énoncé - imagine

D
dt = 1
ax= 0 ay= 0.0005 0.0005 ∗dt
vy
10 4 1
−G mS/r3−→ r G = 1
dt
x=/2y=/3vx= 1 vy= 0

r
r
dt
dt
0.00025

A
X
i
−→
Fi/A =mA
−→
aG(A)
A B A
−→
FB/A =−GmAmB
1
d2
A,B
−→
uB→A.

A B
−→
P=mA
−→
vA+mB
−→
vB
M=mA
−→
rA×−→ vA+mB
−→
rB×−→ vB
Ec=1
2mAv2
A+1
2mBv2
B
−→
P= 0 mA
−→
vA=−mB
−→
vB
M= (−→ rA−−→ rB)×mA
−→
vA∆−→ r=−→ rA−−→ rBM= ∆−→ r×mA
−→
vA
2Ec=mA(1 + mA
mB)v2
A
Ec
∆−→ r
−1−→ vi∆−→ r
t t +dt
t t +dt
t+dt
t t +dt
N(u) = (−→ rA(u)−−→ rB(u))2
N(u)=(−→ rA(t)−−→ rB(t)+(u−t)(−→ vA(t)−−→ vB(t)))2
N(u)=∆−→ r(t)2+ 2(u−t)∆−→ r(t)·∆−→ v(t)+(u−t)2∆−→ v(t)2
u ∂uN(u) = 0
(tm−t) = −∆−→
r(t)·∆−→ v(t)
∆−→ v(t)2
tm< t t
t < tm< t +dt tm
t+dt < tmt+dt
t
t+dt