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00:00Kepler's Laws
00:01Kepler's Laws
00:02Kepler's Laws
00:03Jonas Kepler's Laws
00:04observation-based
00:05Tycho Braho
00:06had a lot of observations
00:07and after
00:08he studied
00:09Jonas Kepler's Laws
00:11no proof
00:12observation-based
00:13First Law
00:14Law of Orbits
00:15he told
00:16the first time
00:17he told
00:18planets move around the sun
00:19in elliptical orbit
00:21having the sun
00:22at one of the foca
00:23so first
00:24he knew
00:25the earth
00:26he knew
00:27the geocentric
00:28model
00:29here
00:30the sun is in the center
00:31but the circular object
00:32is not
00:33elliptical orbit
00:34Kepler's Laws
00:35so
00:36look at this
00:37if there are ellipses
00:38then ellipses
00:39two focaes
00:40in the sun
00:41here
00:42here
00:43here
00:44here
00:45here
00:46here
00:47here
00:48here
00:49here
00:50here
00:51here
00:52elliptical orbit
00:53and two focaes
00:54here
00:55here
00:56here
00:57here
00:58here
00:59here
01:00here
01:01here
01:02here
01:03here
01:04here
01:05here
01:06here
01:07here
01:08here
01:09next
01:10Kepler's Law
01:11what is
01:12second law
01:13the law
01:14of equal area
01:15what is
01:16the radius vector drawn
01:17from the sun
01:18to the planet
01:19sweeps out
01:20equal area
01:21in equal intervals
01:22of time
01:23i.e. the aerial speed
01:24of a planet
01:25remains constant
01:26constant
01:27this area
01:28here
01:29here
01:30where
01:31sun
01:32here
01:33here
01:34here
01:35here
01:36orbit
01:37satellite
01:38here
01:39here
01:40here
01:41here
01:42so
01:43this law
01:44is a consequence
01:45of conservation
01:46of angular momentum
01:47of planet
01:48about the sun
01:49if you can see
01:50angular momentum
01:51here
01:52conserve
01:53why
01:54about the sun
01:55what is
01:56gravitational force
01:57gravitational force
01:58this point
01:59so
02:00gravitational force
02:01there is no torque
02:02if I talk about
02:03about the sun
02:04there is no torque
02:05angular momentum
02:06so what can I write
02:07this is point number one
02:09this is point number two
02:10l1
02:11is equal to
02:12l2
02:13why
02:14torque
02:15due to gravity
02:16is equal to
02:170
02:18l1
02:19ki value
02:20kya hai
02:21here
02:22this was r1
02:23similarly
02:24here
02:25r2
02:26distance
02:27here
02:28velocity
02:29v1
02:30here
02:31l1
02:32ki value
02:33m
02:34v
02:35r
02:36m
02:37into
02:38v1
02:39v1
02:40is equal to
02:41is equal to
02:42angular momentum
02:43m
02:44into v2
02:45r2
02:46mass
02:47same
02:48rada
02:49v1
02:50r1
02:51is equal to
02:52v2
02:53r2
02:54all right
02:55here
02:56area
02:57kawne
02:58area
02:59here
03:00is
03:01position
03:02vector
03:03and
03:04here
03:05we have
03:06position
03:07area
03:08here
03:09here
03:10area
03:11is
03:12constant
03:13here
03:14here
03:15let's say
03:16let's say
03:17let's say
03:18r2
03:19r2
03:20here
03:21here
03:22here
03:23here
03:24here
03:25here
03:26this
03:27distance
03:28that
03:29is
03:30v2
03:31into
03:32dt
03:33here
03:34this
03:35height
03:36here
03:37height
03:38here
03:39here
03:40here
03:41here
03:42here
03:43here
03:44here
03:45here
03:46is
03:47equal to
03:48half
03:49into
03:50r2
03:51into
03:52v2
03:53into
03:54dt
03:55here
03:56here
03:57is
03:58half
03:59r2
04:00here
04:01here
04:02m
04:03and
04:04m
04:05multiply
04:06this
04:07angular
04:08momentum
04:09which
04:10is equal to
04:11l
04:12upon
04:132m
04:14angular
04:15momentum
04:16about
04:17the sun
04:18here
04:192m
04:20this
04:21is
04:23here
04:25but
04:26here
04:27here
04:28here
04:29is
04:30same
04:31interval
04:32of
04:33velocity
04:34here
04:35here
04:36here
04:38here
04:39same
04:40interval
04:41of
04:42time
04:43here
04:45Arial Law, which is the angular momentum conservation, is the second way to write the angular momentum conservation.
05:00Kepler's third law is the law of periods.
05:03What was it called?
05:04Square of the time period of revolution of a planet around the sun is directly proportional to the cube of the semi-major axis of the elliptical orbit.
05:11So, what did we learn?
05:13T2 is proportional to r cube.
05:16This was for circular orbits.
05:18If there is elliptical orbit, there is also a similar law.
05:21First of all, this is radius.
05:24This is a length which we call a.
05:27This is a semi-major axis.
05:29This is a whole major axis.
05:32This is a whole minor axis.
05:34This distance is a semi-major axis.
05:37Where is the sun?
05:38The sun is in any way.
05:39The sun is in any way.
05:40Or it will be here.
05:41Let's say, I have a sun here.
05:42Or it will be here.
05:43Or it will be this way too.
05:44Okay.
05:45So, this time, this was for circular orbits.
05:47For elliptical orbits, the value of t2 is proportional to a cube.
05:52This way, you can see.
05:54Here is the real relation.
05:57Actually, what was the circular orbit?
05:59If I had to talk about it,
06:01t2 is equal to 4 pi square upon gm times r cube.
06:07This time, the value of t2 is equal to 4 pi square upon gm into a cube.
06:15And that is the mass.
06:16The mass is used, which is our unit.
06:18The body is our unit.
06:20The sun is here.
06:21The mass will be here.
06:22The mass will be here.
06:23The mass will be with satellite.
06:24The mass will not be at the same time.
06:26Again, this is the derived of what we call this.
06:28This is the Kepler of observations.
06:29If you want to see elliptical calculations,
06:33you will also derive some more.
06:35But we will not do that.
06:36two planets a and b of equal mass are having their period of revolution ta and tb such that
06:50ta is equal to two times tb these planets are revolving in a circular orbit of radii ra and
06:55rb respectively which out of the following option would be the correct relationship of their orbit
07:00so we know that t2 is proportional to r3 plus law is proportional to r3 or the circular orbit
07:08derived from the video pause and tell which option is correct
07:23correct answer is option number c see here we know that ta upon tb
07:28which is square will be equal to r a upon rb
07:33square sorry cube
07:35here ta value is equal to 2 times tb
07:38so this value is equal to 2 square which is equal to 4
07:42here we know that r a cube
07:45r a cube is equal to 4 times r b
07:49cube option number c is correct answer
07:51the minimum and maximum distances of a planet revolving around the sun are x1 and x2
08:09so we always have to do this
08:11we always have to do this
08:13here we have to let's say my sun here
08:14here we have to have minimum distance
08:17this is x1
08:19and this is x2
08:21we have to do this
08:23we have to do this
08:25because here we have to do this
08:27here we have to do this
08:29velocity along the tangent
08:31here we have to do this
08:32so we have to do this
08:34let's say here we have to do this
08:36satellite
08:37here we have to do this
08:39here we have to do this
08:41we have to do this
08:42velocity
08:43the
08:43come
08:44the
08:44the
08:44the
08:45the
08:45velocity
08:45the
08:46the
08:46the
08:47all right
08:48if the minimum speed of the planet
08:50on its trajectory is we not
08:51actually
08:52the
08:52distance
08:54is
08:54the
08:54speed
08:56speed
08:57you can understand
08:58potential energy plus kinetic energy constant
09:00do you have to do this
09:00the
09:01the
09:02potential energy
09:03is more than the
09:05kinetic energy is less than the
09:06the
09:07right
09:07so here we have to do it
09:09it is actually equal to
09:11v0
09:12the maximum speed
09:13how can we know
09:14here we have to do it
09:15conservation of angular momentum
09:17I have to tell you about
09:18the video
09:18pause
09:18and
09:19solve
09:20correct answer
09:31d
09:32d
09:32we have to have angular momentum
09:34conserve
09:34mvr is equal to constant
09:37to be equal to mv1 into x1
09:41will be equal to m into v0 into x2
09:47here we have to be equal to mv1 into v0 into x2 into x1
09:55option number d is our correct answer
09:59very easy
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