题目

假如太阳的重力*2,那么某Planet轨道的周期如何变化；如果距离再*2,又怎样变化?实在搞不懂了……
原题：
If the mass of the Sun in the diagram(没有) below were doubled,what effect would it have on the planet's period of orbit?
If the radius of the planet's orbit were doubled in the diagram as in Problem 1,what effect would it have on its period of orbit?
另外，如果那个Planet的重力又*2，那又会怎样

提问时间：2021-03-18

答案

就这么几个公式
万有引力F=GMm/r^2 M太阳质量,r就是planet到sun距离
向心力F=mw^2*r w=2pai/T T是周期
所以F=4pai^2*mr/T^2=GMm/r^2
既4pai^2/T^2=GM/r^3----------判断依据
M~2M,那么T^2~T^2/2,就是T变成T/根号2
距离*2就是r~2r,那么T~2*(根号2)T
因为依据里没有planet的质量m,所以m~2m 对T没有影响