1. Explain what is wrong about Newton's depiction of gravity.

2. Why did we make you do all that Newtonian math? Is there still a point to it? If so, what?

3. How does Einstein's theory of general relativity explain gravity?

4. In the trampoline analogy for general relativity, what does the trampoline represent?

5. https://youtu.be/S_GVbuddri8 video: Explain in simple terms what the black part at the center is? Why is it black? What is the bright part around it and why is it there?

6. What is apsidal precession?

7. explain why apsidal precession is a phenomenon caused by general relativity.

8. Explain the evidence related to gravity (not time) that supports Einstein's theory of

9. Under what circumstances will a light beam follow a curved path?

a. when emitted from a moving source

b. when measured from an accelerating space ship

c. when measured in the presence of an extreme gravitational field

d. NEVER

10. There's more! Do some research about "gravitational waves." What are they and what do they have to do with general relativity? (Remember to site your sources.)

Now STOP Thinking About a Ball on a String! Newton described gravity as a force of attraction between all objects that have mass in the universe. In the last lesson we described this as a ball on a string and imagined a person swinging that string above their head in a circle. We said, "Gravity serves a function very similar to the string in our example above. No matter where we are on Earth, there is a force pulling straight to the center of the planet." This is an overly simplistic model. Gravity is not the same as centripetal force, even in Newton's understanding of gravitational force. If it were, why would planets orbit the sun in ellipses as described by Kepler based on Newton's laws? And here's where it gets complicated; even the nice ellipses don't quite work... Instead Think of a Bowling Ball on a Trampoline In the early 19005, Albert Einstein came up with a theory of gravity that actually explains gravity rather than simply describing its effects. Einstein showed mathematically that gravity is not really a force that of attraction between all objects with mass, as Newton thought. Instead, Einstein showed that gravity is a result of the warping, or curving, of space and time, which made up the same space-time \"fabric." These ideas about space-time and gravity became known as Einstein's theory of general relativity. Einstein derived his theory using mathematics. However, you can get a good grasp of it with the help of a simple visual analogy. Imagine a bowling ball pressing down on a trampoline. The surface of the trampoline would curve downward instead of being at. Now imagine placing a lighter ball at the edge of the trampoline. What will happen? It will roll down toward the bowling ball. This apparent attraction to the bowling ball occurs because the trampoline curves downward, not because the two balls are actually attracted to one another by an invisible force called gravity. Einstein theorized that the sun and other very massive bodies affect space and time around them in a way that is similar to the effect of the bowling ball on the trampoline. The more massive a body is, the more it causes space-time to curve. This idea is represented by the Figure below. According to Einstein, objects move toward one another because of the curves in space-time, not because they are pulling on each other with a force of attraction. [Figure 1] This diagram shows how Earth's mass bends the "fabric\" of space and time around it, causing smaller objects such as satellites to move toward Earth. When there is no mass in a volume of space, the space is not curved. An object passing through such space would follow a straight line in our normal way of thinking of a straight line. [Figure 2] When a large mass is placed in the space, however, the space is curved due to the presence of the mass. In this case, an object passing through the space must follow the curvature of the space in order to follow a straight line. Thus the path of the object bends toward the mass. The change in the direction the object appears to be exactly the same as it would have been following Newton's law of gravity. The mathematical expressions describing the properties of a gravitational eld around a mass are given in a set of formulas called the Einstein Field Equations. These formulas are a highly complex system of partial differential equations. Under normal levels of gravitational eld strength, however, the relativistic mathematics for gravity reduce to Newton's mathematics for gravity. When gravitational eld strength is extremely high, however, the correct movement of objects can only be calculated with Einstein's relativistic gravity. Mass tells space how to curve and space tells mass how to move. Notice how the ball moves around the weight in the video below: HSW: A simple demonstration of Einstei 's Theor... ID '.'.-' ' ' Copy link .. l Watch on IIYuuTube m\\\\ How Can We Know This is Happening? Of course, science is based on empiricism. How ca n we know this invisible "fabric of space-time" exists? Experimental tests to garner support for the general theory of relativity were not easy to nd. The rst involved the orbit of the planet Mercury. Kepler's laws based on Newtonian physics predicts an elliptical orbit: [Figure 3] However, notice the movement of the ball around the mass in the video demonstration above. It does not maintain a consistent eliptical orbit. Einstein's theory predicts an orbit that is more like a rosette: [Figure 4] As you can see in this Figure 4, the line that connects the points farthest and nearest to the sun (the perihelon and aphelion) shifts a little with each orbit. This is called apsidal precession. The orbit of Mercury (the closest planet to the sun) exhibits a notable apsidal precession which could not be fully explained using Newton's Law of Universal Gravitation. The motion of Mercury was in much greater agreement with the predictions from the equations of general relativity. The acceptance of the theory of general relativity increased greatly after it was shown to correctly predict the orbit of Mercury. Both Newton's theory of universal gravity and the theory of general relativity predict that light can be deected by gravity. The calculation of the amount of deection predicted by Einstein's theory was approximately double that predicted by Newton's theory. The deection of light by gravity was tested in 1919, ve years after general relativity was proposed. Two British groups took photographs of a region of the sky centered on the sun during the May 1919 total solar eclipse and compared the positions of the photographed stars with those of the same stars photographed from the same locations in July 1919 when the sun was far from that region of the sky