A little background • Mercury’s orbit rotates 5600 arc seconds per century, but 43 arc seconds per century was unaccounted for • Newtonian physics couldn’t explain the extra precession • Einstein’s General Relativity to the rescue
How he did it • Einstein added a relativistic correction term (alpha/r^4) to account for the curvature of space-time caused by mass • This warping of space-time perfectly accounted for the extra arc seconds
How I did it • I multiplied the gravity formula by the relativistic correction term 1+(alpha/r^4) • Calculated rate of rotation of orbit • When alpha is of magnitude 1, it takes about 30 min to complete a full orbit rotation
When you change the magnitude of alpha, the full precession time decreases according to the formula: 0.0032x^2 - 0.1539x + 29.73
But what’s alpha? • In this case, I used the number 6.8e^x from HW 4 • It’s the amount of curvature of space-time caused by the Sun’s mass • All mass, especially large ones, curve space-time around them. Orbiting objects are really just rolling around in the funnel shaped curve of the large mass.
So what? • If all gravitation is caused by warps in space-time, then anything going through a gravity field should be distorted by the field • This leads to all sorts of things, like better simulations of orbits or the existence of Black Holes where the walls of the gravity well are so steep that light can’t escape
Picture credits • Mercury (planet) http://en.wikipedia.org/wiki/Mercury_%28planet%29 • Precession http://en.wikipedia.org/wiki/Precession • Gravity Warps Space http://www.dmns.org/main/en/Professionals/Press/CurrentPressReleases/Press+Releases/Planetarium/blackHolesImagesPress.htm • Black Hole http://en.wikipedia.org/wiki/Black_hole