What would happen if a black hole wandered past our Solar system? Would it suck the Earth into its orbit and carry us away? Would it disturb our orbit and make us fall into the Sun, or fling us out into interstellar space to slowly freeze? This project aims to find out.
For this exercise you will use the 3-body code you have tested in section \ref{sec:computerprog}.
Start with the Earth in its usual nice steady orbit around the Sun. Fling in the black hole from a range of directions and orientations. See what happens if it gives the Sun a near miss, or passes by much further out.
How massive should the black hole be? Dying stars end up as either white dwarfs, neutron stars or black holes, depending on their initial mass and the conditions of their death. Both neutron stars and black holes are thought to form in Supernova explosions, with the final product determined by the initial mass of the dying star. Neutron stars have a maximum mass of \(\sim 2-3\) solar masses, after which they collapse to form a black hole. This gives a lower limit on the range of masses you should play with. There is no upper limit to the size of a black hole, but let’s assume that our wandering black hole was formed from the collapse of a star and has not grown by merging with other black holes since then. Such a black hole could conceivably weigh thousands of times more than the Sun, but since stars massive enough to form such heavy black holes are rare, moderate masses are much more likely. Concentrate on the effects of smaller black holes, but run a few simulations with the really big ones just to find out what happens.
How fast will the Black Hole approach? Stars in our part of the galaxy are typically moving at speeds of about 200 km/s, in their orbits around the centre of our galaxy. If the black hole were in a similar orbit to our Sun, it might sidle up relatively slowly, say 10 km/s. If however it was rotating the other way around the galactic centre, it might be travelling at 400 km/s, and if it was an interloper from intergalactic space, the speed might be higher still.
See where the Earth ends up after each Black hole encounter. If it ends up in orbit around the Black hole, or flung into interstellar space, it is obviously curtains for life on Earth. But what if it ends up in a different and/or distorted orbit around the Sun? Get your program to work out the temperature of the Earth at each point. Assume it is a black body whose only heat source is the Sun, and that it is in thermodynamic equilibrium. Is this assumption reasonable? If we were flung out into interstellar space, how long would we take to cool down?
Write a brief summary of the results of your investigation. Make sure you answer the aims you had at the start.
What happens when two bodies got too close to each other? What does Newton’s equation predict? Is this scenario physical? How could you make your calculations more realistic?
Did you notice any change in speed while running the program, particularly when going from two bodies to three? Do you think this is a realistic method for \(N\)-body simulations where \(N\sim 100\)?