C4M.7 please help

How difficult would this be? Assume that the star in question is a red dwarf that has a mass of about 0.30 times that of the sun (whose mam is 20 x 10" kg) and that the planet has 15 times the mass of Jupiter (whose mass 1/1047 times that of the sun) orbiting at a distance of about 1.5 Im from the star's center (about 10 times the distance rants from the earth to the sunj. single rotates (al About how far is the star's enter of mass from the sys- above the v vers heads, We bem's center of mass? will see in unit N that the appropriate place to attach the b) If the star is 8.1 ly from us, what will be its maximum wire is at the system's center of mass. Where is this point angular distance from the system's center of mass Native to the center of the most massive sphere is seen by a telescope? Express your result in milli arcaseconds (mas), where 1 mas = (1/3,600,p00). CAM Calculate the correct distance between the oxygen (cl Considering that atmospheric disturbances will blur nucleus and the center of mass of a water molecule (see star's apparent size to a blob about 250 mas across, is example C4.2), considering that the angle between the detection of such a planet using this method easy? lines connecting the hydrogen nuclei to the oxygen nuclei Note: I did not choose this problem's parameters randomly. is really 105", not 90'. (Hint: Orlent your reference frame In 1996, George Gatewood at the University of Pittsburgh so that the line connecting the hydrogen nuclei is parallel announced the tentative discovery of a planet of this mass to the & axis. Putting the oxygen nucleus at the origin is and distance orbiting Lalande 21185, a red dwarf star B.1 ly still advantageous.) from earth, after analyzing more than a half-century's worth of measurements of the star's position relative to CAM'S A small asteroid (about d = 100 m in diameter) is distant stars. However, for the reasons described in the spotted moving directly toward Starbase Alpha floating in problem, this measurement is very difficult and has not deep space. The residents plant explosives on the asteroid seen confirmed. Virtually all of the extra-solar planets we and manage to blow it apart into two chunks, one with a know of today were found using the Doppler shift of the mass of 24 times the other, while it is still far from the star- star's light due to its wobbling motion (this turns out to be base. If the center of the lighter chunk passes If - 1800 m from the edge of the starbase, which is D = 2.2 km in diam- ster, how close does the center of the other chunk get to the starbase? (Hint: How does the two-chunk system's center Motion of the of mass move after the explosion?) S seem's canker of miss CIM.6 In a best of a new missile defense system, a missile is fired on a trajectory that would directly strike a certain bunker A laser flash from the bunker ignites the missale's fuel, causing it to explode into two fragments, one with 18 times the mass of the other. If the fragments land at the same time 45 m apart, by how much does the larger fragment miss hitting the bunker? Ignore the effects of air resistance. (Hint: The external gravitational interaction between the missile and the earth would have caused the missile's center of mass to reach the ground at the location of the bunker if the missile had not exploded.) Planet CAM.7 Even with the best telescopes currently available, planets orbiting even the stars closest to the earth are too tim compared to their parent stars to be imaged directly However one might indirectly detect a planet's presence by observing its gravitational effect on the star. Assuming that the star-planet system is very far from other stars, it will be essentially isolated, so its center of mass should move in a straight line, If the planet's mass is large enough. the system's center of mass will be displaced signibeanlly from the star's center of mass When the planet orbit the star, lurefore, the planet and the star really both orbit the Figure C4.7 system's center of mass (like a pair of waltzing ballroom The motion of a star and planet through the sky line large dancer. as shown in figure Of 7. I've might therefore hope ball represents the star and the sins, ball the planet. The to detect a planei by observing how much a star's position solid colored line represents the path of the system's car "willies" around its central line of motion. of mass. (The wobble has been greatly exaggerated ]