为了研究太阳演化的进程需知太阳的质量，已知地球的半径为R，地球的质量为m，日地中心的距离为r，地球表面的重力加速度为g，地球绕太阳公转的周期为T，则太阳的质量为（）A.4π2m

Question

为了研究太阳演化的进程需知太阳的质量，已知地球的半径为R，地球的质量为m，日地中心的距离为r，地球表面的重力加速度为g，地球绕太阳公转的周期为T，则太阳的质量为（　　）
A. (4π2mr3)/(T2R2g)
B. (T2R2g)/(4π2mr3)
C. (4π2mgR2)/(r3T2)
D. (r3T2)/(4π2mR2g)
(4π2mr3)/(T2R2g)
B. (T2R2g)/(4π2mr3)
C. (4π2mgR2)/(r3T2)
D. (r3T2)/(4π2mR2g)(4π2mr3)/(T2R2g)4π2mr34π2mr3π2mr3π2mr32mr3r3r33T2R2gT2R2gT2R2gT2R2g2R2gR2gR2g2g
(T2R2g)/(4π2mr3)
C. (4π2mgR2)/(r3T2)
D. (r3T2)/(4π2mR2g)(T2R2g)/(4π2mr3)T2R2gT2R2gT2R2gT2R2g2R2gR2gR2g2g4π2mr34π2mr3π2mr3π2mr32mr3r3r33
(4π2mgR2)/(r3T2)
D. (r3T2)/(4π2mR2g)(4π2mgR2)/(r3T2)4π2mgR24π2mgR2π2mgR2π2mgR22mgR2R2R22r3T2r3T2r3T2r3T23T2T2T22
(r3T2)/(4π2mR2g)(r3T2)/(4π2mR2g)r3T2r3T2r3T2r3T23T2T2T224π2mR2g4π2mR2gπ2mR2gπ2mR2g2mR2gR2gR2g2g

Answer 1

设T为地球绕太阳运动的周期，则由万有引力定律和动力学知识得：
(GMm)/(r2)=(mv2)/(r)
根据地球表面的万有引力等于重力得：
对地球表面物体m′有
(Gmm′)/(R2)=m′g
两式联立得M=(4π2mr3)/(T2R2g)
故选A． (GMm)/(r2)GMmGMmGMmr2r2r22=(mv2)/(r)
根据地球表面的万有引力等于重力得：
对地球表面物体m′有
(Gmm′)/(R2)=m′g
两式联立得M=(4π2mr3)/(T2R2g)
故选A． (mv2)/(r)mv2mv2mv22rrr
根据地球表面的万有引力等于重力得：
对地球表面物体m′有
(Gmm′)/(R2)=m′g
两式联立得M=(4π2mr3)/(T2R2g)
故选A． (Gmm′)/(R2)Gmm′Gmm′Gmm′R2R2R22=m′g
两式联立得M=(4π2mr3)/(T2R2g)
故选A． (4π2mr3)/(T2R2g)4π2mr34π2mr34π2mr32mr33T2R2gT2R2gT2R2g2R2g2g
故选A．