Every hundred years or so, most of the planets line up on the same side of the S

Question

Every hundred years or so, most of the planets line up on the same side of the Sun. Sun

a) Calculate the total force on the Earth due to Venus, Jupiter and Saturn, assuming all four planets are in a line (see figure). An amateur astronomer measures the masses to be MV = 0.888 ME, MJ = 328 ME, MS = 101.8 ME, and their distances from the Sun are 1.080×10^8 km, 1.500×10^8 km, 7.780×10^8 km and 1.430×10^9 km respectively. The mass of the earth ME is 5.980×10^24 kg and the distance from the earth to the sun is 1.500×10^8 km. The mass of the sun is 1.99×10^30 kg.

b) What fraction of the Sun's force on the Earth is this for this configuration?

Explanation / Answer

Total force on earth = 6.674 x 10^-11 x( 5.980 x 10^ 24)^2 ( 0.888/(0.42 x 10^11) ^2 - 328/(6.28 x 10^11) ^2 -101.8/(12.8 x 10^11) ^2 )

= 238.665 x 10^ 37 ( 5.03 x 10^ -22 - 8.316 x 10^ -22 - 0.621 x 10^ -22)

= 10^17 (9.32 ) N apprx

b)force due to sun= 6.674 x 10^-11 * 5.980 x 10^ 24 x 1.99 x 10^ 30 / (( 1.5 x 10^11)^2

F = 35.3 x 10^ 21 N

Ratio = 9.32 x 10^ 17 / ( 35.3 x 10^21)=0.264 x 10^ -4

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