Name: 廣義相對論的最佳檢驗（由2顆錯位的衛星來檢驗 (The Best Test of General Relativity (by 2 Misplaced Satellites))
Uploaded: 2021-01-14T10:25:27.000Z
Duration: 11 min 52 s
Description: 【看影片學英語】數萬部 YouTube 影片，搭配英漢字典即點即查，輕鬆掌握單字發音與用法，長久累積看電影不必再看字幕。

So, this is good, this is good. You - you're working, can you see me?

Do you know what went wrong in-uh.. during the launch..?

Yes - it's not complicated, but, it's a long chain of events..

On august, 21., 2014, two satellites were launched by the European Space Agency.

They're called Galileo Satellites 5 and 6.

They were intended to become part of the Global Navigation Satellite System, or GNSS.

This is the European version of the American GPS systems.

Now, after successfully blasting off into space,

The satellites were launched with the Russian 5-6 rockets;

The final stage of the rocket was set to inject the satellites into circular orbit around 23000 kilometers above the Earth.

But that - - is when something went wrong

Uhh. there was thermal breach between a line of cold helium, and a line of propellant.

This caused the failure of the altitude control thrusters.

The satellites seemed to have been injected into some random direction.

It was launched, but in the wrong direction.

This sent the satellites into highly elliptical, and seemingly useless orbits.

At their low point, the satellites didn't really get a full view of earth..

Earth sensors, which enabled them to orient their navigation antennas - stopped working,

because the earth just filled their field of view.

At the other extreme, the satellites went too high, experiencing significant radiation exposure

There was a threat, that they would just shut them off..

Okay, who do we have to talk to, to make sure they keep these satellites alive?

They had an idea, for how to use them to make the best tests of general relativity to date;

This was a strike of luck for us, we had been proposing such missions.

When we saw that this accident happened, we were very happy about it, of course.

Now, the satellites did have propellant on board,

intended to allow for periodic course corrections over their planned 10 year lifespan.

And they could use that fuel to attempt to correct their orbits.

They did some of these maneuvers to bring them into stable orbit -

But they didn't have enough to completely turn their elliptical orbits into circular ones.

They couldn't circularize completely, thankfully for our project.

According to general relativity, relative to a reference clock, clocks tick slower in stronger gravitational fields.

That is to say, closer to large masses, like the Earth, deeper in gravitational wells,

so, clocks in satellites should tick faster relative to those on Earth,

because they're in weaker gravitational fields

Here, I'm ignoring the special relativistic effect that works the other way -

making clocks in satellites tick slower than those on Earth,

This velocity effect is very well tested, so we focused on the gravitational parts.

The gravitational effect is hard to measure precisely, for satellites in circular orbit,

but satellites in elliptical orbit, have an advantage - -

they go from their lowest position - perigee,

to the highest position - apogee, and back.

If you want to test the gravitational red-shift of a clock, you need two things - -

you need a very accurate clock, and you need a large change in gravitational potential.

The satellite goes from 17000 to 26000 kilometers.

The difference in altitude is almost 9000 (!!!) kilometers,

meaning they are rapidly, and repeatedly going from lower gravitational potential,

to higher gravitational potential, and back.

So clocks on board, should be ticking slower when they're closer to the Earth,

and then faster when they go to their high point,

and they'll keep oscillating back and forth; slower and faster relative to clocks on Earth.

If you compare a clock on the ground, and a clock on the satellite,

then you will have this variation of time..

Now, what's great about this, is it allows you to eliminate a lot of sources of error -

because, you don't really care about the absolute accuracy of the clocks;

All you want to know, is the difference between the rate of ticking

at the low point compared to the high point.

And since it's the same clock making the measurements at both locations,

you can eliminate a lot of errors, like the noise in the clock, or a systematic drift,

and that's what allows the scientists to achieve such incredible precision.

Why we could do it - is because it's a very predictable effect.

Due to the eccentricity of the orbit - the signal we were looking for, is really the modulation.

All the other effects - that are at other periods - they will not have an influence on your measurements.

Now, I should point out, that if you were traveling with the satellite,

for you - time would not speed up and slow down; time would be passing at a constant rate.

You wouldn't be able to measure any change in the rate the clock is ticking.

The relativity comes when you compare two clocks which are distant enough to feel the curvature of space and time.

The clocks on the satellites - there are a couple of different types - are all atomic clocks.

The primary clock typically is a passive hydrogen MASER clock.

A MASER - is just like a laser, except it uses microwaves.

Atoms of hydrogen interact with one specific frequency of microwaves -

A photon of precisely this frequency, will flip the spin of an electron.

So by tuning the microwaves, so that they best interact with the hydrogen atoms,

and then counting up exactly this number of cycles of that radiation,

that's one second. You can keep track of time with incredible stability.

In fact, over a 30 million years, a clock like this -

Again, if you were traveling with the satellite, you would always observe the frequency of this radiation to be

the same. But, if you sent this radiation out - -

who is not in a strong gravitational field,

they would observe the frequency of your microwaves to be slightly lower than those from their hydrogen maser.

And the closer the satellite is to Earth, the more red-shifted the microwaves would appear.

And hence the slower time would pass, relative to that distant  observer.

Locally, you can not see any relativistic effect

This is called the equivalence principle.

It's only when you compare the satellite clock to one on Earth,

that you would find the yo-yo-ing rate of the satellite's clock due to it's oscillation back and forth

This gravitational redshift was previously measured most precisely in 1976.

That's right, for over 40 years, we haven't improved our measurement of the gravitational effect on time.

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廣義相對論的最佳檢驗（由2顆錯位的衛星來檢驗 (The Best Test of General Relativity (by 2 Misplaced Satellites))

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