[latex]T_{z}=2 pisqrt{frac{l}{g_{o}}} \ T_{z}=1s \ 1=2pi sqrt{frac{l}{g_{o}}} \ frac{1}{2pi}=sqrt{frac{l}{g_{o}}} \ frac{1}{4 pi^{2}}=frac{l}{g_{o}} \ [/latex] [latex]l=frac{g_{o}}{4pi^{2}}=frac{10}{4pi^{2}}[/latex] a)[latex]T_{k}=2pi sqrt{frac{l}{g_{k}}}=2pi sqrt{frac{l}{frac{1}{6}g_{z}}}=2pi sqrt{frac{frac{10}{4pi^{2}}}{frac{1}{6}g_{z}}}=2pi sqrt{frac{3}{2pi^{2}}}=frac{2pisqrt{3}}{sqrt{2}pi}[/latex] [latex]T_{k}=sqrt{6}approx 2,4494897427831780981972840747059 s approx 2,449 s[/latex] b) gm = 0,369 gz [latex]T_{m} = 2pi sqrt{frac{l}{0,369g_{z}}} =2pi sqrt{frac{frac{10}{4pi^{2}}}{3,69}}=\ =frac{2pi}{2pi}sqrt{frac{10}{3,69}}approx 1,6462159944159826774997481536505 approx 1,64[/latex] c)[latex]T_{j}=2pi sqrt{frac{l}{g_{j}}}=2pi sqrt{frac{frac{10}{4pi^{2}}}{2,530g_{z}}}= \ =2pisqrt{frac{1}{10,12pi^{2}}}=frac{2pi}{pisqrt{10,12}} approx frac{2}{3,181} approx 0,628 s[/latex]
a) Przyspieszenie na Księżycu jest 6 razy mniejsze niż na Ziemi; gk = 1/6 gz dane: Tz = 1 s gz = 10 m/s2 gk = 1/6 gz szukane: Tk = ? T = 2TTV(l/g) Tz = 2TTV(l/gz) Tk = 2TTV(l/g/6) = 2TTV(6l/gz) = 2TTV(l/gz) *V6 Tk = Tz * V6 = 1s *V6 Tk = 2,45 s ========== b) Przyspieszenie na Marsie wynosi 3,69 m/s2 : gm = 3,69 m/s2 gm = 0,369 gz dane: Tz = 1 s gz = 10 m/s2 gm = 0,369 gz szukane: Tm = ? Tm = 2TTV(l/0,369gz) = 2TTV(l/gz) * V(1/0,369) = 2TTV(l/gz) * V2,71 Tm = Tz * 1,646 = 1s * 1,646 Tm = 1,65 s =========== c) Przyspieszenie na Jowiszu wynosi 23,1 m/s2 gj = 23,1 m/s2 gj = 2,31 gz dane: Tz = 1 s gz = 10 m/s2 gj = 2,31 gz szukane: Tj = ? Tj = 2TTV(l/2,31gz) = 2TTV(l/gz) * V(1/2,31) = 2TTV(l/gz) * V(0,4329) Tj = Tz * 0,6579= 1s * 0,6579 Tj = 0,66 s ==========
