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.

Answer 1

Answer:

The ratio of the tidal influence of the doctor  to the tidal influence of Mercury is 2.0 × 10¹¹.

Explanation:

Tidal influence (T) is proportional to the mass of a disturbing body (m) and is inversely proportional to the cube of its distance (d).

$T=k.\frac{m}{d^{3} }$

The tidal influence of the doctor (Td) is:

$Td=k.\frac{m}{d^{3} }= k. \frac{85.00kg}{(1m)^{3} } =k.85kg/m^{3}$

The tidal influence of mercury (Tm) is:

$Tm=k.\frac{m}{d^{3} }= k. \frac{3.30 \times 10^{23}  kg}{(9.2 \times 10^{10})^{3} } =k.4.2 \times 10^{-10}kg/m^{3}$

The ratio Td/tm is:

$\frac{Td}{Tm} =\frac{k.85kg/m^{3}}{k.4.2 \times 10^{-10}kg/m^{3}} =2.0 \times 10^{11}$