Author Topic: Acceleration  (Read 5984 times)

Offline ka9q

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Re: Acceleration
« Reply #15 on: June 29, 2018, 05:52:15 PM »
Upward. As you stand on the earth, you feel a force pushing up on the bottom of your feet that's indistinguishable from standing inside a spacecraft in deep space far from any planet or star while a rocket engine under your feet accelerates you in the direction of your head at 9.8 m/s^2.

This is Einstein's "Equivalence Principle" at the heart of general relativity (GR). He assumed this was true and then worked out all the implications. One of those implications is that time passes more slowly in an accelerated frame relative to an inertial frame, and this has been demonstrated experimentally many times.

The atomic clocks on the global positioning satellites appear to run faster than atomic clocks here on the earth because we're being accelerated by gravity to a greater degree due to our lower altitude. That's "gravitational blueshift". At the same time, an observer on a GPS satellite comparing the local spacecraft clocks to time transmissions from clocks on the earth's surface would see the surface clocks appear to run faster than the local spacecraft clock; that's a gravitational red shift.

This is distinct from, but related to, the time dilation from special relativity (SR) that applies to observers in different inertial coordinate systems, i.e., in which all the observers feel "weightless". It also resolves the famous "twin paradox" from SR, in which an astronaut who flies rapidly away from the earth and then returns will be younger than his twin who stayed behind even though during the coasting phases of flight both perceived their twin's time as passing more slowly than their own. The reason is that the astronaut twin had to accelerate to achieve his high departure velocity, then he had to accelerate again to cancel that velocity and create a high velocity back to earth, and then the effects of GR kick in.

Note that in space flight, the effects of GR and SR are often in opposite directions, with one (usually GR) dominating; that's the case with GPS. On earth, GR is also easier to demonstrate with atomic clocks than SR though both have been done. It's easier to just go up a mountain and wait for a while than it is to maintain a high velocity relative to the earth.

Einstein did something similar when he derived special relativity (which he did before general relativity). He made a very simple assumption that the speed of light was exactly the same in every inertial reference frame regardless of the relative velocities of source and observer. And then he followed that to all its logical conclusions.

This is all pretty mind-bending, but both SR and GR are firmly supported by mountains of experimental evidence. That's the difference between real science and pseudoscience; real scientists will accept all sorts of weird and seemingly counter-intuitive things provided they're supported by the evidence.
« Last Edit: June 29, 2018, 05:59:36 PM by ka9q »

Offline smartcooky

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Re: Acceleration
« Reply #16 on: June 29, 2018, 07:52:08 PM »
For a long time, I never understood how a gravity-assist planetary flyby could work to accelerate a spacecraft. To me it seemed that the gravitational attraction of the planet would remain the same before and after closest approach, so any velocity gained while approaching would be lost while receding. That was until I saw a graphical representation of the two Voyager encounters with Jupiter... it was an epiphany, or as Homer Simpson would say... Doh!.

I was thinking in terms of the planet (in this case Jupiter) being the reference frame, when in fact, the Solar System was the reference frame, and the planet itself is moving at orbital velocity. This meant that after closest approach, Jupiter was still moving along in its orbit, along with its gravity well, and not in the same place relative to Voyager as it was on approach, i.e. the approach and recession paths were not identical mirror images of each other....
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Offline ka9q

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Re: Acceleration
« Reply #17 on: June 29, 2018, 09:38:11 PM »
That's right. Actually, the term "slingshot" tells it all. A spacecraft flyby of Jupiter wouldn't do anything if Jupiter wasn't moving in its own solar orbit.

If you fly by the orbital trailing side of Jupiter (the usual case), then Jupiter "drags" it along as it orbits, transferring some of its (enormous) orbital kinetic energy to your spacecraft.

If you fly by Jupiter's leading side, the planet pulls back on you and you lose some of your own energy to the planet. You'd do that if you wanted to fall into the inner solar system (e.g., to closely approach the sun at high speed). Another reason would be to do a big plane change out of the ecliptic, as was done with Ulysses.

All these maneuvers would be very expensive to do on your own with chemical rockets. But if you do have a rocket, you can fire it at perijove and get an even bigger kick thanks to the Oberth effect. That's because the mechanical power a rocket delivers to its payload is directly proportional to its velocity, and you're going pretty fast on a close hyperbolic flyby of a planet as massive as Jupiter.

For the same reason, if you're in an elliptical orbit and you want to escape entirely, do your burn at perigee. I knew this when I saw the SpaceX Falcon 9 Heavy from San Diego as it approached second perigee but I didn't actually expect to see the escape burn because perigee occurred somewhat after LOS to our east. But it made sense given that they probably wanted to observe the burn from SpaceX in Hawthorne, near Los Angeles. Pretty neat sight.

If you really want to go out of the solar system in style you could do a flyby of Jupiter to remove most of your orbital energy, dropping you into a elliptical orbit with a very low perihelion. Then as you're racing around the sun (trying very hard not to burn up) you fire your own engine. I saw a paper proposal to do exactly this to catch up with I1, the first known interstellar asteroid that passed through our solar system last fall. (I forget its Hawaiian name.) The maneuver was actually more complicated than this, it required flybys of both Jupiter and Saturn to get the necessary plane change as well as the necessary velocity to escape the sun and catch up with that thing.
« Last Edit: June 29, 2018, 09:47:11 PM by ka9q »

Offline molesworth

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Re: Acceleration
« Reply #18 on: June 30, 2018, 04:34:36 AM »
My usual explanation, when people ask about gravity assists / slingshots, is to use the example of throwing a ball at e.g. a moving train.  If the train is coming towards you at, say 50 mph, and you throw the ball towards it at 20 mph it bounces off at 120 mph!  (Give or take, adjust for elasticity, velocity vectors etc.)

From the train's point of view, the ball approaches at 70 mph and leaves at 70 mph, but from the thrower's point of view, it gets a huge velocity change.  (And the train loses a tiny amount of speed.)
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Offline Glom

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Re: Acceleration
« Reply #19 on: June 30, 2018, 05:16:00 AM »
There is the small possibility that the context was more cosmological and the theory that the universe is undergoing accelerating expansion until everything is ripped apart.

Offline Peter B

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Re: Acceleration
« Reply #20 on: June 30, 2018, 07:11:04 PM »
That's right. Actually, the term "slingshot" tells it all. A spacecraft flyby of Jupiter wouldn't do anything if Jupiter wasn't moving in its own solar orbit.

If you fly by the orbital trailing side of Jupiter (the usual case), then Jupiter "drags" it along as it orbits, transferring some of its (enormous) orbital kinetic energy to your spacecraft.

If you fly by Jupiter's leading side, the planet pulls back on you and you lose some of your own energy to the planet. You'd do that if you wanted to fall into the inner solar system (e.g., to closely approach the sun at high speed). Another reason would be to do a big plane change out of the ecliptic, as was done with Ulysses.

The way I explained gravitational slingshots to my kids was to point out the ramp they'd roll toy cars down. Roll the car down the ramp and it goes a certain speed when it leaves the ramp. But if the ramp is itself moving forwards the car leaves the ramp with extra speed. And if the ramp is moving backwards the car leaves the ramp with less speed. The moving ramp represents the planet moving around the Sun.

The other analogy which can be useful is the ice-skating relay races, where one skater grabs the hand of their partner and pulls them forward. Momentum is transferred from one skater to the other, one speeding up and the other slowing down; of course, when it's a planet "grabbing the hand" of a spacecraft, the planet loses only a tiny amount of speed and the spacecraft gains massively.

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All these maneuvers would be very expensive to do on your own with chemical rockets. But if you do have a rocket, you can fire it at perijove and get an even bigger kick thanks to the Oberth effect. That's because the mechanical power a rocket delivers to its payload is directly proportional to its velocity, and you're going pretty fast on a close hyperbolic flyby of a planet as massive as Jupiter.

Is the Oberth Effect why Apollo and Space Shuttle launches would initially climb slightly above their intended orbits and then dive back down during powered flight?

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If you really want to go out of the solar system in style you could do a flyby of Jupiter to remove most of your orbital energy, dropping you into a elliptical orbit with a very low perihelion. Then as you're racing around the sun (trying very hard not to burn up) you fire your own engine. I saw a paper proposal to do exactly this to catch up with I1, the first known interstellar asteroid that passed through our solar system last fall. (I forget its Hawaiian name.) The maneuver was actually more complicated than this, it required flybys of both Jupiter and Saturn to get the necessary plane change as well as the necessary velocity to escape the sun and catch up with that thing.

'Oumuamua?

Interesting article about it here: http://www.abc.net.au/news/science/2018-06-28/mysterious-interstellar-visitor-oumuamua-was-a-comet-after-all/9900114

Offline QuietElite

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Re: Acceleration
« Reply #21 on: July 01, 2018, 09:16:47 AM »
Is the Oberth Effect why Apollo and Space Shuttle launches would initially climb slightly above their intended orbits and then dive back down during powered flight?

No. They did that so that the upper stages have more time to get into orbit before falling back to earth since upper stage engines usually have low thrust. Without this you would have to pitch up more during the burn to compensate gravity and this would be overall less efficient.

Offline ka9q

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Re: Acceleration
« Reply #22 on: July 01, 2018, 10:11:07 PM »
I had noticed and wondered about that myself; your explanation is almost certainly correct.