The mass of Saturn is 5.67 x 10^26kg. What is the orbital speed of an ice particle that orbits Saturn at a distance of 102,000 km from the planet's center? Note: The constant of universal gravity (G) equals 6.674 x 10^-11 N • m^2/kg^2.

A. 13.8 km/s

B. 19.3 km/s

C. 27.5 km/s

D. 1.93 km/s

Distinguish between a transverse wave and a longitudinal wave.

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

Suppose a comet has an orbital period of 309.1 years around the sun. what is it’s average distance from the sun?