# Question:What initial conditions am I missing?

## Question:What initial conditions am I missing?

Maple 2023

I've been writing this code to simulate the orbit of Venus in a simple 2D polar plot, but it keeps telling me that I have insufficient initial conditions, here is the code:

restart:with(Physics):with(VariationalCalculus):with(plots):with(plottools):

R[V] := 0.72*AU: #`starting radius for venus`

AU := 1: #`astronomical unit`

G := 6.674*10^(-11): #`gravitational constant`

m[S] := (333*10^3)*m[E]: #`mass of the sun`

m[V] := 0.815*m[E]: #`mass of venus`

m[E] := 1: #`mass of the earth`

x[V] := t -> r[V](t)*cos(theta[V](t)): #`x-coordinate`

y[V] := t -> r[V](t)*sin(theta[V](t)): #` y-coordinate`

x[VP] := t -> diff(x[V](t), t): #` x-velocity`

y[VP] := t -> diff(y[V](t), t): #`y-velocity`

T[V] := m[V]*simplify(x[VP](t)^2 + y[VP](t)^2)/2: #`kinetic energy of the system`

V[V] := (-G)*m[V]*m[S]*1/r[V](t): #`potential energy of the system`

L[V] := T[V] - V[V]; #`lagrangian of the system`

EL[Vr] := diff(L[V], r[V](t)) - diff(diff(L[V], diff(r[V](t), t)), t) = 0: #` e-l for the r-coordinate`

EL[`Vtheta;`] := diff(L[V], theta[V](t)) - diff(diff(L[V], diff(theta[V](t), t)), t) = 0: #`e-l for the theta-coordinate`

EL[V] := [EL[Vr], EL[`Vtheta;`]]; #` system of equations`

F[V] := G*m[V]*m[S]*1/R[V]^2: #`gravitational force for venus starting position`

omega[V] := sqrt(F[V]*R[V]*1/m[V])*1/R[V]: #`angular velocity for venus starting position`

IC[V] := [r[V](0) = R[V], D(r[V])(0) = 0, theta[V](0) = 0, D(theta[V])(0) = omega[V]]; #`initial conditions, r-position, r-velocity, theta-position, theta-velocity`

SOL := dsolve(EL[V], IC[V], [r[V](t), theta[V](t)], numeric, output = listprocedure); #`numerical solution`

Error, (in dsolve/numeric/type_check) insufficient initial/boundary value information for procedure defined problem

I have included both the initial values for r,dr/dt, theta and dtheta/dt.

I'm not sure what other initial conditions I could be missing?

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