09/27/2002 Entry: "Kepler's 3rd Law is Broken"
Posted by Maynard @ 11:32 PM MST

Kepler's 3rd Law is Broken

I've written a short Windows program that uses Kepler's 3rd Law to calculate the mass of an object based on it's orbital time in days and it's distance from its parent, in kilometers. However, I can get the answer in the ballpark but not any closer than that. The answer is correct in magnitude but not accuracy. If you have any ideas why this might be, drop me a line. Here's the program (zipped Windows exe). Click below to see how I do the actual calculation.

In the following C++ code, m_dDistance is the value the user enters, in kilometers, m_dTime is the orbital time, in days, and m_dMass is the mass in kilograms displayed to the user.

// convert to more manageble units
double d = m_dDistance * 1000; // convert kilometers to meters
double t = m_dTime * 24 * 60 * 60; // convert days to seconds

const double pi = 3.14159265358979323846;
const double FourPiPi = 4*pi*pi;
const double r3 = d * d * d ; // meters cubed
const double G = 6.6725985E-11; // big G

double Numerator = FourPiPi * r3;
double Denominator = G * t * t;

m_dMass = Numerator/Denominator; // this is in kilograms
m_dMass /= 1000000; // now it's in millions of kilograms