Tidal influence is proportional to the mass of a disturbing body and is inversel

Question

Tidal influence is proportional to the mass of a disturbing body and is inversely proportional to the cube of its distance. Some astrologers claim that your destiny is determined by the influence of the planets that are above the horizon at the moment of your birth.

Compute the ratio of the tidal influence of the doctor delivering a baby (mass = 85.00 kg, distance = 1 m) to the tidal influence of Mercury (mass = 3.30×1023 kg, distance = 9.2×1010 m). For this calculation, we are assuming that the planet is at its closest point to Earth.

Explanation / Answer

Tidal influence = mass/distance3

For the baby,

Tidal influence = 85/13

For Mercury,

Tidal influence = (3.30*1023) / (9.2*1010)3

Therefore, the required ratio is = (85/1)/(3.30*1023/778.688*1030)

= 85*778.688*1030/(3.30*1023)

=85*(778688/1000)*107 / (330/100)

= 85 * 778688 * 105 / 33

= 66188480 * 105/ 33

Dividing both numerator and denominator by 33 we get,

= 2005711.52 * 105 / 1

= 200571152 * 103 / 1

Thus, the required ratio = 200571152000 : 1

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