A Sense of Proportion: Saturn is about 60,000 km in radius, and its rings are only about 0.01 km thick with ripples 100 m high. Design a really big model with Saturn 60 inches in radius (10 feet in diameter. How thick must the rings be in your model and how high can the ripples be?

Rings = inches thick

Ripples = inches high

Space-time metric ds2= -dt2+at2dx2+bt2dy2+ct2dz2 (a)how does the area of a rectangle with vertices at ( x=0, y=0, z=0 ), (1,0,0 ), ( 0,1,0 ) and (1,1,0 ) changes with time? (b) if a photon moving in the x direction starts from the origin at t=1, when does it reach x=l? (ds=0 for the trajectory of a photon.) (c) the proper time for a particle is defined by cd=ds. what is the proper time for a particle to move along the trajectory ( x(t)=t, y(t)=0, z(t)=0 ) from t=0 to 1 ? what is the condition on the parameter a so that the velocity of the particle never exceeds the speed of light ?

Sawyer is studying diffraction. he draws a diagram of a plane wave to show how light waves travel. which best describes sawyer’s error? the wave fronts should be perpendicular to the direction in which the waves move. the arrow showing the direction of movement of the waves should be pointing to the left. the arrow showing the direction of movement of the waves should be pointing downward. the wave fronts should be both parallel and perpendicular to the direction in which the waves move.

In 1859, charles darwin published the first edition of on the origin of species, which explained his observations of various groups of animals that showed great similarities but minor differences. darwin concluded that if a population of one species separates into two different populations that live in separate locations, then over the course of many generations the different populations can develop into different species. this idea predicted many future biological findings and became the basis of modern biology. darwin’s explanation for why different species exist is best described as a(n) law. theory. inquiry. hypothesis.