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) the total force on the Earth =

=>    6.67 * 10-11 * (5.972 * 1024)2 * (0.815/(42 * 109)2 + 318/(628 * 109)2 + 95.1/(1280 * 109)2 )

=    6.67 * 10-11 * (5.972 * 1024)2 * ( 4.62 * 10-22 + 8.063 * 10-22 + 5.804 * 10-23)

=   3.155 * 1018 N

Part B)    Sun's force on the Earth =   6.67 * 10-11 * (5.972 * 1024) * 1.989 * 1030/(150 * 109)2

                                                       = 3.521 * 1022 N

=>   fraction of the Sun's force on the Earth is this = (3.155 * 1018)/(3.521 * 1022)

                                                                             = 8.96 * 10-5

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