4.A satellite is placed into a circular orbit around the planet Jupiter, which has a mass M = 1.90 x 1027 kg. (a) If the radius of the orbit is R (measured from the center of Jupiter), use Newton's laws to derive an
expression for the orbital velocity.
(b) If the satellite increases its orbital radius, how it would change the orbital velocity? Explain.
(c) If the radius of the orbit is R, derive an expression for the orbital period.
(d) The satellite rotation is synchronized with Jupiter's rotation. This requires an equatorial orbit whose
period equals Jupiter's rotation period of 9 hr 51 min = 3.55 x 104 s. Find the required orbital radius.

To travel at constant speed, a car engine provides 24kw of useful power. the driving force on the car is 600n. at what speed does it travel?

The lights used by mark watley (played by matt damon) during the film the martian seem to be metal halide lamps. metal halide lamps are filled with vaporized mercury and metal-halogen compounds. when an electric current is passed through the lamp, the tube begins to glow a bright white/blue color. if you were to pass this light through a prism to separate the individual light frequencies, you would see a rainbow just as you would if using natural sunlight because of the complexity of the metal halide gas and the vast amount of possible electron transitions. (the study of light in this way is known as spectroscopy and allows astronomers to know exactly what atoms compose distant stars, simply by looking at the light they emit. the spectral lines an atom produces uniquely identifies that atom just like a fingerprint uniquely identifies a person. the momentum equation and energy equation that we have used above can be combined to give the following equation: c = e p where again p is the phonon momentum, e is the photon energy and c is the speed of light. when you divide the photon energy found in #6 by the photon momentum found in #4, do you get the speed of light? (if not, check your work for questions #4 through #6). yes no

Let v1, v2, w be three linearly independent vectors in r 3 . that is, they do not all lie on the same plane. for each of the following (infinite) set of vectors, carefully sketch it in r 3 , and determine whether or not it is a vector space (i.e., a subspace of r 3 ). explain your reasoning