m = mass of the person = 80 kg
M = mass of earth = 5.98 x 10²⁴ kg
R = radius of earth = 6.37 x 10⁶ m
h = height above the earth's surface = 1400 km = 1.4 x 10⁶ m
r₁ = initial distance of the person from the center of earth when on surface = R = 6.37 x 10⁶ m
r₂ = final distance of the person from the center of earth when at some height = R + h = 6.37 x 10⁶ + 1.4 x 10⁶ = 7.77 x 10⁶ m
F₁ = Gravitational force of earth on the person when at surface
Gravitational force of earth on the person when at surface is given as
F₁ = G M m/r₁² eq-1
F₂ = Gravitational force of earth on the person when at some height
Gravitational force of earth on the person when at some height is given as
F₂ = G M m/r₂² eq-2
dividing eq-1 by eq-2
F₁ /F₂ = (G M m/r₁² )/(G M m/r₂²)
F₁ /F₂ = r₂²/r₁²
inserting the values
F₁ /F₂ = (7.77 x 10⁶)²/(6.37 x 10⁶)²
F₁ /F₂ = 1.49
