Chapter 1, Section 1.5, Figure 1.3

Enter the orbital periods of the five major uranian satellites (Miranda, Ariel, Umbriel, Titania and Oberon).

period = {1.413, 2.520, 4.144, 8.706, 13.463};

Take the logarithm (base 10) of each period.

Lperiod = Log[10,period]

Carry out a linear least squares fit to the data using Mathematica's Fit command.  Here i=1 denotes Miranda, i=2 is Ariel, i=3 is Umbriel, i=4 is Titania and i=5 is Oberon.

fn = Fit[Lperiod, {1,i}, {i}]

Now calculate values of this function for each value of i.

calc = Table[fn, {i,1,5}]

Use these to calculate the fitted orbital period.

10^calc

Plot the observed orbital periods ...

lp = 
ListPlot[
Lperiod, Frame->True, PlotRange->{{0,6},{0,1.4}},
AxesOrigin->{0,0}]

... the fitted orbital periods ...

fittedlp = 
Plot[fn, {i,0,6},
Frame->True, PlotRange->{{0,6},{0,1.4}},
AxesOrigin->{0,0}]

... and show them both together.

Show[lp,fittedlp]