- #1
theultimate6
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Homework Statement
http://ipho2013.dk/ipho2013-theoretical-problem-1.pdf
The Attempt at a Solution
Are those correct?
1.1: Velocity in the x direction : [tex] v_x=ω_x r=(π*(θ_2-θ_1)*r/180)/Δt r [/tex]
Velocity in the y direction : [tex] v_y = ω_y r=(π*θ'_1-θ'_2)*r/180)/Δt [/tex]
Then use Pythagorean theorem to get the average [tex] v = 31128.6 m/s [/tex]
1.2a: [tex] F_friction=kρ_atm Av^2=4kρ_atm πR_M^2 v^2=m_M dv/dt =(0.10m_M v_M)/dt [/tex]
[tex] dt=(0.10m_M v_M)/(4kρ_atm πR_m^2 v_M^2 )=(0.10〖 m〗_M)/(4kρ_atm πR_M^2 v_M^2 ) [/tex]
1.2b: [tex] E_k=(mv^2)/2=(30*(2.91*〖10〗^4 )^2)/2=1.2615*〖10〗^10 j [/tex]
[tex] E_melt= mL=30*2.6*〖10〗^5=7.8*〖10〗^6 j [/tex]
[tex] E_kin/E_melt =(1.2615*10^10 )/(7.8*〖10〗^6 )≈1617.307692 [/tex]
1.3a: [tex] L=t^α M^β L^(-3β) L^2γ t^(-2γ) T^(-γ) M^δ L^δ t^(-3δ) T^(-δ) [/tex]
[tex] L:1=-3β+2γ+δ [/tex]
[tex] t:0=α-2γ-3δ [/tex]
[tex] M:0=β+δ [/tex]
[tex] T: 0=-γ-δ [/tex]
Solving the system of equations
[tex]α= 1/2 [/tex]
[tex]β=-1/2[/tex]
[tex]γ=-1/2[/tex]
[tex]δ=1/2 [/tex]
thus :
[tex] x=√((tk_sm)/(ρ_sm c_sm ))[/tex]
[tex] x=√((tk_sm)/(ρ_sm c_sm ))=√((5*2)/(1.2*〖10〗^3*3.3*〖10〗^3 ))=0.00158910 m [/tex]
[tex] x/R_M =0.00158910/0.13=0.012223846 [/tex]
[tex] 1.5: t_Encke=2π√((a_max^3)/(GM_sun ))=2π√((6.16*〖10〗^11 )^3/(6.67*〖10〗^(-23)*1.99*10^30))=2.636*〖10〗^8 s=8.353 years [/tex]