Question: urgent help needed! Supernovae graphs

Hello,

I'm under pressure to complete the following plot for a Masters project. I just can't seem to find where the errors are. I'd be very grateful if anyone can help.

x_*,y_*,z_* are independent variables 

r_*(x_*,y_*,z_*):=(x_*²+y_*²+z_*²)^0.5:

r(x_*,y_*,z_*,t):=  (r_*(x_*,y_*,z_*)^0.5 +30t)^0.5

x(x_*,y_*,z_*,t):=r(x_*,y_*,z_*,t)cos(x_*²+y_*²)sin(x_*+2Z_*)

y(x_*,y_*,z_*,t):=r(x_*,y_*,z_*,t)sin(x_*²+y_*²)sin(x_*+2Z_*)   

z(x_*,y_*,z_*,t):=r(x_*,y_*,z_*,t)cos(x_*²+y_*²)   

δ₀(x_*,y_*,z_*)=piecewise((x_*²+y_*²+z_*²)^0.5≤30,10,0);

Jacobian is the x_* differentiated with respect to x, do the same for other components.

J(x_*,y_*,z_*,t) is the determinant of the Jacobian

D(x,y,z,t):=J(x_*,y_*,z_*,t)δ₀(x_*,y_*,z_*);

I wish to plot the graph of D(x,y,z,t) against r for a particular time say t=10 or something.

Many Thanks