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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