Newtonian Gravitation – An Overview (Preparation for General Relativity)

In this video (GR - 01), some background ideas to General Relativity, namely Newtonian Mechanics and Newtonian Gravitation, are discussed at more or less the High School level. The outcome of that discussion is, hopefully, to see some of the inadequacies of Newton’s Theory of Gravitation, and also to identify a number of ideas and equations from it which will be useful in formulating Einstein’s General Theory of Relativity - the theory that would replace it.

This video is part of a series of videos on General Relativity (GR-01 to GR-20), which has been created to help someone who knows a little bit about “Newtonian Gravity” and “Special Relativity” to appreciate both the need for “General Relativity”, and for the way in which the ‘modelling’ of General Relativity helps to satisfy that need – in the physics sense.

The production of these videos has been very much a ‘one man band’ from start to finish (‘blank paper’ to ‘final videos’), and so there are bound to be a number of errors which have slipped through. It has not been possible, for example, to have them “proof-watched” by a second person. In that sense, I would be glad of any comments for corrections ……. though it may be some time before I get around to making any changes.

By ‘corrections and changes’ I clearly do not mean changes of approach. The approach is fixed – though some mistakes in formulae may have been missed in my reviewing of the final videos, or indeed some ‘approximate explanations’ may have been made which were not given sufficient ‘qualification’. Such changes (in formulae, equations and ‘qualifying statements’) could be made at some later date if they were felt to be necessary.

REPORTED CORRECTION
"Correction: 43:15 The escape velocity here (from the surface of the earth) should read about 11.2 km/s (not m/s)"

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[mathcool]

Just finished all 20 videos and all I can say is wow! If you are truly interested in GR and have the time to invest, then you must make this series a stop along the way. IMO a good math background (multivariate calculus and linear algebra) would definitely help but isn't entirely necessary - you'll still walk away with great admiration for Einstein's field equations and the tensor equations that it is composed of. One recommendation I would give that helped me (along with note taking) is to take two or three breaks at the transitions, go for a walk, clear the head stuff and then return to finish the video. What a great teacher this guy is.

[rydawg]

Thank you for these videos. As a former physics student revisiting GR years later they are really a wonderful resource.

A note about the discussion of vectors at the end - the way I learned them was to use unit vectors, so in this case it would be an “r hat” vector, where “r hat” is a unit vector pointing radially outward from the center of the earth. That way you get vector equations without having the cubic term in the denominator of the force equation as you pointed out.

[sudhagarraghavan]

Thank you for this series of videos. I find them to be the best source on GR in the YouTube by far. You understand GR thoroughly and able to articulate the concepts in a systemic and step by step manner. Most of the others including lectures on GR are shockingly bad and poorly taught. Keep up the excellent work and looking forward to see more such videos on advanced physics.

[axle.student]

Thank you. This presentation is exceptionally well done. I am looking forward to the rest of this series :)

[eddieboyes]

Thanks Michael (M R Davis) - I hadn't noticed this 'typo' in my text and read it out blindly. Well spotted. I will probably leave the video "as is" for the moment to save re-uploading with a new URL Your comment can act as a correction. I may change it in the future. Thanks again. Eddie

[aneikei]

Great stuff. However @43:15 the escape velocity from the surface of the earth is 11.2 kilometers per second, not 11.2 meters per second.

[perdehurcu]

Selamlar. Hocam muhteşem dersler anlatmışsınız. Teşekkürler.

[Gismho]

This really is a superb series of videos. Love the detailed explanations and the gradual build up to serial number 19. There are several very good "general relativity" videos on youtube. This series probably takes first prize, however.

Request: What about a detailed mathematical explanation of general relativity as a sequel to this series?

[Neko-chan-quynu]

Force is a vector in space. Its sign is positive or negative again by convention. In the subjects of strength of materials, structural mechanics or elastic environmental theory, the compressive force is negative when it is an external force directed at the body (which compresses the object), and is positive when the external force stretches the object, point out the object.

[hershyfishman]

37:30 If φ(r) = -4/3 πGρr^2, then why isn't it an upside down parabolla with φ = 0 at r = 0 as its max?

[Neko-chan-quynu]

I see the concept of the acceleration due to gravity is not the problem. It is the viewing of the object drifting in the geodesic at a constant velocity that is problematic.
Compare the force to brake an object at rest at height h and the force to brake an object at rest on the ground to see if it is different? If it is different => the object is not moving with a constant velocity on the geodesic. Therefore, it must be accelerating => there is acceleration due to gravity.
Consider that objects in a gravitational field are always subject to acceleration. And the so-called mass is a consequence of Newton's theory of force, of energy, of momentum. Hence it always makes sense. If Newton's theory is negated, what does the so-called G and M in Einstein's formula mean?
Of course, a problem has many solutions. Maybe Einstein's way is the way to go, but that doesn't mean Newtonian mechanics is wrong. It may be better to conceive that Einstein perfected Newtonian mechanics.

[Yuri-wkj]

There is no confusion in Newton’s gravitation between force of gravity and weight. Those forces are applied to different bodies: force of gravity to the body itself and weight to the body that provides support(e.g., the surface of the chair you sit in or the floor you stand on, etc). When you write equation(s) of body motion you should consider only forces applied to body. In this way there is no confusion when weight is zero, but gravitational force is not.

[michaelricharddavis]

Escape velocity at Earth surface is 11.2 km/s not m/s.