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Every few hundred years most of the planets line up on the same side of the Sun.?

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Every few hundred years most of the planets line up on the same side of the Sun.?

Mars is missing but I assume that is deliberate.

Because we are interested in the ratio of the forces, we can simplify the maths by using units where:

– mass of earth = 1unit (1Me)

– the unit of distance is 1 million km

– G = 1 unit

(conversion factors to SI units will cancel when we take the ratio)

Mass of sun = 1.99 x 10^30 /5.98 x 10^24 = 3.328×10^5 units

Sun-earth force, F = GMm/d^2 = 1 x 3.328×10^5 x 1 / 150^2 = 14.8 units

Venus-earth force, FV = 1 x 0.815 x 1 /(150-108)^2 = 4.62×10^-4 units

Jupiter=earth force, FJ = 1 x 318 x 1 /(778-150)^2 = 8.06×10^-4 units

Saturn-earth force, FS= 1 x 95.1 x 1 /(1430-150)^2 = 5.80×10^-5 units

Total force, FT, from the 3 planets on earth (remembering Venus pulls in the OPPOSITE direction to Jupiter and Saturn) is:

FT = -FV + FJ + FS = -4.62×10^-4 + 8.06×10^-4 + 5.80×10^-5 = 4.02×10^-4 units

The ratio FT/F = 4.02×10^-4 / 14.8 = 2.72×10^-5

Since 1/2.72×10^-5 = 36800, as a fraction the ratio is 1/36800

Note: answer should be to 3 significant figures only, same as the data in the question.

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