The planet mars has two moons.phobos and delmos. (i)phobos has a period 7 hours, 39 minutes and an orbital radius of 9.4xx10^3 km . Calculate the mass of mars. (ii)Assume that earthand mars move in circular orbits around the sun.with the martian orbit being 1.52 times the orbitalradius of the earth. What is the length of the martianyear in days ?

The planet mars has two moons.phobos and delmos. (i)phobos has a perio

1.	The planet mars has two moons.phobos and delmos. (i)phobos has a period 7 hours, 39 minutes and an orbital radius of 9.4xx10^3 km . Calculate the mass of mars. (ii)Assume that earthand mars move in circular orbits around the sun.with the martian orbit being 1.52 times the orbitalradius of the earth. What is the length of the martianyear in days ?
Answer» Solution :(i)We know that `T^2=(4pi^2)/(GM_m)R^3` `M_m=(4pi^2)/G R^3/T^2 = (4xx(3.14)^2xx(9.4)^3xx10^8)/(6.67xx10^(-11) XX(459xx60)^2)` `M_m=(4xx(3.14)^2(9.4)^3xx10^18)/(6.67xx(4.59xx6)^2XX10^(-5))= 6.48xx10^23` kg . (ii)According to Kepler.s third LAW `T_M^2/T_E^2=R_(MS)^3/R_(ES)^3` where `R_(MS)` is the mars-sun distance and `R_(ES)` is the earth-sun distance. `therefore T_M=(1.52)^(3//2) xx365`=684 days.