Black Holes and Uncle Albert

• p2: Feeling light at the top and heavy at the bottom - this is a good example of Newton's second law! Describe the acceleration at the top / bottom?
• p3: Note the relation gravity and acceleration discussed already at this point.This is one of the consequences of the "Equivalence Principle" - that gravitational and inertial mass are equal!
  (There are many occasions for studying this principle at an amusement park. Quite a different example is given bythe "Slänggunga" - where loaded and empty swings hang in the same angle at any time!)

Home from the amusement park, Uncle Albert prepares for Galileo's experiment at Pisa - moving away fromAristoteles' claim that heavy bodies fall faster - and discusses why. The experiment (p7) without air resistance,you have probably seen or done at school - if not, you are welcome to try it out for yourself, just let me know!What do you think will happen on the moon?The Apollo astronauts actually performed the experiment on the moon! (cf p9)

• p11: This discussion starts to sound philosophical - "Cogito, ergo sum"
• p12: What is required of a spacesuit - you may want to read more on-line!
• p12: If gravity is only g/6 on the moon, how much higher can you jump?How much longer time with the jump take?
• p13:" We are out in space , and there's no gravity" This is a good one! (and students,indeed, quite often give comments along this line!) Just for an exercise, you may want to work out the strength of the Earth's gravity at the surface of the moon.
• p13: You have seen the pictures of weightless astronauts in their space craft?How come? - they are still in the gravitational field from the earth!
• p13: ".. how hard to fire the retro-rockets" - this sounds like another nice exercise!
• p13: Note how Gedanken had tried to predict the outcome of the experiment - but found herself wrong. A learning experience! (see also p17, where Albert states that "he had a hunch it might turn out like that")
• p15-16. Note the details needed for a space walk!
• p16 "The surface of the earth was a hundred miles or so away" - so, what is the period of the orbit? How fast is she moving? What fraction of the earth can you see from that height?
• p17 Why does she not fall? What is "above" and "below"? What is the positionof the Space Shuttle in orbit?
• p18: "Keys and paper fall in exactly the same way" - another example of the "equivalence principle"
• p19: You may want to work through the acceleration in a circular motion:(x=r cos w t, y= r sin wt, a_x=d²/dt²= -w ²x, a_y=- w² y, directed towards the center). For a more down-to-earth exercise,try one of the circular motion attractions at Liseberg!
• p19: "the Shuttle and you - floating together side by side, in the same orbit. The Shuttle is much heavier than you - Equivalence priniple in action!

2 Wonky Space

• p19: Newton's first law:
• p19-20: We will return later in the book to the discussion about gravity as a property of space rather than a force (another conseqence of the equivalence principle.)
• p27-37 or so. This is just a fantastic section. I have used parts of it several times for story reading in class. Read it carefully, reread it again and reflect onparallell lines, curved space etc. E.g. You might want to take a look at the map, find Alexandria and Syene (Assuan) where Erathostenes measured the solar elevation to determine the size of theearth with amazing accuracy. From the measurements needed to construct the map, they must have noted that the same difference in longtude corresponded to different distances at different latitudes. The recurring flooding of the Nile created a need for good geometrists!
• p 38: "is it alright to think of gravity instead of wonky space?" Note the discussion about "Depends on wheteher they come out with the same result"This is important! - Verification - falsification (Kuhn).
• p 38: My (at the time) 9-year old son jumped up to measure pi for himself when we were half-way through this chapter!
  P40: The discussion about the cause of the low number (flat battery) - great!
  p41 - For a gedanken experiment of your own, you may think about determining the ratiowith the center of the circle at hte North pole. What value would you get for a radius of 10000 km?
• p42: Back again. Is it the tape measure that has shrunk of the ground that has been stretched?If it gives the same results?
  If you get hold of "Mr Tompkins", take a look at "Hookham's circus" in this context!
• The discussion about the lengths and squashed eyeballs of course brings about the question of how we could oberve the effect, it is there. Let's move on!

3. The Big Bang

• p50 "Your are made of stardust!" ?
• Lots of questions here: Why do not galaxies lump together?
• p51-2 "What i s a "WEIR"? And why is there a weir in this place of the story?
• p 53: Gedanken examines the movements of galaxies. You may want to take a look at Maria Sundin's simulations of galaxies (available?) Or picture galleries? Take a look at "Powers of ten" to find our place in the galaxy!
• p55: All galaxies moving away. How can we know if a galaxy is moving away?Why is the galaxy further away moving away even faster?Good work: Noting down the distances and their speed, trying to find the relation.(Sometimes you will need to do lots of plots to find the right relation - if any!)"Twice as far away, twice the speed..:" This is "Hubble's law", discovered ???(The Space telescope is, of course named after Edward Hubble)
• p56-57 One day, they may slow right down and start to fall back again. On theother hand, they might be moving to fast for gravity to bring them back - like a rocket leaving the pull of Earth's gravity (oops, how far away is that?) This is an important - and still unanswered - question. The mass of theuniverse is known to be very close to the limit required to cause a "Gnab Gib" - i.e. we don't know the long-term future of the Universe!
• p58: A quick tour of the Nucleo-synthesis!
• p59: "sitting at the center of the universe" - because everything moves away from us at a speed proportional to the distance." Why is this conclusion not correct? The stretching rubber is a good analogy. Other analogies suggested include a raising dough with raisins moving in all directions.
• p 71: "Globe, long-horn, a ring-doughnut, a saddle." Try to draw these shapes with e.g. matlab or Mathematica..

5 Bent light

• p 82 "acceleration faking gravity again"
• p89: 25 cm - how large is the acceleration required to cause this deflection? (you have to estimate the size of the spacecraft to work it out)
• p90 "The light beams will be pulled downward, too" - this is the "strong equivalence principle" (?)leading to the general theory of relativity.
  In this context, you may also want to take a look atMr Tompkins, where an apple is thrown across an accelerating elevator and "the floor will eventually overtake the apple". (Another exampleof the same basic thoughts)
• p92: How could one detect a black hole? Astronomers now think they have seen a few.How can they know?

6 Children older than their parents

More to come ...

• Einstein fotoalbum och Einstein on-line
• Relativitetsteori , St. Andrews, Skottland
• Numerisk Relativitetsteori (NCSA Relativity Group)
• Virtuellt besök hos ett svart hål.
• Light Cone A multimedia introduction to the theory of relativity. Initially written for use in a non-science major course. Lecture notes. By Rob Salgado, Syracuse University.

"It is not easy for one person to be in two places simultaneously"
"It is not even easy for two people to be in two places simultaneously. Yours, Albert"