Spinning satellites are particularly stable. suppose that the astronauts launching a particular satellite decide to increase its
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The maximum height is reached when the vertical component of the velocity is zero.
vertical direction:
acceleration: a = -g = -9.81m/s²
velocity: v = -g*t + v₀
position: y = -0.5*g*t² + v₀*t + y₀
For v= 0:
0 = -g*t + v₀ => t = v₀/g
Insert into position equation gives:
y(max) = (-0.5*v₀²/g) + (v₀²/g) + y₀ = (0.5*v₀²/g) + y₀
vertical direction:
acceleration: a = -g = -9.81m/s²
velocity: v = -g*t + v₀
position: y = -0.5*g*t² + v₀*t + y₀
For v= 0:
0 = -g*t + v₀ => t = v₀/g
Insert into position equation gives:
y(max) = (-0.5*v₀²/g) + (v₀²/g) + y₀ = (0.5*v₀²/g) + y₀