Astrology, that unlikely and vague pseudoscience, makes much of the position of the planets at the moment of birth. The only known force a planet exerts on earth is gravitational.
(a) Calculate the gravitational force exerted on a 4.00 kg baby by a 90 kg father 0.200 m away at birth (assisting so he is close).
(b) Calculate the force on the baby due to Jupiter if it is at its closest to the earth, some 6.29 ✕ 1011 m away, showing it to be comparable to that of the father. The mass of Jupiter is about 1.90 ✕ 1027 kg. 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.)
To calculate the gravitational force exerted between two objects, we can use Newton's law of universal gravitation, which states that the force F between two objects is given by:
F = (G * m1 * m2) / r^2
Where:
G is the gravitational constant (6.67430 × 10^-11 N m^2/kg^2)
m1 and m2 are the masses of the objects
r is the distance between the centers of the two objects
(a) Calculating the gravitational force between the father and the baby:
Given:
Mass of the father (m1) = 90 kg
Mass of the baby (m2) = 4.00 kg
Distance between them (r) = 0.200 m
Using the formula, we can plug in the values:
F = (G * m1 * m2) / r^2
F = (6.67430 × 10^-11 N m^2/kg^2) * (90 kg) * (4.00 kg) / (0.200 m)^2
Calculating the above expression will give us the value of the gravitational force between the father and the baby.
(b) Calculating the gravitational force between the baby and Jupiter:
Given:
Mass of Jupiter (m1) = 1.90 × 10^27 kg
Mass of the baby (m2) = 4.00 kg
Distance between them (r) = 6.29 × 10^11 m
Using the same formula as before:
F = (G * m1 * m2) / r^2
F = (6.67430 × 10^-11 N m^2/kg^2) * (1.90 × 10^27 kg) * (4.00 kg) / (6.29 × 10^11 m)^2
Calculating the above expression will give us the value of the gravitational force between the baby and Jupiter.
Comparing the values obtained for the two forces will show whether the force due to Jupiter is comparable to that of the father.