The force of gravity is determined by the equation:
Fɢ = G • (Me) • (Mo) ⁄ (Re + h)² = (Mo) • g
... where: mass of object = Mo
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~…
The acceleration due to gravity or "g" is:
g{ h } = G • (Me) ⁄ (Re + h)² ... equation 1
g{ 0 } = G • (Me) ⁄ (Re)² ... g{ 0 } = g_e (surface) ≈ 9.8 m/sec²
... where: h = height or altitude of object
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~…
g{ h } ⁄ g{ 0 } = (Re)² ⁄ (Re + h)² = 0.75
(Re)² ⁄ (Re + h)² = 0.75
(0.75)(Re)² + (1.5)(Re)h + (0.75)h² = (Re)²
(0.75)h² + (1.5)(Re)h − (0.25)(Re)² = 0 ... Re = 6.37 ×10^6 m
(0.75)h² + (9.555 ×10^6)h − 1.014 ×10¹ ³ = 0
h = [ -b ± √ ( b² − 4ac ) ] ⁄ (2a)
h = [ -9.555 ×10^6 ± 11.03 ×10^6 ] ⁄ 1.5
h = 985 ×10³ m
h = 985 Km ... altitude (only positive solution)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~…
Check of Solution:
g{ h } = G • (Me) ⁄ (Re + h)² ... equation 1
g { 985 ×10³ } = (6.673 ×10 ‾ ¹ ¹ ) • (59.8 ×10² ³ ) ⁄ [ (6.37×10^6) + ( 985×10³ ) ] ²
g { 985 ×10³ } = 7.38 m/sec² ... which is about 75% of g{ 0 } ≈ 9.8 m/sec²
Fɢ = G • (Me) • (Mo) ⁄ (Re + h)² = (Mo) • g
... where: mass of object = Mo
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~…
The acceleration due to gravity or "g" is:
g{ h } = G • (Me) ⁄ (Re + h)² ... equation 1
g{ 0 } = G • (Me) ⁄ (Re)² ... g{ 0 } = g_e (surface) ≈ 9.8 m/sec²
... where: h = height or altitude of object
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~…
g{ h } ⁄ g{ 0 } = (Re)² ⁄ (Re + h)² = 0.75
(Re)² ⁄ (Re + h)² = 0.75
(0.75)(Re)² + (1.5)(Re)h + (0.75)h² = (Re)²
(0.75)h² + (1.5)(Re)h − (0.25)(Re)² = 0 ... Re = 6.37 ×10^6 m
(0.75)h² + (9.555 ×10^6)h − 1.014 ×10¹ ³ = 0
h = [ -b ± √ ( b² − 4ac ) ] ⁄ (2a)
h = [ -9.555 ×10^6 ± 11.03 ×10^6 ] ⁄ 1.5
h = 985 ×10³ m
h = 985 Km ... altitude (only positive solution)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~…
Check of Solution:
g{ h } = G • (Me) ⁄ (Re + h)² ... equation 1
g { 985 ×10³ } = (6.673 ×10 ‾ ¹ ¹ ) • (59.8 ×10² ³ ) ⁄ [ (6.37×10^6) + ( 985×10³ ) ] ²
g { 985 ×10³ } = 7.38 m/sec² ... which is about 75% of g{ 0 } ≈ 9.8 m/sec²