Final answer:
To calculate the gravitational force exerted on a human standing on the surface of Mars, we can use Newton's Law of Universal Gravitation. We can also calculate the gravitational force exerted by the human on Mars, as well as the gravitational force of the human on another human standing 4 meters away.
Step-by-step explanation:
In order to calculate the magnitude of the gravitational force exerted by Mars on a 70 kg human standing on the surface of Mars, we can use Newton's Law of Universal Gravitation. The formula is F = (G * m1 * m2) / r², where F is the force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers.
(a) To calculate the force exerted by Mars on the human, we substitute the known values into the formula: F = (6.674 × 10^-11 N·m²/kg² * (70 kg) * (6.4 × 10^23 kg)) / (3.4 × 10^6 m)². Solving this equation gives us the magnitude of the gravitational force exerted by Mars on the human.
(b) To calculate the force exerted by the human on Mars, we use the same formula but substitute the masses of the objects: F = (6.674 × 10^-11 N·m²/kg² * (70 kg) * (6.4 × 10^23 kg)) / (3.4 × 10^6 m)². This will give us the magnitude of the gravitational force exerted by the human on Mars.
(c) To calculate the approximate magnitude of the gravitational force of the human on a similar human standing 4 meters away, we use the formula: F = (6.674 × 10^-11 N·m²/kg² * (70 kg) * (70 kg)) / (4 m)². This will give us the magnitude of the gravitational force of the human on another human standing 4 meters away.