Newton's Law of Universal Gravitation
F = G · m₁ · m₂ / r²
G = 6.674×10⁻¹¹ N·m²/kg² · 1 px = 10,000 km
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Distance r
2.90×10⁶ km
Force F
9.43×10²⁵ N
a₁ = F/m₁
1.58×10¹ m/s²
a₂ = F/m₂
4.74×10⁻⁵ m/s²
Escape vel. from M₁
5.24×10⁻¹ km/s
Masses
M₁:5.97×10²⁴ kg
M₂:1.99×10³⁰ kg
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Inverse Square Law
F at multiples of current distance r:
9.4×10²⁵1r
2.4×10²⁵2r
1.0×10²⁵3r
5.9×10²⁴4r
F ∝ 1/r² · double r → F ÷ 4
Real-World Comparisons
Earth–Moon1.98×10²⁰ N
Earth–Sun3.54×10²² N
You (70 kg)–Earth6.87×10² N
Your weight = 6.87×10² N ≈ 70 kgf (= mg)
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