Because one of the values in your data is not finite (see below). And interpolation in between infinite set of points is rather un-defined (for the lack of a better word).
%% AEM 588 HW1 Question 2
clear all;
close all;
clc;
global A_const;
global B_const;
global C_const;
mu = 398600; %km^3/s^2
% % nu0 = 1e-3;
Isp = 100;
r0 = 2378 + 12800; %km
m0 = 8; %kg
T = 12/1000;
v0 = sqrt(mu/r0);
rho0 =1;
tau0 = 0;
nu0 = T/m0/9.81;
T0 = nu0*(mu*m0)/r0^2*1000.;
mdot = T0/Isp/9.81;
A_const = T0*r0^2/1000;
B_const = mu*m0;
C_const = mdot*sqrt(mu*r0^3);
tspan = [0 10000];
initialConditions = [1.;0.;1.];
%Solve ODE
[tau,rho] = ode45(@odefun,tspan,initialConditions);
t = tau;
r = rho(:,1);
min(r)
rMoonNorm = ones(length(r),1).*(384400/r0);
b_line = polyfit(t,rMoonNorm,1);
y_line2 = polyval(b_line,t);
min(y_line2-r)
x_int = interp1((y_line2-r),t,0)
y_int = polyval(b_line,x_int);
figure(1); clf(1);
plot(t,r)
hold on
plot(t,rMoonNorm)
xlabel('Time, Non-Dimensional')
ylabel('Radius, Non-Dimensional')
t = tau./sqrt(mu/r0^3);
r = rho(:,1).*r0;
rMoon = ones(length(r),1).*384400;
time_intercept = x_int/sqrt(mu/r0^3);
hours_intercept = time_intercept/3600;
days_intercept = hours_intercept/24;
Prop_mass = mdot*time_intercept;
fun = @(x) T0./(m0-mdot*x)
dV = integral(fun,0,time_intercept);
figure(2); clf(2);
plot(t,r)
hold on
plot(t,rMoon)
plot(x_int,y_int,'rx')
xlabel('Time (s)')
ylabel('Radius (km)')
function dydt = odefun(t,y)
global A_const;
global B_const;
global C_const;
dydt = zeros(3,1);
dydt(1) = y(2);
dydt(2) = ((y(3)^2)-y(1))/(y(1)^3);
dydt(3) = (A_const/(B_const - C_const*t))*y(1);
end
