One of the tenets of the pseudoscience (i.e., "false science") of astrology is that, in some mysterious way, the positions of the planets at the time of a person's birth somehow influence the characteristics of that person. To see if this proposition seems plausible, let us compare the gravitational influence of Mars when it is closest to earth with the gravitational influence of the medical doctor who delivers a baby. For a rough calculation, we shall assume that the doctor is 50.0 cm from the baby (she is likely to be even closer at delivery), has a mass of 75.0 kg, and can be modeled as a uniform sphere.
A. What is the minimum distance between earth and Mars?
B.Calculate the ratio of the gravitational force the doctor exerts on the baby to the gravitational force that Mars exerts on the baby.
C.If there is any influence, which is greater, that of Mars or that of the doctor?
a. Of Mars
B. Of the doctor
Isn't this Newtons Law of gravity equation?
7.84*10^10
To compare the gravitational influence of Mars and the doctor on a baby, we need to calculate the gravitational forces involved.
A. The minimum distance between Earth and Mars varies due to the elliptical orbits of both planets. The closest possible distance is known as the "opposition," where Earth and Mars are on opposite sides of the Sun. This occurs roughly every 2 years and 2 months. During opposition, the minimum distance between Earth and Mars is approximately 56 million kilometers or about 3.48 x 10^10 miles.
B. To calculate the gravitational force, we can use Newton's law of universal gravitation:
F = (G * m1 * m2) / r^2
Where F is the gravitational force, G is the gravitational constant (6.674 x 10^-11 N m^2/kg^2), m1 and m2 are the masses of the two bodies interacting, and r is the distance between them.
In this case, the doctor's mass is 75.0 kg, and the distance between the doctor and the baby is 50.0 cm (or 0.5 meters). We assume the doctor can be modeled as a sphere for simplicity.
The mass of a baby is typically around 3.5 kg, which we'll use for our calculation.
Calculating the gravitational force exerted by the doctor on the baby:
F_doctor = (G * m_doctor * m_baby) / r^2
F_doctor = (6.674 x 10^-11 N m^2/kg^2 * 75.0 kg * 3.5 kg) / (0.5 m)^2
Simplifying this equation will give us the gravitational force exerted by the doctor on the baby.
C. To compare the gravitational force exerted by Mars on the baby, we need to take into account the minimum distance between Earth and Mars (calculated in part A) and Mars' mass. The mass of Mars is approximately 6.42 x 10^23 kg.
Calculating the gravitational force exerted by Mars on the baby:
F_mars = (G * m_mars * m_baby) / r^2
F_mars = (6.674 x 10^-11 N m^2/kg^2 * 6.42 x 10^23 kg * 3.5 kg) / (minimum_distance_Mars)^2
Comparing the two calculated gravitational forces, we can determine whether the doctor or Mars has a greater influence on the baby.
a. If the gravitational force exerted by Mars on the baby is greater, then Mars has a greater influence.
b. If the gravitational force exerted by the doctor on the baby is greater, then the doctor has a greater influence.
By calculating the values and comparing the forces, we can determine which influence is greater between Mars and the doctor.