Question

Astrology, that unlikely and vague pseudoscience, makes much of the position of the planets at the moment of one's birth. The only known force a planet exerts on Earth is gravitational.
(a) Calculate the magnitude of the gravitational force exerted on a 4.20 kg baby by a 100 kg father 0.200 m away at birth (he is assisting, so he is close to the child).
(b) Calculate the magnitude of the force on the baby due to Jupiter if it is at its closest distance to Earth, some $6.29 \times 10^{11} \textrm{ m}$ away. How does the force of Jupiter on the baby compare to the force of the father on the baby? Other objects in the room and the hospital building also exert similar gravitational forces. (Of course, there could be an unknown force acting, but scientists first need to be convinced that there is even an effect, much less that an unknown force causes it.)

Final Answer

a) $7.01 \times 10^{-7} \textrm{ N}$

b) $1.34 \times 10^{-6} \textrm{ N}$. The force of gravity due to Jupiter is greater than that of the father by a factor of $1.9$.

### Solution video

# OpenStax College Physics for AP® Courses, Chapter 6, Problem 39 (Problems & Exercises)

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Video Transcript

This is College Physics Answers with Shaun Dychko. The force of gravity between the father and his newborn baby will be the gravitational constant, times the mass of the father, times the mass of the baby, divided by the distance between the father and the baby squared. So 6.673 times ten to the minus eleven times 100 kilograms, mass of the father, times 4.2 kilograms mass of the baby, divided by the 20 centimeters squared between the father and baby which we read in meters as 0.2 meters. This is 7.01 times ten to the minus seven newtons which is a very small number, much smaller than the other forces the baby is experiencing during childbirth I can tell you. The force due to Jupiter is gravitational constant times the mass of Jupiter which is 1.898 times ten to the twenty-seven kilograms, multiplied by the mass of the baby divided by the distance between Jupiter and the earth at its closest, which is 6.29 times ten to the eleven meters, we square that. That gives 1.34 times ten to the six, negative six newtons. The ratio between those two forces, force due to Jupiter and the force due to the father, is 1.34 times ten to the minus six divided by 7.01 times ten to the minus seven which is about 1.9. So the force of gravity due to Jupiter is greater than that of the father by a factor of 1.9. But even though the force due to Jupiter is two times greater than the force of gravity due to the father, this is still something that's negligible because it's two times greater than something that's really, really, really, really small.