Question

Cele 4 probleme
1) g=k*m/10r
R=r+h=r+9r=10r
La 2 îmi dă 25, dar în carte scrie 2,5 și nu înțeleg unde greșesc.
G1/G2=M1g1/M2g2=M1/M2*g1/g2=M1/M2*M1/M2*R2^2/R1^2=(M1/M2)^2*(R2/R1)^2=100/4=25
g1=kM1/R1^2
g2=kM2/R2^2
M1/M2=10
R2/R1=(R1/R2)^(-1)=2^(-1)=1/2

Answer 1

1.

g=F/m=kMp/r²=kMp/(R+h)²=kMp/(R+9R)²=kMp/10R²

go=kMp/R²

g=go/10=9,81/10=0,981 m/s²

2.R1/R2=2=>R1=2R2

M1/M2=10=>M1=10M2

g1=F1/m=kMp1/R1²=10kM2/(4R2²)

g2=F2/m=kMp2/R2²

G1=mg1=m10kM2/(4R2²)

G2=mg2=mkMp2/R2²

G1/G2=m10kM2/(4R2²)/mkMp2/R2²=10/4=2,5

3.ρ=5,5 g/cm³=5500 kg/m³

g=kMp/R²=>Mp=gR²/k

V=4πR³/3

ρ=Mp/V=gR²/k/4πR³/3=3g/4πkR=>R=3g/4πkρ=3*9,8/(4*3,14*6,67*10⁻¹¹*5500)=29,4/(460,7*10⁻⁸)=0,063*10⁸=63*10⁵=6300*10³ m=6300 km

4.Mp/Ml=81=>Mp=81Ml

Γo=F/m=kMp/R²

Γ=kMp/(R+h)²

Γ=Γo/4<=>kMp/(R+h)²=kMp/4R²<=>4R²=(R+h)²<=>4R²=R²+h²+2Rh<=>h²+2Rh-3R²=0

Δ=4R²+12R²=16R²

h=(2R+4R)/2=8R/2=4R=4*6300=25200 km

Fp=Fl=>kmMp/x²=kMMl/(d-x)²<=>81Ml(d-x)²=Mlx² |:Ml=>9(d-x)=x=>x=9d/10=9*384400/10=34200 km