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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.)
Question by OpenStax is licensed under CC BY 4.0.
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 Solution, Chapter 6, Problem 39 (Problems & Exercises) (1:36)

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Video Transcript
ed1ch06pe39 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. 

Comments

Submitted by bryanlovell on Tue, 09/18/2018 - 10:54

In the video @ 45 seconds you have (1.898*10^27) but on the calculator you just do (1.898^27) Can you still get the correct answer doing it like that?

Submitted by ShaunDychko on Tue, 09/18/2018 - 11:04

Hi bryanlovell, thanks for the question. With a closer look at the calculator screenshot, notice the capital "E" between 1.897 and 27. This is my favorite shorthand way of writing "times 10^". It has an advantage over typing "* 10^27" since the calculator understands that 1.897E27 should be treated as a single number. This means that when dividing by 1.897E27, the 10^27 factor stays in the denominator where it belongs with the 1.897 factor. To explain by example, for the problem $\dfrac{20}{10} = 2$, typing "20 / 1E1 = 2" which is correct, whereas "20 / 1 * 10^1 = 200" which is not the expected answer since the capital E wasn't used. Of course, one could type "20 / (1 * 10^1) = 2" to get the correct answer with brackets, but avoiding the trouble of typing those brackets is the whole point of the capital E shortcut.

I hope you enjoy the solutions,

Shaun

In reply to by bryanlovell