The Objective

This project will give you practice using loops, the switch, mixing data types and writing functions.

The Background

Mathematicians and other scientists find unexpected applications for power series approximation. In 1772, the astronomer J. E. Bode proposed a rule for calculating the distance from the sun to each of the planets known at that time. To apply that rule, which subsequently became known as Bode's law, you begin by using the sequence:

where each subsequent element in the sequence is twice the preceding one. It turns out that an approximate distance to the ith planet can be computed from this series by applying the formula

The distance is given in astronomical units; an astronomical unit (AU) is the average distance from the sun to the earth, which is approximately 93,000,000 miles. Except for a disconcerting gap between Mars and Jupiter, Bode's law gives reasonable approximations for the distances to the seven planets that were known in Bode's day:

Distance from the Sun

Mercury      0.5 AU   4.650000e+07 miles
Venus        0.7 AU   6.510000e+07 miles
Earth        1.0 AU   9.300000e+07 miles
Mars         1.6 AU   1.488000e+08 miles
?            2.8 AU   2.604000e+08 miles
Jupiter      5.2 AU   4.836000e+08 miles
Saturn      10.0 AU   9.300000e+08 miles
Uranus      19.6 AU   1.822800e+09 miles

Concern about the gap in the sequence led astronomers to discover the asteroid belt, which they decided was left over after the destruction of a planet that had once orbited the sun at the distance specified by the missing entry in Bode's table.

The Task

You are to write a program that calculates each of the distances in both astronomical units using Bode's formula and the number of miles (shown in exponential notation), where 1 AU = 93,000,000 miles. You will first need to calculate the value of the current term in the series. Do this within a function called GetTermValue. You are not allowed to #define the values of the terms of the sequence, or hard code these values in any way. Your program should print out a table exactly like the one shown above.

You'll be expected to write a minimum of four functions, other than main, for this project.

Here are the function prototypes you are to use (without modification):

void   PrintExplanation (void);
int    GetTermValue (int index);
double FindAU (int termValue);
double FindMiles (double au);

Function Descriptions:

• PrintExplanation - should print a message to the user, explaining what the program will do. Since this function returns nothing, it can also be called a procedure.
• GetTermValue - This function will take an integer (the index of the term) as its single argument, index, and return the value of that term in the sequence. The values of the first two terms in the series are 1 and 3, respectively. The values of all of the other terms are to be calculated based on the index of the term. DO NOT HARD CODE THE TERM VALUES for the terms of index > 2.
• FindAU - This function will take the integer value of a term as its single argument and, using Bode's formula, calculate the distance from the sun in astronomical units then return that distance.
• FindMiles - This function will convert astronomical units to miles, where 1 AU = 93,000,000 miles.

Submitting the Program

To submit the file you should use the command:

submit cs201 Proj2 proj2.c

You can check your submission by using the command:

submitls cs201 Proj2