According to Kepler's third law,the orbital period T of a planet is related to the radius R of itsorbit by T2 R3.A planet's orbit is larger than Earth's by a factor if4.97.What is the planet's orbital period?(Earth's orbital period is 1 yr.)
问题描述：
According to Kepler's third law,the orbital period T of a planet is related to the radius R of its
orbit by T2 R3.
A planet's orbit is larger than Earth's by a factor if4.97.What is the planet's orbital period?(Earth's orbital period is 1 yr.)
答
结合牛顿万有引力定律和开普勒第三定律可得
答
T ^ 2 / R ^ 3=t ^ 2 / r ^ 3 (小写为地球)
即T ^ 2=t ^ 2 * R ^ 3 / r ^ 3 (R / r=4.97,故R ^ 3 / r ^ 3 =122.763473)
两边开方：T=t * (R ^ 3 / r ^ 3) ^ 0.5=11.07986791 (years)