Final answer:
The force between the Earth and the moon is calculated using Newton's law of universal gravitation, with given values for the masses of the Earth and the moon and their separation distance. By plugging the values into the gravitational force equation, the gravitational force in newtons can be obtained.
Step-by-step explanation:
The force between the Earth and the moon can be calculated using Newton's law of universal gravitation, which states that the force (F) between two masses is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance (r) between their centers. The formula is expressed as F = G * (m1 * m2) / r2, where G is the gravitational constant (6.674 x 10-11 N m2/kg2).
Given the Earth's mass (me) is 5.98 x 1024 kg, the moon's mass (mm) is 7.35 x 1022 kg, and the radius of the moon's orbit (r) is 3.85 x 108 m, we can substitute these values into the formula:
F = (6.674 x 10-11 N m2/kg2) * ((5.98 x 1024 kg) * (7.35 x 1022 kg)) / (3.85 x 108 m)2
To find the force, simply perform the multiplication and division as indicated in the equation above. The result will give us the force in newtons (N).