Chapter 10, Problem 19E

(a)

To determine

To Explain: the distances to construct a model for the Distance from the sum on the basis of the planet’s position.

Explanation of Solution

Given:

  

Calculation:

Position	Distance from sun	Log(distance from sun)
1	36	1.5563
2	67	1.8261
3	93	1.9685
4	142	2.1523
5	484	2.6848
6	887	2.9479
7	1784	3.2514
8	2796	3.4465
9	3707	3.5690

Graph:

Scatter plot:

  

Residual Plot:

  

From the result of the equation of the regression line is

  $\log \left(\text{Distance}\right)=1.244+0.271\text{Position}$ , Therefore, this is the required model. R-squared of the model is 0.981, it implies that about 98 percent of the variability in the log (Distance) is estimated for by the model.

(b)

To determine

To Explain: on the basis of model, would agree with this international Astronomical union that Pluto is not Planet.

Explanation of Solution

Given:

Position	Distance from sun
1	36
2	67
3	93
4	142
5	484
6	887
7	1784
8	2796

Calculation:

Position	Distance from sun	Log (distance from sun)
1	36	1.5563
2	67	1.8261
3	93	1.9685
4	142	2.1523
5	484	2.6848
6	887	2.9479
7	1784	3.2514
8	2796	3.4465

The model of part (a) not get aenough proof to help the statement of the astronomers. Pluto looks to fit this pattern well but Pluto's distance from the sun is about less than expected the distance. Suppose finding the distance of Pluto from Sun expected by the previous model.

  $\begin{array}{c}\log \left(\text{Distance}\right)=1.244+0.271\left(9\right)\\ =1.244+2.439\\ =3.683\end{array}$

  $\begin{array}{c}\text{Distance}={10}^{3.683}\\ =4819.48\end{array}$

Therefore, the distance of the Pluto from Sun expected by the above model is 4819.48 million miles, it is less than actual distance.

Graph:

Scatter plot without Plot

  

Residual plot without Pluto

  

  $\begin{array}{c}\log \left(\text{Distance}\right)=1.203+0.284\left(9\right)\\ =1.203+2.556\\ =3.759\\ \text{Distance}={10}^{3.759}\\ =5741.16\end{array}$

In the solar system, Pluto does not match the pattern for location and distance. Currently, the model created. It's not nice with Pluto included, because Pluto affects those predictions. The ModelWithout Pluto, Pluto's distance from the Sun is predicted to be 5741.16 million miles. There is proof, therefore, in its relationship to location and space, Pluto does not function like a planet if the IAU is right.