Beth Drops a Bouncy Ball Which Bounces Back Up Again

Get fix.

Nosotros're going to start with an ordinary baseball game and an ordinary basketball, and we're going to finish up on a grand bout of the solar system. Really.

What practice I need?
A lawn tennis brawl
A basketball

You've probably noticed that if you drop even the bounciest of tennis balls from a height, it never bounces back higher than where it started. When you drop the brawl, gravity pulls it downwards and it picks up speed. It hits the ground and squashes at the moment of impact. Equally the squashed ball springs back to its original shape, information technology pushes on the floor and the floor pushes back. The force of the floor pushing confronting the ball throws the ball back up into the air.

The reason it doesn't bounce higher than where it started is elementary: some of the ball's energy is lost as heat when information technology bounces, and so it doesn't have as much going up every bit it did coming down. Knowing that, y'all might figure that a ball could never bounciness higher than the summit from which is was dropped. And you might remember that this word doesn't accept much to do with expanding the orbit of the world. But, equally happens then often with science, y'all'll exist surprised on both counts.

Try this!

Hold the basketball and the tennis brawl at the aforementioned height, one in each paw. Drib them both to the floor at the aforementioned fourth dimension. If you scout, you'll see that both balls volition only bounce most iii-quarters of the height from which they were dropped.

Now, hold the lawn tennis ball on peak of the basketball, and drop the two together. What happens to the tennis ball? Information technology takes off like a rocket, bouncing back much higher than where it started.

What's going on?

The assurance accelerate toward the floor and are going about 4 meters/2nd when they hitting. The basketball hits the floor first and reverses direction, heading upward at 4 meters/second. The tennis ball is still going down at 4 meters/2nd.

At least, that's how fast the tennis brawl is going if you're watching it from the ground. But what if you lot were a tiny person standing on the surface of the basketball? You'd see the tennis ball traveling toward yous at eight meters/second. Its speed relative to you would exist 8 meters/second.

If that sounds hard to comprehend, think of this analogy: Let's say you're driving down the road at 60 miles per hour. A car on the other side of the route is coming toward you at sixty mph. Relative to the road, you're both traveling threescore mph. Merely if you were to run into each other, the impact would be the sum of how fast each of you were travelling -- in other words, 120 mph.

Now, back to the bouncing balls. The lawn tennis ball smacks into the basketball and heads in the other direction. Since little free energy is lost in the collision, the tennis ball leaves the basketball at virtually the aforementioned speed at which it arrived. Considering the basketball is more massive than the tennis ball, the collision doesn't ho-hum down the basketball much. The lawn tennis brawl, on the other hand, reverses direction. From your viewpoint on the basketball, the relative speed of the assurance remains abiding. After the balls hit, they separate at 8 meters/second.

Ah, but here's the catchy bit. For a person standing on the ground and watching the assurance bounce, the picture is unlike. That basketball game is still moving up at 4 meters/second. The tennis ball is going up viii meters/second faster than the basketball. So, relative to someone exterior either of the balls, the tennis ball is moving up at 12 meters/2nd, rather than just 4 meters/2d. That's triple its original speed with respect to the globe! With and so much speed, the ball bounces 9 times higher than the tiptop from which information technology was dropped, over your head and hopefully not into whatsoever household furnishings.

Where did it become the energy to do this? From the basketball. It takes a lot of energy to move that massive basketball game. When the tennis brawl bounced off the basketball game, it gained just a little bit of the basketball's kinetic energy. If you watched really closely, you'd discover that the basketball dropped in tandem with the tennis ball doesn't bounciness quite as high as the basketball dropped solitary. That's because the tennis ball stole a chip of the basketball's energy.

The general rule is easy: when a ball bounces off a much heavier moving object and doesn't lose any free energy to heat, it reverses its management and gains twice the speed of the object information technology bounced off of. This means that a baseball leaves the batter at the speed the pitcher threw the ball plus twice the speed of the bat (minus some speed lost as a result of estrus). It besides means that a golf ball that is initially at rest leaves the tee at twice the speed of the striking club head (once more minus a bit for heat).

That'southward nice. Simply what does it have to exercise with spacecraft and orbits?

Permit's start with the gravitational assists fabricated by NASA spacecraft. These "slingshots" advance the spacecraft, helping it make the distance to Jupiter, Saturn, or whatsoever its destination may be.

Allow's say you've got a spacecraft that's orbiting the sun at the same distance as the earth. The spacecraft is traveling in the opposite management as the world--the earth orbits counterclockwise, and the spacecraft orbits clockwise. Both are going thirty kilometers/second. The spacecraft comes in towards the planet, swings around it in a cosmic do-se-exercise, and leaves moving out along the line of its approach.

Fifty-fifty though the spacecraft went around the Earth, rather than running into it, it's considered a planetary collision, sort of similar the lawn tennis ball and basketball game hitting each other. Information technology's chosen a collision because the spacecraft acts like it'due south merely hit something: it reverses direction and heads back the other way at well-nigh the same speed. Or at least that's what you see if yous're standing on the Earth. But suppose you back upwardly and look at the standoff in the frame of the afar stars. And so y'all see a spacecraft initially orbiting the sun at 30 kilometers/second. After the standoff, you run across a spacecraft going 90 kilometers/2d! The spacecraft is leaving the earth at 60 kilometers/second and the earth is going thirty kilometers/second and so lx + 30 = 90! That'due south fast enough to requite the spacecraft escape velocity from the sun, heading out toward interstellar space along a hyperbolic trajectory. The spacecraft gains kinetic free energy in this encounter. Where does that energy come from? Well, just every bit the come across with the tennis ball slowed the basketball down, the encounter with Galileo slowed the earth down. Not past much, of course. When the Galileo spacecraft swung by earth, it sped up by over 16,000 kilometers per hour with respect to the dominicus, and the globe slowed down by ten billionths of a centimeter per year. To increase the diameter of the Earth's orbit, we'd but need to switch roles; use a slingshot to advance the Earth, rather than the Earth to accelerating a spacecraft. That would entail a very massive enough object -- say, 1018 kilograms (the size of a large asteroid). If the asteroid were brought in from the aforementioned management as the Earth is orbiting, it would all the same swing by and be sent back the way it came into space. Merely because of its mass, information technology would exert a gravitational pull on the planet, nudging us just a wee bit wider in our orbit. According to Korycansky, who devised the Earth-moving idea, if we arranged for 6000 fly-bys of the navigational asteroid over the next billion years, we could slowly move the planet into what would exist a habitable distance from the dominicus once information technology'due south begun its expansion. At present that'southward planning ahead.

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Source: https://www.exploratorium.edu/theworld/slingshot/encounters.html