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Calculate the force of gravity that the moon (7.34767309 × 10^22 kg) has on you (70kg). The moon (r = 1,737,400 m), when directly "above" you, is at a distance of 384,400,000 m.

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Answer:

1.71 × 10^19 Newtons

Step-by-step explanation:

G = 6.67430 × 10^-11 Nm^2/kg^2

m1 = 7.34767309 × 10^22 kg

m2 = 70 kg

r = 384,400,000 m

F = (G * m1 * m2) / r^2

F = (6.67430 × 10^-11 Nm^2/kg^2 * 7.34767309 × 10^22 kg * 70 kg) / (384,400,000 m)^2

F = (4.904114577 × 10^11 Nm^2/kg^2 * 5.143371163 × 10^24 kg) / 1.4771776 × 10^17 m^2

F = 2.523038681 × 10^36 N / 1.4771776 × 10^17 m^2

F ≈ 1.71 × 10^19 N

Therefore, the force of gravity between the moon and you, when the moon is directly above you, is approximately 1.71 × 10^19 Newtons.

To calculate the force of gravity between the moon and you, we can use the equation:

F = (G * m1 * m2) / r^2

where:

F is the force of gravity,

G is the gravitational constant (approximately 6.67430 × 10^-11 Nm^2/kg^2),

m1 is the mass of the moon,

m2 is your mass, and

r is the distance between the centers of the moon and you.

Given:

Mass of the moon (m1) = 7.34767309 × 10^22 kg

Your mass (m2) = 70 kg

Distance between the centers (r) = 384,400,000 m

Substituting the values into the equation:

F = (6.67430 × 10^-11 Nm^2/kg^2 * 7.34767309 × 10^22 kg * 70 kg) / (384,400,000 m)^2

Simplifying:

F = (4.904114577 × 10^11 Nm^2/kg^2 * 5.143371163 × 10^24 kg) / 1.4771776 × 10^17 m^2

F = 2.523038681 × 10^36 N / 1.4771776 × 10^17 m^2

F ≈ 1.71 × 10^19 N

Therefore, when the moon is directly above you, it exerts a force of approximately 1.71 × 10^19 Newtons on you due to gravity.

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