Force of gravity = 'G' (mass₁)(mass₂) / (distance)²
'G' is the gravitational constant for SI units = 6.67 x10⁻¹¹ newton-meter²/kg²
You said that the force is 2.99 x 10⁻¹⁰ = (6.67x10⁻¹¹) (4) (7) / D²
Multiply each side by D² : 2.99 x 10⁻¹⁰ D² = (6.67x10⁻¹¹) (28)
Divide each side by 2.99 x 10⁻¹⁰ : D² = (28) (6.67 x10⁻¹¹) / (2.99 x 10⁻¹⁰)
Take the square root of each side: D = square root of all that
Stuff it through my calculator:
D = square root of [ (28) (6.67 x10⁻¹¹) / (2.99 x 10⁻¹⁰) ] =
√ ( 6.2462...) meters² =
2.5 meters (rounded)
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To get the feel:
-- The book weighs about 8.8 pounds (big book)
-- The lamp weighs about 15.4 pounds
-- They're about 8.2 feet apart.
-- The strength of the gravitational force
between them is about 0.000 000 001 075 of an ounce .
