(a) (i) State how measurements of transit times of Jupiter-sized planets can potentially detect other planets...

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(a) (i) State how measurements of transit times of Jupiter-sized planets can potentially detect other planets orbiting the same star. (ii) Write down an equation that quantifies how this effect depends on the parameters of the system being observed, defining the terms in the equation. Use the nomenclature where Mi is the mass of the transiting Jupiter-sized planet, and M2 is the mass of the other planet orbiting in the same system. (b) Consider a planetary system containing a transiting planet of mass M = 1 M, and a planet of mass M2 = 0.02 M, both in orbit around a star of mass M, = 1 Mo. The orbital periods of the two planets are P = 10 days and P, = 15 days. (i) State the significance of the relative lengths of these orbital periods. (ii) Calculate the approximate size of the maximum effect that would be measured for this system, giving your answer in appropriate units. (a) (i) State how measurements of transit times of Jupiter-sized planets can potentially detect other planets orbiting the same star. (ii) Write down an equation that quantifies how this effect depends on the parameters of the system being observed, defining the terms in the equation. Use the nomenclature where Mi is the mass of the transiting Jupiter-sized planet, and M2 is the mass of the other planet orbiting in the same system. (b) Consider a planetary system containing a transiting planet of mass M = 1 M, and a planet of mass M2 = 0.02 M, both in orbit around a star of mass M, = 1 Mo. The orbital periods of the two planets are P = 10 days and P, = 15 days. (i) State the significance of the relative lengths of these orbital periods. (ii) Calculate the approximate size of the maximum effect that would be measured for this system, giving your answer in appropriate units.