## GR0877 Problem 53

**PROBLEM STATEMENT**: *This problem is still being typed*.

**SOLUTION**: (**D**) According to the problem statement, the angular momenta are the same: , therefore . For the orbital periods one has and (orbits are circles!). Thus, . Think about why cannot we apply Kepler’s third law in its usual form.

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The main reason we can’t apply Kepler’s third law is that the corresponding masses of their suns are different.

Why isn’t it stated in the question that two solar system has different solar mass? At first I thought they meant they observed two suns, like two stars with identical solar mass of 1.

It’s stupidly worded. Thanks again, ETS. You’re always so clear and concise.

Alternatively, remember that L=m*(dA/dt), where dA/dt is the rate at which area swept out by the planet. Integrate both sides from t=0 to t=T to get that LT=mA, or rather, m=LT/A. This says that the ratio (m1/m2) is equal to (L1*T1/A1)/(L2*T2/A2). But L1=L2 and A1=A2, so (m1/m2)=(T1/T2).