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formula for gravitational force
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Newton's law of universal gravitation (magnitude):
F = G m1 m2 / r^2
Vector form (force on mass 1 due to mass 2):
F_12 = -G m1 m2 (r1 - r2) / |r1 - r2|^3
(or equivalently F_12 = -G m1 m2 r̂ / r^2, directed toward the other mass)
Where
- G = 6.67430 × 10^−11 m^3 kg^−1 s^−2 (gravitational constant),
- m1, m2 are the masses,
- r = |r1 − r2| is the separation,
- r̂ is the unit vector from one mass to the other.
Gravitational field (acceleration due to mass M):
g = -G M r̂ / r^2, (magnitude g = G M / r^2)
Notes: This is the Newtonian expression; for very strong gravity or high precision (e.g., near black holes or for GPS-level accuracy) use general relativity.
F = G m1 m2 / r^2
Vector form (force on mass 1 due to mass 2):
F_12 = -G m1 m2 (r1 - r2) / |r1 - r2|^3
(or equivalently F_12 = -G m1 m2 r̂ / r^2, directed toward the other mass)
Where
- G = 6.67430 × 10^−11 m^3 kg^−1 s^−2 (gravitational constant),
- m1, m2 are the masses,
- r = |r1 − r2| is the separation,
- r̂ is the unit vector from one mass to the other.
Gravitational field (acceleration due to mass M):
g = -G M r̂ / r^2, (magnitude g = G M / r^2)
Notes: This is the Newtonian expression; for very strong gravity or high precision (e.g., near black holes or for GPS-level accuracy) use general relativity.
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