Question

at some movement two planets Jupiter and saturn of the solar system are in the same line as seenfrom earth. find the total gravitational force due to them on a person of mass 50 kg on the earth. could force due to plants be important.
mass of Jupiter 2*10^7kg.
mass of saturn is 6*10^26kg.
distance from Jupiter from earth 6.3*10^11 m.
distance of saturn from earth is 1.28*10^12m.
G =6.67*10^-11.
acceleration due to gravity 9.8m/sec.

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{mass}\mathrm{of}\mathrm{jupiter},{\mathrm{m}}_{\mathrm{J}}=2\times {10}^{27}\mathrm{kg} \\ \mathrm{mass}\mathrm{of}\mathrm{saturn},{\mathrm{m}}_{\mathrm{S}}=6\times {10}^{26}\mathrm{kg} \\ \mathrm{distance}\mathrm{of}\mathrm{jupiter}\mathrm{from}\mathrm{earth},{\mathrm{d}}_{\mathrm{JE}}=6.3\times {10}^{11}\mathrm{m} \\ \mathrm{distance}\mathrm{of}\mathrm{saturn}\mathrm{from}\mathrm{earth},{\mathrm{d}}_{\mathrm{SE}}=1.28\times {10}^{12}\mathrm{m} \\ \mathrm{G}=6.67\times {10}^{-11}{\mathrm{Nm}}^2/{\mathrm{kg}}^2 \\ \mathrm{mass}\mathrm{of}\mathrm{man},\mathrm{m}=50\mathrm{kg} \\ \mathrm{Force}\mathrm{of}\mathrm{jupiter}\mathrm{on}\mathrm{man}\mathrm{on}\mathrm{the}\mathrm{earth}, \\ {\mathrm{F}}_{\mathrm{J}}=\frac{{\mathrm{Gm}}_{\mathrm{J}}\mathrm{m}}{{\left({\mathrm{d}}_{\mathrm{JE}}\right)}^2} \\ {\mathrm{F}}_{\mathrm{J}}=\frac{6.67\times {10}^{-11}\times 2\times {10}^{27}\times 50}{{\left(6.3\times {10}^{11}\right)}^2} \\ {\mathrm{F}}_{\mathrm{J}}=16.8\times {10}^{-6}\mathrm{N} \\ \mathrm{Force}\mathrm{of}\mathrm{saturn}\mathrm{on}\mathrm{the}\mathrm{man}\mathrm{on}\mathrm{the}\mathrm{earth}, \\ {\mathrm{F}}_{\mathrm{S}}=\frac{{\mathrm{Gm}}_{\mathrm{S}}\mathrm{m}}{{\left({\mathrm{d}}_{\mathrm{SE}}\right)}^2} \\ {\mathrm{F}}_{\mathrm{S}}=\frac{6.67\times {10}^{-11}\times 6\times {10}^{26}\times 50}{{\left(1.28\times {10}^{12}\right)}^2} \\ {\mathrm{F}}_{\mathrm{S}}=1.22\times {10}^{-6}\mathrm{N} \\ \mathrm{Total}\mathrm{force}\mathrm{on}\mathrm{man},\mathrm{F}={\mathrm{F}}_{\mathrm{J}}+{\mathrm{F}}_{\mathrm{S}} \\ \mathrm{F}=16.8\times {10}^{-6}+1.22\times {10}^{-6} \\ \mathrm{F}=18.02\times {10}^{-6}\mathrm{N} \\ \mathrm{Force}\mathrm{due}\mathrm{to}\mathrm{planets}\mathrm{is}\mathrm{not}\mathrm{at}\mathrm{all}\mathrm{important}. \end{gathered}$$