中央研究院物理研究所 高中科學培訓計畫 蘋果與月亮 劉源俊 96年5月5日.

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? Galileo Galilei ( )

Dialogues Concerning Two New Sciences 1638

v ～ h ?

h/2 h v/2 ? v

v ～ h ? v ～ t ? v = g t 重力加速度g = 常數 ─等加速度運動 h = ½ (0+g t)‧t= ½ g t ²  v² = 2 g h

g = 9.8 m/s²

Isaac Newton( )

Principia Mathematica
1687

‘On 15 April 1726 I paid a visit to Sir Isaac
‘On 15 April 1726 I paid a visit to Sir Isaac...he told me he was just in the same situation as when, formerly, the notion of gravitation came into his mind. It was occasioned by the fall of an apple, as he sat in a contemplative mood.’ William Stukeley English Physician and antiquary Memoirs of Newton’s Life (1752) ?

－N W N －N' N' －W 地球 地球

─王陽明( )

r r r

△s : r = △v : v ∴ v t / r = a t / v ∴ a = v² / r

gmoon = v² / r = 4π² r / T² r ≒ 60 × 6400 Km T = 28.2 × 24 × 60 × 60 s gmoon ≒ m/s² 9.8 m/s² / 60² = m/s² ≒ gmoon 於是猜測 g ～ 1 / r² 於是 F ～ 1 / r²

F = G m1 m2 / r² gE = G ME / RE²

Kepler’s laws 刻普勒行星運動三律

m h g

Analytical Mechanics (1788) V = m g h

m 梯度 = m g h / l l h

─力是想像的，勢能更是推想的