Question

Planet Average Surface
Temperature (K) Average Orbital
Velocity (km/s)
Mercury 440 47.87
Venus 737 35.00
Earth 288 29.78
Mars 208 24.13
Jupiter 163 13.07
Saturn 133 9.69
Uranus 78 6.81
Neptune 73 5.43

Use the data table above to describe the relationship between average surface temperature and average orbital velocity (how fast they orbit) of the planets of our solar system. Use numerical data from the table to support your answer.

Answer 1

use Lagranges interpolation formula....or Newton Divided difference formula to find the relation....
take Temperature = T, and orbital velocity as v ... and use those interpolation technique to find v(T) = ???? or T(v) = ???? ... prefer T(v)=???

Answer 2

Looks like the ratio of temperature to orbital velocity is roughly 10:1

So, take the ratios and then do statistics on mean and standard deviation.

Or explore power law T = k v^a
log T = log k + a log v
and again look at mean and standard deviation?

or
note that sun controls mean temperature, with intensity falling off as 1/r^2, and the planet intercepts with area proportional to R^2 but radiates with rate proportional to R^2, so this evens out.

Use relationship between distance and periods to determine the velocity as a function of distance to help explain your results.