Movies of ice skaters 1, 2
 

If global warming proceeds during the this century as anticipated, it is possible that the polar ice caps will melt, substantially raising sea levels around the world (flooding coastal cities like New York, etc.).  Would this shorten, lengthen or have strictly no effect on the duration of a day?  (A "day "here means from one sunrise to the next one.)

a. lengthen the say
b. shorten the day
c. have strictly no effect on the length of a day

Kepler's Second Law

This can be restated in terms of the area swept out (dA) in some time interval (dt).
 
 

The area of the triangle can be found by taking 1/2 of the parallelogram's area-

dA= 1/2 R * v dt 

By using the definition of angular momentum (of a point particle) we can rewrite the triangle's area as-

dA= L/ 2m dt

So,

dA/ dt= L/ 2m= constant

Angular momentum has to be conserved as we only have a central force acting on the orbitting body (it cannot exert a torque), so the body sweeps out equal areas in equal time intervals.
 
 

Kepler's second law implies that as a planet's distance from the sun increases in an elliptical orbit, its orbital speed

a. increases
b. decreases
c. remains the same
d. it depends