How far would you have to go to escape gravity? - Rene Laufer

568,131 views ใƒป 2018-11-06

TED-Ed


ืื ื ืœื—ืฅ ืคืขืžื™ื™ื ืขืœ ื”ื›ืชื•ื‘ื™ื•ืช ื‘ืื ื’ืœื™ืช ืœืžื˜ื” ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืกืจื˜ื•ืŸ.

ืชืจื’ื•ื: Ido Dekkers ืขืจื™ื›ื”: Allon Sasson
00:06
More than six thousand light years
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ื‘ืžืจื—ืง ืฉืœ ื™ื•ืชืจ ืžืฉืฉืช ืืœืคื™ื ืฉื ื•ืช ืื•ืจ
00:08
from the surface of the earth,
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ืžืคื ื™ ื›ื“ื•ืจ ื”ืืจืฅ,
00:10
a rapidly spinning neutron star
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ื›ื•ื›ื‘ ื ื™ื•ื˜ืจื•ื ื™ื ืฉืžืกืชื•ื‘ื‘ ื‘ืžื”ื™ืจื•ืช
00:12
called the Black Widow pulsar
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ื•ื ืงืจื ืคื•ืœืกืืจ ื”ืืœืžื ื” ื”ืฉื—ื•ืจื”
00:14
blasts its companion brown dwarf star with radiation
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ืžืคืฆื™ืฅ ืืช ืฉื•ืชืคื• ื”ื ื ืก ื”ื—ื•ื ื‘ืงืจื™ื ื”
00:18
as the two orbit each other every 9 hours.
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ื›ืฉื”ืฉื ื™ื™ื ื—ื’ื™ื ืื—ื“ ืกื‘ื™ื‘ ื”ืฉื ื™ ื›ืœ 9 ืฉืขื•ืช.
00:22
Standing on our own planet,
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ืื ืขื•ืžื“ื™ื ืขืœ ื”ืคืœื ื˜ื” ืฉืœื ื•,
00:24
you might think youโ€™re just an observer of this violent ballet.
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ืืชื ืื•ืœื™ ื—ื•ืฉื‘ื™ื ืฉืืชื ืจืง ืฆื•ืคื™ื ื‘ื‘ืœื˜ ื”ืืœื™ื ื”ื–ื”.
00:27
But in fact, both stars are pulling you towards them.
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ืื‘ืœ ืœืžืขืฉื”, ืฉื ื™ ื”ื›ื•ื›ื‘ื™ื ืžื•ืฉื›ื™ื ืืชื›ื ื›ืœืคื™ื”ื.
00:31
And youโ€™re pulling back,
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ื•ืืชื ืžื•ืฉื›ื™ื ื—ื–ืจื”,
00:33
connected across trillions of kilometers
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ืžื—ื•ื‘ืจื™ื ืžืžืจื—ืง ืฉืœ ื˜ืจื™ืœื™ื•ื ื™ ืงื™ืœื•ืžื˜ืจื™ื
00:35
by gravity.
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ืขืœ ื™ื“ื™ ื›ื‘ื™ื“ื”.
00:37
Gravity is the attractive force between two objects with massโ€”
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ื”ื›ื‘ื™ื“ื” ื”ื™ื ื”ื›ื•ื— ื”ืžื•ืฉืš ื‘ื™ืŸ ืฉื ื™ ื’ื•ืคื™ื ืขื ืžืืกื” --
00:42
any two objects with mass.
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ื›ืœ ืฉื ื™ ืื•ื‘ื™ื™ืงื˜ื™ื ืขื ืžืืกื”.
00:44
Which means that every object in the universe attracts every other object:
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ืžื” ืฉืื•ืžืจ ืฉื›ืœ ืขืฆื ื‘ื™ืงื•ื ืžื•ืฉืš ื›ืœ ืขืฆื ืื—ืจ:
00:49
every star, black hole,
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ื›ืœ ื›ื•ื›ื‘, ื—ื•ืจ ืฉื—ื•ืจ,
00:51
human being, smartphone, and atom
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ืื“ื, ืกืžืจื˜ืคื•ืŸ, ื•ืื˜ื•ื
00:54
are all constantly pulling on each other.
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ื›ื•ืœื ื›ืœ ื”ื–ืžืŸ ืžื•ืฉื›ื™ื ืื—ื“ ืืช ื”ืฉื ื™.
00:57
So why donโ€™t we feel pulled in billions of different directions?
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ืื– ืœืžื” ืื ื—ื ื• ืœื ืžืจื’ื™ืฉื™ื ื ืžืฉื›ื™ื ืœืžื™ืœื™ืืจื“ื™ ื›ื™ื•ื•ื ื™ื ืฉื•ื ื™ื?
01:01
Two reasons: mass and distance.
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ืฉืชื™ ืกื™ื‘ื•ืช: ืžืืกื” ื•ืžืจื—ืง.
01:05
The original equation describing the gravitational force between two objects
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ื”ืžืฉื•ื•ืื” ืžืงื•ืจื™ืช ืœืชืื•ืจ ื”ื›ื•ื—ื•ืช ื”ื›ื‘ื™ื“ืชื™ื™ื ื‘ื™ืŸ ืฉื ื™ ื’ื•ืคื™ื
01:09
was written by Isaac Newton in 1687.
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ื ื›ืชื‘ื” ืขืœ ื™ื“ื™ ืื™ื™ื–ื™ืง ื ื™ื•ื˜ื•ืŸ ื‘ 1687.
01:13
Scientistsโ€™ understanding of gravity has evolved since then,
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ื”ื”ื‘ื ื” ืฉืœ ืžื“ืขื ื™ื ืืช ื”ื›ื‘ื™ื“ื” ื”ืชืคืชื—ื” ืžืื–,
01:17
but Newtonโ€™s Law of Universal Gravitation
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ืื‘ืœ ื—ื•ืง ื ื™ื•ื˜ื•ืŸ ืฉืœ ื”ื›ื‘ื™ื“ื” ื”ืื•ื ื™ื‘ืจืกืœื™ืช
01:20
is still a good approximation in most situations.
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ื”ื•ื ืขื“ื™ื™ืŸ ืงื™ืจื•ื‘ ื˜ื•ื‘ ื‘ืจื•ื‘ ื”ืžืงืจื™ื.
01:24
It goes like this:
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ื”ื•ื ืื•ืžืจ ื›ืš:
01:25
the gravitational force between two objects
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ื”ื›ื•ื— ื”ื›ื‘ื™ื“ืชื™ ื‘ื™ืŸ ืฉื ื™ ืขืฆืžื™ื
01:28
is equal to the mass of one
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ืฉื•ื•ื” ืœืžืืกื” ืฉืœ ืื—ื“
01:30
times the mass of the other,
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ื›ืคื•ืœ ื”ืžืืกื” ืฉืœ ื”ืฉื ื™,
01:31
multiplied by a very small number
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ื›ืคื•ืœ ืžืกืคืจ ืžืื•ื“ ืงื˜ืŸ
01:34
called the gravitational constant,
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ืฉื ืงืจื ื”ืงื‘ื•ืข ื”ื›ื‘ื™ื“ืชื™,
01:36
and divided by the distance between them, squared.
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ื•ืžื—ื•ืœืง ืขืœ ื™ื“ื™ ืจื™ื‘ื•ืข ื”ืžืจื—ืง ื‘ื™ื ื”ื.
01:40
If you doubled the mass of one of the objects,
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ืื ืชื›ืคื™ืœื• ืืช ื”ืžืืกื” ืฉืœ ืขืฆื ืื—ื“,
01:42
the force between them would double, too.
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ื”ื›ื•ื— ื‘ื™ื ื”ื ื™ื•ื›ืคืœ ื’ื ื”ื•ื.
01:45
If the distance between them doubled,
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ืื ื”ืžืจื—ืง ื‘ื™ื ื™ื”ื ื™ื•ื›ืคืœ,
01:47
the force would be one-fourth as strong.
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ื”ื›ื•ื— ื™ืงื˜ืŸ ืคื™ ืืจื‘ืข.
01:50
The gravitational force between you and the Earth pulls you towards its center,
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ื”ื›ื•ื— ื”ื›ื‘ื™ื“ืชื™ ื‘ื™ื ื™ื›ื ืœื‘ื™ืŸ ื›ื“ื•ืจ ื”ืืจืฅ ืžื•ืฉืš ืืชื›ื ืœืžืจื›ื–ื•,
01:55
a force you experience as your weight.
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ื›ื•ื— ืฉืืชื ื—ื•ื•ื™ื ื›ืฉืืชื ื ืฉืงืœื™ื.
01:57
Letโ€™s say this force is about 800 Newtons
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ื”ื‘ื” ื ื’ื™ื“ ืฉื”ื›ื•ื— ื”ื–ื” ื”ื•ื ื‘ืขืจืš 800 ื ื™ื•ื˜ื•ืŸ
02:00
when youโ€™re standing at sea level.
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ื›ืฉืืชื ืขื•ืžื“ื™ื ื‘ื’ื•ื‘ื” ืคื ื™ ื”ื™ื.
02:02
If you traveled to the Dead Sea,
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ืื ืชื˜ื™ื™ืœื• ืœื™ื ื”ืžืœื—,
02:04
the force would increase by a tiny fraction of a percent.
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ื”ื›ื•ื— ื™ื’ื“ืœ ื‘ื›ืžื•ืช ืžื–ืขืจื™ืช.
02:08
And if you climbed to the top of Mount Everest, the force would decreaseโ€”
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ื•ืื ืชื˜ืคืกื• ืœืคืกื’ืช ื”ืจ ืื•ื•ืจืกื˜, ื”ื›ื•ื— ื™ืคื—ืช --
02:12
but again, by a minuscule amount.
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ืื‘ืœ ืฉื•ื‘, ื‘ื›ืžื•ืช ืžื–ืขืจื™ืช.
02:15
Traveling higher would make a bigger dent in gravityโ€™s influence,
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ื˜ื™ืกื” ื’ื‘ื•ื” ื™ื•ืชืจ ืชื™ืฆื•ืจ ื™ืจื™ื“ื” ื—ื“ื” ื™ื•ืชืจ ื‘ื”ืฉืคืขื” ืฉืœ ื”ื›ื‘ื™ื“ื”,
02:19
but you wonโ€™t escape it.
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ืื‘ืœ ืืชื ืœื ืชื‘ืจื—ื• ืžืžื ื”.
02:21
Gravity is generated by variations in the curvature of spacetimeโ€”
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ื”ื›ื‘ื™ื“ื” ื ื•ืฆืจืช ืžืฉื™ื ื•ื™ื ื‘ืขื™ืงื•ื ื”ืžืจื—ื‘ ื–ืžืŸ --
02:25
the three dimensions of space plus timeโ€”
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ืฉืœื•ืฉืช ื”ืžื™ืžื“ื™ื ืฉืœ ื—ืœืœ ื•ืขื•ื“ ื–ืžืŸ --
02:28
which bend around any object that has mass.
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ืฉืžืชืขืงืžื™ื ืกื‘ื™ื‘ ื›ืœ ืขืฆื ืฉื™ืฉ ืœื• ืžืืกื”.
02:32
Gravity from Earth reaches the International Space Station,
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ื”ื›ื‘ื™ื“ื” ืฉืœ ื›ื“ื•ืจ ื”ืืจืฅ ืžื’ื™ืขื” ืœืชื—ื ืช ื”ื—ืœืœ ื”ื‘ื™ืŸ ืœืื•ืžื™ืช,
02:35
400 kilometers above the earth,
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400 ืงื™ืœื•ืžื˜ืจ ืžืขืœ ืคื ื™ ื›ื“ื•ืจ ื”ืืจืฅ,
02:38
with almost its original intensity.
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ืขื ื›ืžืขื˜ ื”ืขื•ืฆืžื” ื”ืžืงื•ืจื™ืช ืฉืœื”.
02:40
If the space station was stationary on top of a giant column,
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ืื ืชื—ื ืช ื”ื—ืœืœ ื”ื™ืชื” ื ื™ื™ื—ืช ืขืœ ืขืžื•ื“ ืขืฆื•ื,
02:44
youโ€™d still experience ninety percent
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ืขื“ื™ื™ืŸ ืชื—ื•ื• ืชืฉืขื™ื ืื—ื•ื–
02:46
of the gravitational force there that you do on the ground.
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ืžื”ื›ื•ื— ื”ื›ื‘ื™ื“ืชื™ ืฉื ืฉืชื—ื•ื• ืขืœ ื”ืงืจืงืข.
02:50
Astronauts just experience weightlessness
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ืืกื˜ืจื•ื ืื•ื˜ื™ื ื—ื•ื•ื™ื ื—ื•ืกืจ ืžืฉืงืœ
02:52
because the space station is constantly falling towards earth.
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ืจืง ื‘ื’ืœืœ ืฉืชื—ื ืช ื”ื—ืœืœ ื›ืœ ื”ื–ืžืŸ ื ื•ืคืœืช ืœื›ื“ื•ืจ ื”ืืจืฅ.
02:57
Fortunately, itโ€™s orbiting the planet fast enough that it never hits the ground.
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ืœืžืจื‘ื” ื”ืžื–ืœ, ื”ื™ื ื—ื’ื” ืกื‘ื™ื‘ ื”ืคืœื ื˜ื” ืžื”ืจ ืžืกืคื™ืง ืฉื”ื™ื ืืฃ ืคืขื ืœื ืคื•ื’ืขืช ื‘ืื“ืžื”.
03:02
By the time you made it to the surface of the moon,
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ืขื“ ืฉืชื’ื™ืขื• ืœืคื ื™ ื”ื™ืจื—,
03:04
around 400,000 kilometers away,
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ื‘ืžืจื—ืง ืฉืœ ื‘ืขืจืš 400,000 ืงื™ืœื•ืžื˜ืจ,
03:07
Earthโ€™s gravitational pull would be
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ื›ื‘ื™ื“ืช ื›ื“ื•ืจ ื”ืืจืฅ ืชื”ื™ื”
03:09
less than 0.03 percent of what you feel on earth.
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ืคื—ื•ืช ืž 0.03 ืื—ื•ื– ืžืžื” ืฉืืชื ืžืจื’ื™ืฉื™ื ื‘ื›ื“ื•ืจ ื”ืืจืฅ.
03:14
The only gravity youโ€™d be aware of would be the moonโ€™s,
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ื”ื›ื‘ื™ื“ื” ื”ื™ื—ื™ื“ื” ืฉืชืจื’ื™ืฉื• ืชื”ื™ื” ืฉืœ ื”ื™ืจื—.
03:17
which is about one sixth as strong as the earthโ€™s.
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ืฉื”ื™ื ื‘ืขืจืš ืฉื™ืฉื™ืช ืžืขื•ืฆืžืชื” ืฉืœ ื”ื›ื‘ื™ื“ื” ื‘ื›ื“ื•ืจ ื”ืืจืฅ.
03:20
Travel farther still
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ื”ืชืจื—ืงื• ืืฃ ื™ื•ืชืจ
03:22
and Earthโ€™s gravitational pull on you will continue to decrease,
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ื•ืžืฉื™ื›ืช ื›ื“ื•ืจ ื”ืืจืฅ ืขืœื™ื›ื ืชืžืฉื™ืš ืœืคื—ื•ืช,
03:26
but never drop to zero.
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ืื‘ืœ ืœืขื•ืœื ืœื ืชื’ื™ืข ืœืืคืก.
03:28
Even safely tethered to the Earth,
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ืืคื™ืœื• ืžื—ื•ื‘ืจื™ื ื‘ื‘ื˜ื—ื” ืœื›ื“ื•ืจ ื”ืืจืฅ,
03:31
weโ€™re subject to the faint tug of distant celestial bodies and nearby earthly ones.
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ืื ื—ื ื• ื ืชื•ื ื™ื ืœืžืฉื™ื›ื” ื—ืœื•ืฉื” ืฉืœ ื’ื•ืคื™ื ืฉืžื™ืžื™ื™ื ืžืจื•ื—ืงื™ื ื•ื›ืืœื” ืงืจื•ื‘ื™ื ืขืœ ื›ื“ื•ืจ ื”ืืจืฅ.
03:38
The Sun exerts a force of about half a Newton on you.
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ื”ืฉืžืฉ ืžืคืขื™ืœื” ื›ื•ื— ืฉืœ ื‘ืขืจืš ื—ืฆื™ ื ื™ื•ื˜ื•ืŸ ืขืœื™ื›ื.
03:41
If youโ€™re a few meters away from a smartphone, you'll experience
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ืื ืืชื ื‘ืžืจื—ืง ืฉืœ ื›ืžื” ืžื˜ืจื™ื ืžืกืžืจื˜ืคื•ืŸ, ืชื—ื•ื•
03:44
a mutual force of a few piconewtons.
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ื›ื•ื— ื”ื“ื“ื™ ืฉืœ ื›ืžื” ืคื™ืงื• ื ื™ื•ื˜ื•ื ื™ื.
03:48
Thatโ€™s about the same as the gravitational pull
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ืฉื–ื” ื‘ืขืจืš ืื•ืชื” ืžืฉื™ื›ื”
03:50
between you and the Andromeda Galaxy,
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ื‘ื™ื ื›ื ื•ื’ืœืงืกื™ื™ืช ืื ื“ืจื•ืžื“ื”,
03:53
which is 2.5 million light years away
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ืฉื ืžืฆืืช ื‘ืžืจื—ืง ืฉืœ ื‘ืขืจืš 2.5 ืžืœื™ื•ืŸ ืฉื ื•ืช ืื•ืจ
03:56
but about a trillion times as massive as the sun.
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ืื‘ืœ ืžืกื™ื‘ื™ืช ื‘ืขืจืš ืคื™ ื˜ืจื™ืœื™ื•ืŸ ืžื”ืฉืžืฉ.
04:00
But when it comes to escaping gravity,
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ืื‘ืœ ื›ืฉื–ื” ืžื’ื™ืข ืœื‘ืจื™ื—ื” ืžื”ื›ื‘ื™ื“ื”,
04:02
thereโ€™s a loophole.
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ื™ืฉ ืคืจืฆื”.
04:04
If all the mass around us is pulling on us all the time,
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ืื ื›ืœ ื”ืžืืกื” ืกื‘ื™ื‘ื ื• ืžื•ืฉื›ืช ืื•ืชื ื• ื›ืœ ื”ื–ืžืŸ,
04:07
how would Earthโ€™s gravity change
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ืื™ืš ื”ื›ื‘ื™ื“ื” ืฉืœ ื›ื“ื•ืจ ื”ืืจืฅ ืชืฉืชื ื”
04:09
if you tunneled deep below the surface,
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ืื ืชื—ืคืจื• ืžื ื”ืจื” ืขืžื•ืง ืžืชื—ืช ืœืคื ื™ ืฉื˜ื—,
04:11
assuming you could do so without being cooked or crushed?
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ื‘ื”ื ื—ื” ื•ืชื“ืื’ื• ืœื ืœื”ืฆืœื•ืช ืื• ืœื”ืžืขืš?
04:15
If you hollowed out the center of a perfectly spherical Earthโ€”
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ืื ื”ื™ื™ืชื ืžืจื•ืงื ื™ื ืืช ื”ืžืจื›ื– ืฉืœ ื›ื“ื•ืจ ืืจืฅ ืกืคืจื™ ืžื•ืฉืœื --
04:19
which it isnโ€™t, but letโ€™s just say it wereโ€”
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ืžื” ืฉื”ื•ื ืœื, ืื‘ืœ ื”ื‘ื” ื ื ื™ื— ืฉื”ื•ื ื›ืŸ --
04:22
youโ€™d experience an identical pull from all sides.
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ืชื—ื•ื•ื• ืžืฉื™ื›ื” ื–ื”ื” ืžื›ืœ ื”ื›ื™ื•ื•ื ื™ื.
04:25
And youโ€™d be suspended, weightless,
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ื•ืชื”ื™ื• ืชืœื•ื™ื™ื, ื—ืกืจื™ ืžืฉืงืœ,
04:28
only encountering the tiny pulls from other celestial bodies.
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ื•ืชืจื’ื™ืฉื• ืจืง ืืช ื”ืžืฉื™ื›ื•ืช ื”ื–ืขื™ืจื•ืช ืžื’ื•ืคื™ื ืฉืžื™ืžื™ื ืื—ืจื™ื.
04:32
So you could escape the Earthโ€™s gravity in such a thought experimentโ€”
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ืื– ืชื•ื›ืœื• ืœื‘ืจื•ื— ืžื›ื‘ื™ื“ืช ื›ื“ื•ืจ ื”ืืจืฅ ื‘ื ื™ืกื•ื™ ืžื—ืฉื‘ืชื™ ื›ื–ื” --
04:36
but only by heading straight into it.
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ืื‘ืœ ืจืง ืื ืชื›ื ืกื• ื™ืฉืจ ืœืชื•ื›ื•.
ืขืœ ืืชืจ ื–ื”

ืืชืจ ื–ื” ื™ืฆื™ื’ ื‘ืคื ื™ื›ื ืกืจื˜ื•ื ื™ YouTube ื”ืžื•ืขื™ืœื™ื ืœืœื™ืžื•ื“ ืื ื’ืœื™ืช. ืชื•ื›ืœื• ืœืจืื•ืช ืฉื™ืขื•ืจื™ ืื ื’ืœื™ืช ื”ืžื•ืขื‘ืจื™ื ืขืœ ื™ื“ื™ ืžื•ืจื™ื ืžื”ืฉื•ืจื” ื”ืจืืฉื•ื ื” ืžืจื—ื‘ื™ ื”ืขื•ืœื. ืœื—ืฅ ืคืขืžื™ื™ื ืขืœ ื”ื›ืชื•ื‘ื™ื•ืช ื‘ืื ื’ืœื™ืช ื”ืžื•ืฆื’ื•ืช ื‘ื›ืœ ื“ืฃ ื•ื™ื“ืื• ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืกืจื˜ื•ืŸ ืžืฉื. ื”ื›ืชื•ื‘ื™ื•ืช ื’ื•ืœืœื•ืช ื‘ืกื ื›ืจื•ืŸ ืขื ื”ืคืขืœืช ื”ื•ื•ื™ื“ืื•. ืื ื™ืฉ ืœืš ื”ืขืจื•ืช ืื• ื‘ืงืฉื•ืช, ืื ื ืฆื•ืจ ืื™ืชื ื• ืงืฉืจ ื‘ืืžืฆืขื•ืช ื˜ื•ืคืก ื™ืฆื™ืจืช ืงืฉืจ ื–ื”.

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