How do I calculate acceleration when I have instantaneous values of velocity?

I have the x, y, and z components of velocity of Uranus 30 days (can also use 1 day apart data) apart since 1800. I want to calculate its acceleration using this velocity data.

I have used the folowing two equations but neither is giving me a result I expect.

5 point differetiation:

h=0.0833; %step size
for i=3:2697 %I have a total of 2699 data points
    V1(i,:)=1/(2*h)*(v_u(i-2,:)-8*v_u(i-1,:)+8*v_u(i+1,:)-v_u(i+2,:)); %v_u is the velocity vector of Uranus
end

Derrivative from first principles:

for i=1:2698
   X(i)= (V_u(i+1)-V_u(i))./(0.0833); %V_u is the velocity vector of Uranus
end

[Walter Roberson]

gradient()

Answer 1

[Wan Ji]

Use pddiff function attached here, this is easy to use.

t = linspace(0,3*pi,19)';
f = sin(t); % assume this is the velocity
[ft_pd, ftt_pd] = pddiff(f, t); % using pddiff method
ft_true = cos(t); % true value
ft_cen = cendiff(f, mean(diff(t)));% using centro diff method
figure(1); clf
plot(t, ft_pd, 'b--');hold on
plot(t, ft_true, 'r-');
plot(t, ft_cen,'k-.');
legend('dfdt-pddiff','dfdt-exact', 'centro-difference')

It is from the picture that pddiff method works fine!