Which exerts more gravitational force on the baby, Mars or the obstetrician, given that Mars has a mass of 6.4 1023 kg and is 8. 1010 m from Earth?
To determine which exerts more gravitational force on the baby, we can use Newton's law of universal gravitation, which states that the gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The formula for the gravitational force is:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2)
m1 and m2 are the masses of the objects
r is the distance between their centers
Given that Mars has a mass of 6.4 * 10^23 kg and is 8 * 10^10 meters from Earth, and assuming the obstetrician has a mass of approximately 90 kg, we can calculate the force separately for each scenario and compare the results.
For Mars:
F_mars = (G * m1 * m_mars) / r_mars^2
For the Obstetrician:
F_obstetrician = (G * m1 * m_obstetrician) / r_obstetrician^2
Calculating each force:
F_mars = (6.67430 × 10^-11 N m^2/kg^2) * (5.972 × 10^24 kg) * (6.4 × 10^23 kg) / (8 × 10^10 m)^2
F_obstetrician = (6.67430 × 10^-11 N m^2/kg^2) * (5.972 × 10^24 kg) * (90 kg) / (0.5 m)^2
After calculating these values, we can compare the magnitudes of the forces to determine which one is greater. The force with the larger magnitude will exert more gravitational force on the baby.
Please note that the gravitational force exerted by the obstetrician is extremely small compared to the gravitational force exerted by Mars due to the vast difference in mass and distance.