Question

Use the following data values:

At time 13, observed position was (1, 3, 7)

At time 84, observed position was (23, -5, 10)

You want to find the position at time 50"

My question is; what equation can I use to solve for [x3, y3, z3] knowing [t1, x1, y1, z1,] and [t2, x2. y2, z3] and [t3]?

Is there a Python function I can use for this?

Answer 1

import numpy as np
# assuming the array format as [t,x,y,z] and t=13 as the initial point
# then by assuming a linear line through t=13 and t=84, we can calculate
l13 = np.array([13,1,3,7])
l84 = np.array([84,23,-5,10])
l50 = (50-13)*(l84-l13)/(l84[0]-l13[0])+l13
print(l50)

Output

I think this is what you are mentioning as there are no further details about the position and other details.

If you found this answer satisfactory, please do give it a thumbs up, else leave a comment and I will get back to you at the earliest. Thanks :)