(4 part question) You discover an exoplanet orbiting a star that is 2.5 solar masses (M=2.5 M☉). Using the astrometry me

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(4 part question)
You discover an exoplanet orbiting astar that is 2.5 solar masses (M=2.5 M☉). Using theastrometry method, you determine the period of the exoplanet aroundits parent star is 41 days and that its mass is 8x1025kg.
(a) What is the semi-majordiameter of the orbit of this exoplanet? Give the value in km andin AU.
(b) Using the transitmethod, you estimate that the radius of the planet is 15,000 km.What is the average density of this planet? (density =mass/volume)
(c) If we assume that the planetis a mixture of metal (iron, mostly) of density 8000kg/m3 and rocky mantle of density 3000 kg/m3,what fraction of this exoplanet is rock? {Hint:Assume that, like Earth, this exoplanet is layered with a sphericalcore of metal and a surrounding spherical shell of rock}
(d) Asthe discoverer of this exoplanet you have the honor of naming it.What would you name this exoplanet?