Thanks! My students and I are huge fans of your lectures. Keep up your great work! One question. Is it "semi-major axis" or "major semi-axis". I always thought the latter. 🤔
Who noticed that Mr. P- from 1973-2084😅 BTW, ur lecture was amazing as usual 😄 Just now thought of learning Kepler's laws😀 And also, do we have any unit for eccentricity?
The units for eccentricity work out to be (distance)/(distance), in other words, whatever units are used for distance, they cancel out and eccentricity has no units.
No, that's not it. It doesn't explain why planets have different eccentricities, and why some comets orbiting the sun have very squished, elliptical orbits (their eccentricities are close, but below 1). The real question you should be asking is "Why would the orbit even be a circle?". Sure, the circular trajectory is one of the ways you can have a stable, closed-path orbit. But to have a perfectly circular orbit, the satellite needs to be at a precise distance from the primary body, and it has to have an initial velocity that is exactly perpendicular to the force of gravity, and with exactly the precise value so that the centripetal force vector needed to maintain that circular trajectory is exactly the same as the Newtonian force of gravity. If you think about it, those are quite demanding initial conditions. If that was the only way one body could orbit another body on a closed path, it would be a miracle anything would be orbiting in the whole universe! But let's ask another question: what if we spoiled our circular orbit a bit, and placed a body at a slightly different distance from the primary body keeping velocity the same, or with a slightly different initial velocity vector but at the same distance? What trajectory would the body follow in such a case? This is called the "Kepler problem" or "one-body problem". Just to clarify - the assumptions are that there are only two bodies in the system, the primary body, and the satellite. The primary body is "pinned" in place serving as the frame of reference, there are no external forces, and the only force is the Newtonian force of gravity (inverse-square law) which is always pointing from the satellite to the primary body. The math to solve this problem is a bit beyond the scope of AP physics (and certainly a youtube comment), but if you solve it, you discover that the satellite can have only one of the 3 types of trajectories: elliptical, parabolic, hyperbolic. Only the elliptical orbit is a closed trajectory, parabolic and hyperbolic are open. And a circular orbit is only a very specific case of an elliptical orbit when the eccentricity of an ellipse is equal to 0. To get a feel of what's happening, you can use some online gravity simulators, where you can place planets, give them initial speeds and simulate their movement. If you play with them a bit, you will discover that it's actually almost impossible to put a body only by your eye so that it would orbit on a perfectly circular trajectory. I mean, you might get something that will be visually very close to a circle, but I bet it will actually be an ellipse with a slight eccentricity (just like Mr. P demonstrated with the planets in our solar system) And if you give the satellite too much speed (thus energy), it will "escape" from the primary body on a parabolic/hyperbolic open trajectory.
And by the way - those three (four, including circle) curves are called the "conic curves", because you can obtain them by slicing a cone with a plane. And all of them share the same parameter called eccentricity to describe their shape. When eccentricity is 0, it's a circle, when eccentricity is greater than 0 and smaller than 1 it's an ellipse, when eccentricity is equal to 1 it's a parabola, when eccentricity is greater than 1 it's a hyperbola. Eccentricity is also related to the total energy of the system, which can also be used to determine what trajectory a body will take when given the initial conditions.
![How the Bizarre Path of Mars Reshaped Astronomy [Kepler's Laws Part 1]](http://i.ytimg.com/vi/Phscjl0u6TI/mqdefault.jpg)
I WAS LITERALLY SEARCHING ABOUT KEPLER'S LAWS RIGHT NOW U HAVE NO IDEA HOW GREATFUL I AM !!!
Wonderful!
(You can find my other videos about Kepler's Three Laws in this playlist: ruclips.net/p/PLPyapQSxH6mYjCmJSl0w8_dAs6FTS3LgZ )
@@FlippingPhysics Thank you so much!
Aspiring astronomer here who was looking for AP Physics help but got distracted-- this is super cool! Thanks for making these videos Mr. P
Today I was searching this video on your channel but I didn't found it and here you Posted it thank you very much!!! God bless you!
You are very welcome!
(You can find my other videos about Kepler's Three Laws in this playlist: ruclips.net/p/PLPyapQSxH6mYjCmJSl0w8_dAs6FTS3LgZ )
uh really deserve more views... my physics exam is the day after tomorrow...it really helped!
Best of luck on your exam!
Thanks! My students and I are huge fans of your lectures. Keep up your great work!
One question. Is it "semi-major axis" or "major semi-axis". I always thought the latter. 🤔
I think both are correct.
(Which is always fun.)
Now that I see it here, I like this option even better. It's so official looking.
Yeah. Placed there with 4 _official_ scientists...
love your lectures
Thanks for the love!
u are really helpful thank you so much sir . i am an arabic guy we dont have teachers like u 💯
Ah, but you do. I am right here!!
You are the man whom I love
thanks so much for uploading this video, you are awesome !🔥
Thanks for the love!
How exactly u got 0.95773a^2, can u please reply(I'm a bit weak in maths)
I don't know why i'm learning this.
but its interesting..
Are you learning it because it is interesting...?
@@FlippingPhysics yeah.
Sir can you teach topics like mechanical properties of solids and fluids . If you can teach this i will be very grateful to you .
Someday, however, it will not be for quite a while.
Who noticed that Mr. P- from 1973-2084😅
BTW, ur lecture was amazing as usual 😄
Just now thought of learning Kepler's laws😀
And also, do we have any unit for eccentricity?
The units for eccentricity work out to be (distance)/(distance), in other words, whatever units are used for distance, they cancel out and eccentricity has no units.
@@FlippingPhysicsOh ok! Thank you so much😊
how would you actually define fociii?, :(
It’s the other way round, you define an ellipse from two points called focii.
Why is it not a circle?
Is it because the Sun is moving and this wasn't considered by Kepler?
No, that's not it. It doesn't explain why planets have different eccentricities, and why some comets orbiting the sun have very squished, elliptical orbits (their eccentricities are close, but below 1).
The real question you should be asking is "Why would the orbit even be a circle?". Sure, the circular trajectory is one of the ways you can have a stable, closed-path orbit. But to have a perfectly circular orbit, the satellite needs to be at a precise distance from the primary body, and it has to have an initial velocity that is exactly perpendicular to the force of gravity, and with exactly the precise value so that the centripetal force vector needed to maintain that circular trajectory is exactly the same as the Newtonian force of gravity.
If you think about it, those are quite demanding initial conditions. If that was the only way one body could orbit another body on a closed path, it would be a miracle anything would be orbiting in the whole universe!
But let's ask another question: what if we spoiled our circular orbit a bit, and placed a body at a slightly different distance from the primary body keeping velocity the same, or with a slightly different initial velocity vector but at the same distance? What trajectory would the body follow in such a case?
This is called the "Kepler problem" or "one-body problem". Just to clarify - the assumptions are that there are only two bodies in the system, the primary body, and the satellite. The primary body is "pinned" in place serving as the frame of reference, there are no external forces, and the only force is the Newtonian force of gravity (inverse-square law) which is always pointing from the satellite to the primary body.
The math to solve this problem is a bit beyond the scope of AP physics (and certainly a youtube comment), but if you solve it, you discover that the satellite can have only one of the 3 types of trajectories: elliptical, parabolic, hyperbolic.
Only the elliptical orbit is a closed trajectory, parabolic and hyperbolic are open.
And a circular orbit is only a very specific case of an elliptical orbit when the eccentricity of an ellipse is equal to 0.
To get a feel of what's happening, you can use some online gravity simulators, where you can place planets, give them initial speeds and simulate their movement. If you play with them a bit, you will discover that it's actually almost impossible to put a body only by your eye so that it would orbit on a perfectly circular trajectory.
I mean, you might get something that will be visually very close to a circle, but I bet it will actually be an ellipse with a slight eccentricity (just like Mr. P demonstrated with the planets in our solar system)
And if you give the satellite too much speed (thus energy), it will "escape" from the primary body on a parabolic/hyperbolic open trajectory.
And by the way - those three (four, including circle) curves are called the "conic curves", because you can obtain them by slicing a cone with a plane. And all of them share the same parameter called eccentricity to describe their shape. When eccentricity is 0, it's a circle, when eccentricity is greater than 0 and smaller than 1 it's an ellipse, when eccentricity is equal to 1 it's a parabola, when eccentricity is greater than 1 it's a hyperbola.
Eccentricity is also related to the total energy of the system, which can also be used to determine what trajectory a body will take when given the initial conditions.
@@MrSzybciutki
Thank you for replying.
I will read ASAP
According to the dates below his picture (1973-2084), he’s going to live to the ripe old age of 111…give or take a year!
I've got plans
2084?
Yep. 111 years. That's my plan.