Astrology makes much of the position of the planets at the moment of one\'s birt

Question

Astrology 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 gravitational force (in N) exerted on a 4.32 kg baby by a 104 kg father 0.250 m away at birth (he is assisting, so he is close to the child). (Enter the magnitude.) (b) Calculate the force (in N) on the baby due to Jupiter if it is at its closest distance to Larth, some 6.29 × 1011 m away. (Enter the magnitude.) 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 bullding 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.) ugiter Additional Materials ?eBook -11 points My NotesAsk Your Teach The acceleration due to gravity on the surface of a planet is eight times as large as it is on the surtace of Farth. The mass density ot the planet is known to be five times that of Earth. What is the radius ot this planet in terms of Larth's radius?

Explanation / Answer

(A) Fg = G M1 m2 / r^2

F = (6.67 x 10^-11)(4.32)(104) / (0.250^2)

F = 4.79 x 10^-7 N

(B) F = (6.67 x 10^-11)(4.32)(1.898 x 10^27) / (6.29 x 10^11)^2

F = 1.38 x 10^-6 N .........Ans

ratio = (4.79 x 10^-7) / (1.38 x 10^-6)

= 0.35
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a = G M / R^2

so a R^2 / M = constant

and M = rho (4 pi R^3 / 3)

so a R^2 / (rho R^3) = constant

a / rho R = constant

a1 / rho1 R1 = a2 / rho2 R2

a2 = 8 a1

rho2 = 5 rho1

a1 / rho1 R1 = (8 a1) / (5 rho1)(R2)

R2 = 1.6 R1

Ans : 1.6

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