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

Question

Every few hundred years most of the planets line up on the same side of the Sun. Part A Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line,(Figure 1) . The masses are mV=0.815mE, mJ=318mE, mSat = 95.1mE, and the mean distances of the four planets from the Sun are 108, 150, 778, and 1430 million km. Express your answer to three significant figures and include the appropriate units. Part B: What fraction of the Sun's force on the Earth is this? Express your answer to three significant figures.

Explanation / Answer

Part A )

given

mV=0.815mE, mJ=318mE, mSat = 95.1mE

the mean distances of the four planets from the Sun are 108, 150, 778, and 1430 million km

Mass of sun = 1.99 X 1030kg

Mass of earth = 5.98 X 1024 kg

the sun and earth force is

F = G X M X m / d2

= 14.8 Unit

in the same way

the Venus and earth force

FV = 4.622 X 10-4 Unit

jupitor and earth force

FJ = 8.061 X 10-4 Unit

saturn and earth force

FS = 5.81 X 10-5 Unit

Total force is FT = -FV + FJ + FS  

= - 4.622 X 10-4 + 8.061 X 10-4 + 5.81 X 10-5

= 4.022 X 10-4 Unit

Part B )

the fraction is

FT / F = 4.022 X 10-4 / 14.8

= 2.719 X 10-5

and the value of 1 / 2.719 X 10-5 = 36778.22729

then as the fraction is 1 / 36778.22729

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