## Orbit Simulators

It follows Newton´s equations! That is why it is a simulation and not simply an animation.

**Orbit Simulator 1-** Lower velocities and fixed masses>>

**Orbit simulator 2 -** Change the mass and investigate further>>

Having said that, we must find some parameters that makes it viable to be seen in a computer (or phone) screen. The orbits cannot take a very long time (as for instance our orbit around the Sun which takes one year) nor can they be too long (hundreds of thousand of kilometers). For this purpose the gravitational constant G was attributed the value 1, which is a lot higher than its real value of 6.6 x 10^{-11}. The important thing here is that the orbits shown are calculated using the relevant physical equations. If you want you can think of this as a representation of another universe, with different fundamental constants (but the same physical laws), where G=1!

Those simulate orbits which could involve any kind of orbiting object: the moon orbiting the Earth, the Earth orbiting the Sun, the Sun orbiting the Milk Way, the Milk Way orbiting the local group of galaxies, a star orbiting a black hole, etc...

It is nice to get a feeling of the gravitational force at work, as it is the dominant force in the universe, which makes our life possible! Using basic calculations like these, it was possible to find out about the great mysteries of today´s cosmology which are dark matter and dark energy.

Simulator 2 will allow the use of larger masses and** chaotic orbits can be produced**, when small velocities are used. Chaotic orbits don´t repeat themselves and lots of different trajectories, allowed by the Principle of Conservation of Energy, will be possible. The movement can be monitored using the graphs on the right.

Both simulators allow you to choose the components x e y of the initial velocity. Notice (on the velocity graph) that simulator 2 allows for higher velocities, to counteract its larger gravitational field.

### SIMULATORS USAGE TIPS AND INFORMATION

-The graphs record kinetic energy (KE) and gravitational potential energy (PE). Notice that when KE is at a maximum PEis at a minimim and vice-versa. This result comes directly form the equatiins and it is expected according to the Principle of Conservation of Energy, so that PE and KE add up to a constant value at al times. This value is negative when PE is larger than KE, which is the condition for a stable orbit.

-PE is negative because it is zero at an infinite distance, when there is no gravitational interaction. This same convention is used for the energy of "orbiting" electrons in an atom.

-To restart the graphs you can refresh the browser (press F5)

-In some older smart phones the simulation may be a bit too slow. You should lose the simulation, or stop it, when you leave the page, so that it won´t be consuming your device resources (memory and CPU). This simulations require a lot of calculations so that they are quite demanding.

If the velocities chosen are too low, the orbiting object will collapse into the larger mass. That will be similar to a rock falling on the ground. Tangencial velocity is needed to establish an orbit. In this way, orbital motion and projectile motion are very similar, or very much the same thing. The difference is that when the projectile, launched above the Earth, has enough velocity it will not fall to the ground but instead it will go round the planet! Newton had already proposed a thought experiment involving a cannon placed at the top of a mountain (newton´s mountain). If the projectile could be fired fast enough, it would circle the planet and come back!

Note that sometimes the object, after collapsing, is ejected at high speed. That is an unphysical situation that occurs because the equations go to infinity when the distance between the objects is zero. It is like dividing something by zero.

**Orbit Simulator 1 **

- The mass of the central object is 100000 kg (1 million). Each component of the velocity ranges from 0 to 70 m/s. You can check the value chosen using the sliders by looking at the velocity graph. The values are displayed as you slide if you use Internet Explorer.

-When you use full speed, for both Vx and Vy, the planet initially goes away but it returns and you will be able to see it behind the graphs on the right hand side. It will eventually complete the orbit.

**Orbit Simulator 2**

- The mass of the central object can be chosen using the slider and the allowed values range between 1000000 kg and 4000000 kg (1 and 4 million kg). Each component of the velocity ranges from 0 to 120 m/s. You can check the value chosen using the sliders by looking at the velocity graph.

-Notice that the scale of the energy graphs is larger, to allow for the higher energies involved in the movement with a larger mass,

Check also the projectile simulator>>

::::::::::::::::::::Ricardo Esplugas 2016::::::::::::::::::::::::::::::::::::::