Calculate Period & Center of Mass in Binary Star Systems | Newtons Law of Gravity & Kepler's 3rd Law
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- เผยแพร่เมื่อ 20 ต.ค. 2024
- Commonly called the 'Two Body Problem' or the 'Kepler Problem', apply Newton's Law of Universal Gravitation to the circular motion of two celestial bodies in orbit around each other.
Looking at centripetal force, we can show that the two objects will orbit their mutual center of mass which is known as the Barycenter.
Then, relating the centripetal force we can calculate the period of orbit for the two bodies. The key concepts here are that the distance from one star to the other is the sum of the two orbitial radii. Additionally it is important to recognize that the orbital periods are the same, and the orbital velocities are different. Ultimately the derivation results in the equation commonly referred to as Kepler's 3rd Law.
This problem commonly comes up in early physics courses including AP Physics C Mechanics.
and yes I added a watermark. People have been ripping off my work.
Wow, very interesting video! Keep up the great work!
Thank you very much!
Very interesting. I am also blown away by how intelligent Kepler was.
great video thanks
You bet
Definitely is a great video
Thank you so much, your videos are helping to prepare for JEE exam
Happy to help.
Sir while finding apparent acceleration due to gravity due to earth's speed on a body ,we take the frame of body so that the force is centrifugal (outwards) and we get a reduced net acceleration.
But on viewing from outside inertial frame of refrence we have to take a centripetal force(inwards) thereby getting an increase in net acceleration. But the net acceration can't be different in different frames. Plz tell me where am i wrong ?
Well done! Thank you so much!
Glad it was helpful!
awesome!!! underrated asf
Appreciate it!
please do more astronomy videos
Will do.
About 2:03 on Fc1 = Fc2 "...and those are both equal to one another. It's that same force by gravity that's pulling them together." Can you elaborate on what this means?
Yes, the gravitational force is responsible for acting as the centripetal force on BOTH objects. As a rule the gravitational force will act with equal magnitude on both bodies.
Very useful thanks 🙏
glad you found it helpful.
thank you thank you. you have saft my life
I am willing to wager that in the entirety of human history nobody has died because they did not correctly calculate the period of a binary star system... but thanks!