Question

This is my exact question. But i need a step by step process example in understanding how to use Kepler's 3rd law to solve this.

Write a program that asks the user for the name of a planet and the distance of that planet from the Sun in AU’s. The program should than calculate a ‘year’ on that planet in Earth years and output the information to the user. Use user friendly prompts. Be sure to include a comment at the beginning of the program with your name, date, and a short description of the program.

Answer 1

As per Kepler's Law $T^2 \propto R^3$ where T is the period of rotation and R is the distance from the sun. Hence
$\frac{T_P^2}{T_E^2} = \frac{R_P^3}{R_E^3}$

where $T_P,R_P,T_E,R_E$ are the time period of the planet, distance of the planet, time period of Earth, the distance of Earth respectively.

Note that the time period of Earth is 1 year, while the distance is 1 AU.

Hence where the time period is in Earth years, and the distance is in AU. This gives
Тр RA
.

Here is the code which does this as required (in C++), let me know if you need some other language:

# include <iostream>
# include <cmath>
using namespace std;

int main() {
//take user input
string name;
double dist;
cout << "Please enter the name and the distance of the planet from the sun: ";

//output the time period using Kepler's law now
cin >> name >> dist;
cout << "The rotation period of " << name << " in Earth years is: " << pow(dist, 1.5) << endl;
return 0;
}

Please enter the name and the distance of the planet from the sun: Venus 0.723 The rotation period of Venus in Earth years is: 0.614763

Please enter the name and the distance of the planet from the sun: Mars 1.524 The rotation period of Mars in Earth years is: 1.88138

Comment in case of any doubts.