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. Calculate 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). Calculate the force on the baby due to Jupiter if it is at its closest distance to Earth, some 6.29×10^11 m away. How does the force of Jupiter on the baby compare to the force of the father on the baby?

a) (a) 1.33 N, (b) 4.00×10^-5 N, Father's force is greater
b) (a) 1.33 N, (b) 4.00×10^-5 N, Jupiter's force is greater
c) (a) 1.33 N, (b) 4.00×10^5 N, Father's force is greater
d) (a) 1.33 N, (b) 4.00×10^5 N, Jupiter's force is greater

Answer 1

The gravitational force exerted on the baby by the father is 1.33 N, while the gravitational force exerted on the baby by Jupiter is 4.00 x 10^-5 N. The force of the father on the baby is greater than the force of Jupiter on the baby.

Step-by-step explanation:

The gravitational force can be calculated using the formula:

F = G * m1 * m2 / r^2

where F is the gravitational force, G is the gravitational constant (6.67430 x 10^-11 N.m^2/kg^2), m1 and m2 are the masses of the two objects (in this case, the baby and the father), and r is the distance between the two objects.

Using the given values:

F = (6.67430 x 10^-11 N.m^2/kg^2) * (4.20 kg) * (100 kg) / (0.200 m)^2

F = 1.33 N

The force of Jupiter on the baby can also be calculated using the same formula, with the mass of Jupiter (1.898 × 10^27 kg) and the closest distance between Jupiter and Earth (6.29 x 10^11 m):

F = (6.67430 x 10^-11 N.m^2/kg^2) * (4.20 kg) * (1.898 × 10^27 kg) / (6.29 x 10^11 m)^2

F = 4.00 × 10^-5 N

Comparing the two forces, the force of Jupiter on the baby is smaller than the force of the father on the baby.