We are in the ultimate round of gravity versus expansion saga…

In earlier episodes we found that gravitational pull is in a constant battle with "push" by thermal pressure or quantum pressure. Stars fates were decided by that battle. In the case of the universe as a whole the situation is somewhat more complicated. The universe is expanding not due to a constant pressure, but because all of its components had initial velocities. It is therefore important to learn some of the basic properties of gravity and how it "fights" initial velocities. It is also important to see how our "naïve" understanding of gravity can lead us towards the wrong description.
 
 

Get an object in your hand. It can be a pen, a calculator or an eraser. Drop it from ~30 inches above your desk.

1. What was the initial speed of the object? _____zero_____
2. Was the final speed larger? ______yes_____
3. What was the force that was responsible for that change in speed? Gravitational pull by the earth
4. Now throw the object upwards, to height of about ~30 inches. As it was moving up, what happened to the object’s speed? The speed is decreasing.
5. What happened to the object when it reached the top? ____It seems to stop for an instance, then moving downwards (it really is changing speed all the time, though).____
6. What happened to it right after that? ______Speed up as it is moving downwards______
7. Gravity was acting on the object throughout, and was responsible for the object’s change of speed. Now imagine yourself as an astronaut standing on a small asteroid and throwing the same object upwards (hey, the astronaut Allan Shepherd brought a golf ball to the moon, so that’s OK). Describe the motion of that object _________________If the object is given an initial speed that’s very small it will go up & down as on earth. _________________________________________________________________________________________________
8. Now assume that you hurl the object from the asteroid with all your might upwards. Describe the motion now: _________ If the initial speed is large it will slow a bit at first, than slow less and less as it is further from the asteroid. The asteroid will always slow it down a bit, but never enough to make it return to the asteroid – even if that asteroid was the only thing in the unliverse! The object is described as having a velocity larger than the escape velocity. _____________________________________________________________________________________________________________ Note that the object may never return!
9. Now consider a different situation: The whole class is standing on a Very light asteroid (the mass of the asteroid is much smaller than the mass of your class mates) and everybody jumps. If you jumped with an initial velocity that is higher than everybody else’s is than you are affected by their gravity (every body is attractive! Remember!?). Describe your speed as a function of time: _________As the class is jumping the faster ones are moving ahead of the peck, and slowing down a little in the process. They are further from the center so the force slowing them down is smaller, BUT all classmates closer to the center pull on them DESPITE OF THE FACT THAT THEY ARE MOVING. The class mates closer to the center have larger gravity due to their closeness, but less gravity because fewer class mates pull on them. (this situation is analogous to that in the Olbers paradox in which the 1/r^2 decline in light intensity is counteracted by the growing number of shining objects). _____________________________________________________________________________________________________________
10. Are you going to meet your peers again? What is it that will determine your fate? _______The fate of the jumpers (all of them!) is going to be determined by their jumping abilities AND their initial density. (the asteroid is not a point, so the density can be determined for the initial state). If the class is very densely packed and doesn’t jump high they will all fall back again onto the asteroid. If they aren’t closely packed they will fly away forever._______________________________________________________________________________________________________________
11. Consider a universe made of objects that are hurled away from each other. Assuming that there are as many slow objects as there are fast objects, describe the expected DENSITY of the universe. A picture/diagram will be helpful here. ________________As in 9, the effect is a density that is decreasing in time, but not in space. However, unlike the class examples of raisin breads, Adam, Eve and the snake, and growing balloons, the objects are flying in ABSOLUTE space. That is: objects IN SPACE are flying into EMPTY SPACE. The problems with this scenario are: 1. There is no explanation of the microwave background radiation. Radiation coming from the initial "asteroid" would go outwards, not come back to us in the center. 2. There are strong reasons to believe that there will be different abundances of matter at different distances, as in a huge supernova, but that’s not what we see. 3. This solution is highly contrived, and is humanity centered. It is not clear why we should be the center. (actually we are not even the center. We are falling towards the "great-attractor," a fact that can be discerned from red-shifts of nearby galaxies.). 4. Newtonian cosmology, the theory that we used for this solution, was proven to be inaccurate for distances of order of the solar system. Einstein’s theory of gravity is still valid for these distances. ______________________________________________________________________________________________________

12. The universe is actually uniform in density, and as shown above has many other properties hard to reconcile with a Newtonian cosmology. In order to concoct such a universe with our naïve model above we have to contrive an unbelievably complicated initial blast. The idea described in Friday’s and Monday’s classes -- that space and the objects in it are expanding at the expense of the original speed of objects in that space – can better account for the uniform density of space. Explain how: _________________See class explanations.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
 
 

Note that the rate of motion of objects in an expanding-space universe works exactly the same as the rate of motion in the universe that you constructed in your imagination (although the density doesn’t).