Final answer:
The gravitational force between Earth and the moon can be determined by Newton's Law of Universal Gravitation using the provided masses and the distance between them with the formula F = G * (m1 * m2) / r². The gravitational constant (G) and the quantities given in the question are substituted into this formula to find the force.
Step-by-step explanation:
The student is asking for the gravitational force between the Earth and its moon. To calculate this, we use 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 equation for this law is F = G * (m1 * m2) / r², where G is the gravitational constant (6.674 × 10¹± N·(m/kg)²). Using the provided mass of Earth (6 × 10²´ kg), the mass of the moon (7 × 10²² kg), and the distance between the Earth and the moon (4 × 10¸ m), the force can be calculated as follows:
F = (6.674 × 10±± N·(m/kg)²) * ((6 × 10²´ kg) * (7 × 10²² kg)) / (4 × 10¸ m)²
By solving this equation, we can find the force between Earth and the moon in Newtons (N).