Lecture on: Newton s and Einstein s theories of gravity

Transcription

1 University of Sulaimani Faculty of Science and Science Education School of Science Education Physics Department Lecture on: Newton s and Einstein s theories of gravity By Halo Anwar Abdulkhalaq May 2014

2 Overview Aim of the lecture Introduction Newton s theory gravity Newton s failure Einstein s theory of gravity The successful tests of Einstein theory

3 1. Aim of the lecture The Aim of this lecture is studying the gravity in two important theories (Newtonian and General relativity). By the end of the lecture we should be able to recognise both theories and be able to understand the failure of Newton s theory and the need to Einstein s correction.

4 2.Introduction Throughout the history of physics there were many attempts to understand natural forces in the Universe. Gravity is one of the four fundamental forces exist in nature and it is the weakest one Newton published the idea of gravity in his book the Principa on 5 th of July While Einstein published his famous paper on general relativity theory in November 1915.

5 3.Newton s theory of gravity states that any two objects exert a gravitational force of attraction on each other. The magnitude of the force is proportional to the product of the gravitational masses of the objects, and inversely proportional to the square of the distance between them (fig. 1). For example in the case of Earth and moon it is given as: F grav G M em 2 r m G: is universal gravitational constant = 6.67 x N m 2 /kg 2

6 Figure 1

7 In the case of an object on earth the force of gravity is given as: M em Fgrav G 2 Re it can be written as: F grav mg where M e = 5.98 x kg is the mass of the Earth and R e = 6.38 x 10 6 m is the radius of the earth hence: g G M R e 2. 8 e 9 s m 2

8 4. Newton s failure Newton claimed, gravity was a constant, instantaneous force, the information about a sudden change of mass would have to be somehow communicated across the entire universe at once. And even the action between two very distant masses would happen faster than the velocity of light which is ultimate speed exist in the Universe and nothing would exceed that speed according to Einstein. The light from sun takes 8 minutes to reach earth, but according to Newton if Sun disappears we on earth feel it instantaneously.

9 5. Einstein s theory of gravity Einstein states that the gravity is geometry through his famous equation (the Einstein field equations), more specifically he says the curvature of spacetime is gravity. The idea is that the massive objects in the Universe warp spacetime and produce a curvature around themselves which let the other small particles to move according to it.

10 The path that each body takes in the curved spacetime is called geodesic, and the body moves according to geodesic equation which is equivalent to equation of motion in classical mechanics.

11 Einstein Field Equations G is Einstein tensor which describes the geometry of spacetime, G is Newtonian constant. T is stress-energy tensor which describes the properties of matter, c is the speed of light. It is easy to notice that this equation is linking geometry to matter as Einstein himself claims. In this formula matter tells geometry how to be and geometry tells matter how to move (fig. 2,3)

12 Figure 2

13 Figure 3

14 6. The successful tests of Einstein theory Every theory goes under tests to examine its success, Einstein s general relativity theory (Gravity theory) passed many tests successfully in the macro scales. One of those tests is bending of light, as it was believed that light is move in the straight path but Einstein corrected this and stated that even light will follow the path on the curved spacetime produced by massive objects (fig. 4) Another test was a perihelion precession of mercury (fig.5), Newton formula was not precise to explain this problem in exact way.

15 On the other hand Einstein s formula was successful to find this precession. The precession observationally is (5600 arcsec/century), Einstein s theoretical value was exactly the same, while Newton s value was (5557 arcsec/century)

16 Figure 4

17 Figure 5

18 References 1. S. M. Carroll, lecture note on general relativity, html 3.