Kepler's Second Law

[@WolfyMarcus]

GOSH This is the best explanation I have ever come across!!!! Thanks Professor!!!!!!!!

[@yoprofmatt]

Wonderful debate you two! Let me know if you need any clarification. Cheers, Dr. A

[@user-lf3rd2is1v]

Thank you 🙏 You are the only person i understod kepler's second law from him .

[@williamhensley8322]

@Momo2017 vdt is the right-hand side of the differential equation relating the instantaneous position with respect to time. dr/dt = v and so multiplying the differential dt to the side with v is vdt. dr is nothing but a differential distance/infinitesimally small distance swept by the planet or satellite.

[@spacegeek6166]

The way he explained it so calmly is amazing!

[@elmaaal5607]

What a wonderful teacher, greetings to you from Syria❤

[@asr0007]

Such a great explaination Love from India 🤞🏻

[@gomemego3417]

Thanks, professor. it helped me a lot in understanding the Kepler second law

[@ChekGun]

Thank you so much, i think i only now truly understood what the derivation actually means. Love the visual aid. Please keep producing those videos.

[@yoprofmatt]

You're very welcome. Cheers, Dr. A

[@Li01018]

Wow! what a brilliant guy! Both Kepler and Pr. Anderson

[@zainabidi7724]

+Matt Anderson These videos are very helpful, thank you. I have an unrelated question, do you write backwards on a glass surface?

[@akutagawaslosteyebrows314]

Zain Abidi it’s a mirror surface

[@moonpearl4711]

Cookies dumbo that would still need him to write in a sideway so that we see the ordered words.

[@saravananen9196]

He just mirrored the video as u can see him writting with his left hand in the video, i am sure he is a rightee

[@fourierfoyer365]

Anyone else blown away about how he's writing backwards so legibly?

[@Riya-pf3oc]

Thank you sir, for this good explanation. A student from India. Loves your explanation sir.

[@mystory9840]

thankyou so much sir it helped me a lot, lot's of love from India

[@yoprofmatt]

Most welcome! Always glad to help another Fanderson from India. Glad you're finding them useful. Cheers, Dr. A

[@theifalienwriter9659]

Thanks for your video...It really helps me a lot...HAVE A GREAT DAy

[@thejaswiamarendra9602]

Sir, When you considered the area, wasn't it supposed to be a sector rather than a triangle????

[@yoprofmatt]

Correct, but for very small arcs we can approximated it as a triangle. Cheers, Dr. A

[@anuragthakur4341]

He assumed the distance to be small.

[@adityaprakash3518]

But when the time duration is much more, and more area has been swept, like 5 months for the earth, won't considering it a traingle affect the calculation?

[@domkakuzu]

​@@adityaprakash3518 Well, if you prove it to a small triangle, you can imagine the whole sector as being a lot of little triangle opposing each other to do the comparison

[@akvs2002]

Nailed it, Sir. Thank you so much.

[@sunir9500]

Why area of triangle formula is use for change in area?pls reply

[@yetdark]

Thank you so much for the explanation! I have only one question left: at 6:20 you came to the conclusion that the magnitude (not vector) of the angular momentum is constant. However, in a few seconds, you wrote that actually the L[vector] is constant (so, the direction is constant as well). Isn't it wrong, since L[vector] = m * r[vector] * v[vector]; thus, the direction of angular momentum is changing? After all, it still works, but then we should just write that L = m * r * v * sin(theta), where theta is angle between r[vector] and v[vector], right?

[@A_Random_Ghost]

r and v are always perpendicular to each other.

[@bedahfisika]

Use RHL and you'll see that direction of L vector isn't changing

[@susheelakajle7641]

Amazing Explanation Professor 🤗

[@khushipatel1723]

excellent explanation ...really liked it 👍👍

[@yoprofmatt]

Khushi Patel, Thanks for the comment, and keep up with the physics! You might also like my new website: www.universityphysics.education Cheers, Dr. A

[@mansoorazami5333]

To whom it may concern, How did Dr. A get 1/2 L/Mp *dt from 1/2 |r * v * dt|? Thanks.

[@josebarria3233]

I think he used a triangle area where is base*height/2 so if you take your base as dr and your height as r, then the area will be( r x dr )* 1/2 and the cross product is because you are multiplying two perpendicular vectors (if u use dot-product it will give you 0)

[@affinix887]

Formula of p (linear momentum is p=mv. So v= p/m r*p is angular momentum

[@kavin699]

In the equation angular equation L=Mp(R x V) => L/Mp =(R x V) ....from that we substitute dA =1/2 |R x V dt| to dA = 1/2 L/Mp dt . and the this whole by dt , you get dA/dt = 1/2 Mp...I think you get this point

[@TA16888]

I also wonder why

[@ChristAliveForevermore]

Classical physics is so damned sexy. The human mind figured out how heavenly bodies move and *why* they move how they do. In spite of all the achievements of modern science, this fact still floors me above all else.

[@yoprofmatt]

Your opening line is my new favorite. Well put. Cheers, Dr. A

[@Monika-jt4jx]

Ur way of explanation is superb😊

[@flippert0]

Let me guess: the professor is not a lefty and does not write like Galileo in mirror-writing, but video was flipped horizontally.

[@yoprofmatt]

Correct. Cheers, Dr. A

[@teodorghinea425]

Great demostration

[@RadioNul]

I wish I could write forwards as good as this guy can write backwards

[@patbanglephoto]

was going to make this same comment 🤣

[@Sibasish07]

What a legend. Thank you so much

[@ramk1985]

this isn't related to the topic but can you tell me what is motion confined to a plane means thnx for the nice lecture

[@yoprofmatt]

It means it is moving in two dimensions (x-y) but not three dimensions (z). Planets basically move in a plane. Cheers, Dr. A

[@adityaravindran8942]

Very good explanation BTW.....how is he writing backwards!!?

[@yoprofmatt]

Not writing backwards. Check it here: www.learning.glass Cheers, Dr. A

[@acinorevbonik3147]

Matt Anderson thanks sir it's great

[@asmazaynab8927]

I didn't understand wat my air said I could easily understand ur , TQ mr .Anderson , ur awesome ........

[@terrainaheadpullup3092]

because L = mvr can you simplify (1/2)(L/m) to (1/2)(vr) because (1/2)(L/m) = (1/2)(mvr/m) You can then divide top and bottom by m to get (1/2)(vr/1) = (1/2)(vr)

[@georgemathew8218]

sir, how do you write inverted on the board? are you left handed or right handed, or ambidextrous?Sir,George Here.That Question is from my students Mohammed and Alifiyah.

[@nolanyoung4480]

Absolutely brilliant!

[@AnithaS-yj3cq]

Delta z heat?

[@gauthambalu2071]

Sir I'm having a doubt on where to put the vector symbols ..can you please explain me

[@yoprofmatt]

Gautham Tharun, Join the discussion on my new website: www.universityphysics.education Cheers, Dr. A

[@MovieTheater69]

Incredible! Thank you for your explanatin

[@Abdullah_klx]

الله يستر طريقك ❤

[@yoprofmatt]

And yours. Cheers, Dr. A

[@Oly1]

How is he writing backwards? Can this power be learnd?

[@lea2856]

omg i finally understood thank you!!!!

[@nobisphysics7651]

Why you involved torque if it's the component in rotational mechanics? I mean planet revolves in elliptical path and not rotational?

[@flippert0]

This seems to be a very succinct and simple explanation. One thing that puzzles me is "r^" (vectorial postion vector). Shouldn't be this the vector the planet is currently heading? Or would the be "v^" (vectorial velocity vector)?

[@yoprofmatt]

Your second statement is correct. r^ is from the Sun to the planet. v^ is along the line of motion. Cheers, Dr. A

[@juancarlossanchezveana1812]

Wonderful 👍

[@al-feeqz8147]

How he can write backwards?

[@yoprofmatt]

m w, Not writing backwards (I'm not that talented). The board is called Learning Glass. You can check it out at www.learning.glass Cheers, Dr. A

[@whatabouttheearth]

You could learn to promote the development of ambidextrous writing, backwards writing, backwards reading and Manual Simultaneous Handwriting by decoupling brain hemisphere dominance by doing off set finger excercises (like rapid mudras), practicing double reflective (not mirror) drawing and writing, and learning a writing system from right to left such as Hebrew. "Mirror writing" should be easier. Also find "sdrawcab" writing on the net and practice reading it. It also helps to work im mirrored physical practoce like piano or practicing an instrument you know opposite (ex. instead of playing your right handed guitar play a left handed guitar but practice the piece reversed). It's related to hemisphere dominance in your brain. It's almost like forming temporary dyslexia for a little while than that chills out. But you have to work at it a bit because your muscles and brain wont be developed or conditioned for it yet. hguoht lacitcarp taht ton yllaer ,drah taht ton yllaer s'ti

[@ravaelbass5819]

Professor, what can happend if planet on the far side of the orbit

[@taeyo3240]

How the 2nd law says that the planet sweeps equal area in equal time .. even though the planet moves faster when its near the sun?

[@carultch]

Because it trades speed for radius from the sun A body inn eccentric orbit around the sun (like a comet) that moves twice as fast at its perihelion than its aphelion, would be twice as far from the sun at aphelion as it is at perihelion. The product of v*r is a constant.

[@whatabouttheearth]

So around winter solstice and Perihelion each month is literally covering more spaciality than the months around summer solstice and Aphelion?

[@carultch]

I don't know what "spaciality" means, but the Earth is travelling faster relative to the sun, around the time when it is at the perihelion. The solstices have nothing to do with this, and it is just a coincidence that they occur about 2 weeks prior to the aphelion/perihelion.

[@SeemaSharma-ci5zg]

Thnx profu✌️

[@khirgis7224]

interesting only, but 50 more than doing,, just focus it is difficult, into the simpler things zu werden und analysieren

[@vs6x3]

Thanks a lot

[@gummy7102]

o único vídeo que me fez de fato entender o conteúdo é gringo pqp

[@pcb1143]

thanks soooooooo much

[@farissesco871]

ana bahebak walahy

[@fizikoloji]

👍thanks good

[@yoprofmatt]

welcome good cheers dr. a

[@jimkeller3868]

Would have been nice if he explained a bit more about what he was conceptually trying to achieve. Never fond of purely mathematical explications without explanation of where it's going and why?

[@yoprofmatt]

Duly noted. Thanks for the feedback. Cheers, Dr. A

[@rajisa1435]

Sir how did u find dA which is in 7:49 sec...sir plzzz help me...

[@yoprofmatt]

Area of a triangle is 1/2 base times height. Cross product give us "direction" for that area. Cheers, Dr. A

[@victorsanalysis3463]

Mr.anderson where is kepler's third law of planetary motion

[@carultch]

Kepler's third law is the law of periods and semimajor axis. The square of the period is proportional to the cube of the semimajor axis.

[@abeni4383]

what is dr

[@carultch]

Infinitesimal change in position. Lowercase d is Leibnitz's notation for "infinitesimal change in the following qty", which stands for the Latin word "differentia".

[@collincharlespaul5509]

why does the planet move slower when it is away from the sun ?

[@blackspell2097]

less gravitation force from the sun as it is far away

[@nicolasbarbosa8270]

Think of it as throwing a rock upwards. At the top of the trajectory it stops, as it begins to fall it gains speed again Now imagine you throw that rock upwards as you walk. At the top of the motion an outside observer will see that the rock still has some velocity in the direction you are walking. They are able to notice that the rock is the slowest when at the top of the movement even though it still has some speed. This is because the initial velocity of the stone is a summ between your horizontal walking velocity and the vertical velocity it had after you accelerated it upwards. At the top of the movement the vertical component of the velocity is negatively accelerated to 0 by gravity, you now have only your horizontal component that is your walking velocity. Since one of the components of the velocity is now 0, we can say the magnitude you your velocity is smaller than at the start of the movement, we say it has less speed The same principle applies to the orbital movements, just as the closest the rock is to the ground, the higher their speed, the closer the planets are to the sun the higher their speed

[@anushaverma696]

Professor, are you really write on board from wrong side, please ans my question🙋. By the way I am from india🇮🇳.

[@yoprofmatt]

Hello India! Yes, I'm writing from the back side, but the image is flipped so it comes out reading correctly. Cheers, Dr. A

[@khirgis7224]

2

[@necattasdelen7153]

Newton's law says: attraction force is radial.F=Fr. A side force,Fp perpendicular to radial does not exist.Then Fp=m*dVp/dt=0=does not exist.That is dVp/dt=0 and this means,when integrated,Vp=0.Then what about Kepler's area law,1/2*r*Vp=Constant .How can one prove this.Is Newton or Kepler false? Choose.

[@necattasdelen7153]

+Necat Tasdelen a correction When Fp=m*dVp/dt=0 this means Vp=Constant

[@surprisedpikachu3782]

Necat Tasdelen omg ...you are a.intellectual savage

[@pitbull6098]

a Trumpian intellectualist

[@nitrozox212]

Nope.. when integrated Vp = constant not 0

[@khirgis7224]

1 no jiwon, 2 hard make me think high school physics, calculus and 3 will be. Highschool no - torque.. head.. bokseup hagi sittae juyi

[@officialmoh380]

Sir, at 8:04 how did you find 1/2(L/Mp)dt ????????????

[@Sibasish07]

Area of a triangle

[@necattasdelen7153]

Hi, When you say the velocity is slower at aphelion and faster at perihelion,you mean a difference of velocity between these pionts.Then you believe that the body on this orbit have an acceleration.When do we feel this acceleration? Newer! Then an acceleration does not existe.That is to say Vp=Constant.

[@carultch]

+Necat Tasdelen We do not feel this acceleration, because gravity causes it. The only time you feel acceleration, is when something other than gravity cause it. Like traction on the tires of a car, which cause the car to accelerate, and the seat has to cause the acceleration of your body to be consistent. When gravity causes acceleration, it is applied uniformly to each unit of mass, throughout the entire body. This causes the entire target object to accelerate as one body, without requiring any internal forces to maintain continuity. This is in contrast with localized forces that we experience in other examples. You cannot feel gravity or acceleration. You feel the other kinds of forces that either counteract gravity or cause acceleration. You can feel tidal forces, which are distortions due to non-uniformness of gravitational fields. But that isn't what we are discussing, when we treat Earth as a point object.

[@carultch]

+Necat Tasdelen At the aphelion and perihelion, the velocity vectors are perpendicular to gravity. Gravity only causes centripetal acceleration at these points. Speed is at either an instantaneous maximum (perihelion) or minimum (aphelion), and the instantaneous rate of change in speed is therefore constant at these points. Due to the fact that it is changing direction, it is accelerating. And perpendicular gravity from the sun, indeed causes it. At other points, these two vectors will not be perpendicular. They will mostly be perpendicular for a nearly circular orbit, but given any eccentricity, there will be a component of gravity that is either aligned or opposite of velocity. THIS IS THE GRAVITY THAT CAUSES THE SPEED UP/SLOW DOWN of a planet in orbit.

[@necattasdelen7153]

+carultch Sorry ,I think you are wrong.Kepler's area law is deducted from the orbit law of Kepler.It is not proved.but estimated.The prove of Vp=Constant is due to Newtons's attraction force.: no side force component.No force perpendicular to the radial attraction.So Fp=m*dVp/dt=0 means when integrated Vp=Constant.Kepler says r*Vp=area law=Constant. Is the prove correct or the estimation correct ?.When Vp=Constant there is no acceleration.And the human bodies feel nothing.Then r*Vp=Constant should be wrong.

[@carultch]

Necat Tasdelen Draw a scaled drawing of an exaggerated ellipse, and mark one of the focus points. Now draw a line joining one of the foci points with any point other than the apsis and periapsis. Measure the angle between the tangent line at this point, and the line joining it to the focus. If your work all checks, it will not be perpendicular, except at the apses. Use the two tacks and a string method for drawing the ellipse. The tacks mark the foci. BTW: Kepler's laws ARE proven, by Newton. They started as empirical from Brahe and Kepler, but Newton developed calculus to prove them from first principles (N's 2nd law, N's law of gravity, conservation of angular momentum).

[@necattasdelen7153]

+carultch Hi, Sorry I am not of the same advise. Newton did not proved the area law of Kepler but he preferred to chose the estimation of Kepler .They said :Orbits should be a conical section.And the only closed version of the conical section was an ellipse.In the mean time Newton calculated that the orbits could not be spiraled as the body on these orbits will go ad infinitum.(See page 290 of A.Motte translation of PRINCIPIA).A wrong estimation of Kepler and Newton.But Newton's universal attraction says that.the attraction force is radial,a side attraction does not exist.A perpendicular attraction force does not exist.Then Fp=m*dVp/dt=0 means Vp=Constant.And Kepler continues to say wrongly r*Vp=Constant.The spiraled orbits of Newton are not going ad infinitum. They are not open end type but closed.The spiraled orbits are closing after billions of cycling around the sun.And angular momentum has nothing to do with the orbits but energy conservation differentiel equation gives r=-4*a*t^2+4*t*T-4*T^2/6 as celestial motion equation.

[@ShahidAli-zf3gd]

Are u lefty professor??🤔

[@yoprofmatt]

SS Edit Shahid, The board is called Learning Glass. You can check it out at www.learning.glass Cheers, Dr. A

[@gilbertodeoliveirafrota8601]

In my country i need To fight against flat Earth ideas.

[@radhyack]

Yeah me too

[@whatabouttheearth]

I have a feeling no flat earther is doing anything of technical or scientific importance...or even getting a science degree.... 😄 or even taking a science class 😄

[@ronitmandal7301]

Is he lefty ?

[@yoprofmatt]

Nope. Flipped the image. See www.learning.glass Cheers, Dr. A

[@saquibwarsi4098]

He not lefty

[@zack_120]

Why this teacher appears so arrogant, or is it my misperception?

[@yoprofmatt]

He's totally arrogant, and also not as tall as he looks. Cheers, Dr. A

[@BabySagan]

This is cool, but my channel is better.

[@robertm.vaccato1334]

It's probably wrong!