time. Escape velocity is how fast an object needs to be traveling relative to Earth (or another planet) in order for it never to fall back down again. It requires more energy than anything else because of Newton’s first law of motion: Objects in motion stay in motion unless acted upon by an outside force.

 

Elliptical Orbit

The path an object in space takes when it is being held around a planet by gravity. The main points of an elliptical orbit are that they have one main focus point, two points on either side where it is at its farthest away from that point, and two opposite points on either side where it is at its closest distance. The orbital velocity depends on your current distance from your center of mass. For example, if you are closer to your center of mass, then your orbital velocity will be lower than if you were farther away from it.

 

Hyperbola & Ellipse Combined

The two curves can be combined into a single ellipse by flattening both ends of a hyperbola, producing an ellipse with two foci (the center of an ellipse), as shown at right. The eccentricity in that case is: e = 1 − cot ⁡ θ {\displaystyle e=1-\cot \theta } . Another way to combine them is by making one end of a hyperbola tangent to an ellipse, which produces an elliptic orbit. In particular, if either focus of an ellipse lies on its major axis, then moving along any curve drawn from that focus will trace out a hyperbola.

 

Kepler’s 3rd Law

According to Kepler’s third law, which every physics student learns in school, every planet or satellite orbits its host star at a speed that is proportional to its distance from that star. The mathematical formulation of this law is somewhat complex, but in practical terms it means that planets orbiting further away from their stars will orbit slower than planets orbiting closer. This is because if an object travels a greater distance in one second, it must have been going faster—and so traveling further requires more energy. For example, an object traveling twice as far (and therefore moving at half speed) would require four times as much energy per second—that is, it would require four times more energy overall over time.

 

Earth & Mars Trajectories

So, let’s say you have a spaceship on Earth. If you could get that ship moving at a speed of 7 miles per second (11 km/s), it would escape Earth’s gravity. On Mars, though, you would need about 24 miles per second (39 km/s) to escape—over 3 times faster than Earth! So why is that? Well, in part because of how massive each planet is; for instance, Mars has roughly half of Earth’s mass.

 

Orbital Period and Semi-Major Axis

The two quantities that define an orbit’s size (and its shape) are orbital period and semi-major axis. The semi-major axis, semi for short, is a geometric figure of merit that equals half of an object’s average distance from its center of mass. In a circular orbit, at any given time interval t after launch, a spacecraft has traveled approximately 2*(semi) times around in its orbit. Since we know that x = v * t where x = distance traveled in meters, v = speed at which you’re traveling in m/s, and t = amount of time that has passed since launch in seconds, then all we need to do is solve for v when we plug our data into x=v*t!

 

Escape Velocity

The speed at which an object needs to travel in order to escape a gravitational field, like that of Earth. The escape velocity of Earth is about 11.2 km/s (7 miles per second). For comparison, current space vehicles travel at speeds around 7–8 km/s. To achieve escape velocity from Earth, a rocket would need to accelerate for about ten minutes. More advanced space travel systems might be able to reduce or eliminate that time by accelerating for a longer period of time, or by approaching perpendicular or on-plane with respect to Earth’s gravity well. But no matter how you slice it, achieving escape velocity requires serious power—and heavy machinery doesn’t come cheap!

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