A First C++ Project

reading

Cyganek section 2.5 has a different first project (an interest calculator) than we do here.

Kepler’s third law

Kepler’s third law relates the period of a planet’s orbit, \(P\), to its semi-major axis, \(a\):

\[P^2 = a^3\]

Note

This version has \(P\) in years and \(a\) in astronomical units and the mass of the Sun in solar masses. In those units, the gravitational constant is \(G = 4 \pi^2\).

We want to write a program that allows us to specify either \(P\) or \(a\) and print the other quantity.

Looking at this expression, we need to learn how to raise something to a power. In C++, this is done by the std::pow() function, which is part of cmath.

Let’s try this out:

#include <cmath>
#include <iostream>

int main() {

   std::cout << std::pow(2.0, 3.0) << std::endl;

}

We need to tell C++ what type of data we are going to be storing. We’ll talk about data types next, but for now we’ll use double, which is double precision floating point format (more on that later).

Important

C++ is statically typed—this means we need to declare what type of data is to be stored in each variable we use before we can use that variable. For instance:

double P;

creates a variable P that can store a double precision number.

We will also want to take input. For this we need to use std::cin. Let’s look how this works:

#include <iostream>

int main() {
   double P = 0.0;
   std::cout << "Enter the period (P): ";
   std::cin >> P;

   std::cout << "P = " << P << std::endl;
}

Notice that we initialize P to 0.0 just to be safe (we’ll see a more compact way of initializing later).

Now we will look at the complete code. We shouldn’t be expected to be able to write something like this yet, but this will show us some of the C++ constructs that we will learn in the next weeks.

Listing 1 kepler.cpp

#include <iostream>
#include <cmath>
#include <string>

int main() {

    std::cout << "solve for P or a? ";

    std::string response{};

    std::cin >> response;

    bool solve_for_a{};

    if (response == "a" || response == "A") {
        solve_for_a = true;
    } else if (response == "p" || response == "P") {
        solve_for_a = false;
    } else {
        std::cout << "invalid value" << std::endl;
        return -1;
    }

    double a{};
    double P{};

    if (solve_for_a) {
        std::cout << "enter semi-major axis (a): ";
        std::cin >> a;

        if (a < 0.0) {
            std::cout << "error: a must be positive" << std::endl;
            return -1;
        }

        P = std::pow(a, 1.5);
        std::cout << "period, P = " << P << std::endl;

    } else {
        std::cout << "enter period (P): ";
        std::cin >> P;

        if (P < 0.0) {
            std::cout << "error: P must be positive" << std::endl;
            return -1;
        }

        a = std::pow(P, 2.0/3.0);
        std::cout << "semi-major axis, a = " << a << std::endl;

    }
}