# Interpolation

#### Se_Dan95

##### New member
I've encountered some problems during my space dynamics homework. The task tells me to use interpolation to solve the issue, but I have yet to learn it (I'm not even sure that I will ever have to study it during my major).
The task is the following:
" What is the temperature:
During atmospheric reentry in 35 km height, if there t0 = –40°C? You can determine the velocity from the data of the graph by using interpolation. (The data is the reentry speed of the Space Shuttle in different heights).
The data:
H=75km->v=7,68m/s
H=47km->v=6,24m/s
H=25km->v=0,95m/s
H=35km->v=???"

I have all the formulas to solve the rest of the task, but the only thing I can't solve is the velocity by using interpolation.
If this would be linear interpolation, I could figure it out, but since it can't be linear, I have no idea how to solve it. If someone could share a formula or just some ideas that I can use to determine the missing data, that would be a great help for me.

#### tkhunny

##### Moderator
Staff member
There are MANY ways to go about it. It really depends on what you want it to do and what theory you are trying to impose.

With only three data points, it is unlikely that you will produce anything particularly robust.

1) If you were willing to do linear, what's stopping you from building a quadratic polynomial?
2) Perhaps you would prefer exponential or logarithmic, since your basic re-entry problem might have terminal characteristics like that?
3) Why not just create an x-y scatter plot and see where the 35 point makes the most sense based on some idea in your head? I did a scatter plot, laid a quadratic over it, and moved 35 around a bit. 4 m/s seemed nice enough for something, I suppose.
4) Using a logarithmic least squares function, maybe 3.4-3.6 seemed a little better.

Just take a shot at it.