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#### Lab Activities

This is a computer lab which uses a shareware program called "Gravitation_Ltd_4_0" to simulate the motions of bodies moving solely under the influence of gravitational forces. The program allows the creation of up to 10 bodies which can have masses between the values of 1 to 900. The user can adjust the initial positions and velocities of the bodies. The program is easy to use and will run on a Macintosh 512KE up to a PowerPC 7600 using either System 6.0.x.or System 7.x.x. Documentation is available.

In the current lab writeup, the students are asked to perform four experiments:

1. The first experiment is to create a large stationary planet at the center of the screen and one satellite to be put in orbit around it. The user adjusts the initial conditions (position and velocity) to give the planet a circular orbit. Once a circular orbit is achieved, the student is asked to use the formula to calculate a value for the gravitational constant (which in this program is 5). The student then tries various values of v, R and Mp to see if G is constant in this program.

2. The second experiment is to create a large planet on the far left of the screen and a small "rocket" a small distance to its right. The rocket is given a positive x-velocity. By adjusting the x-velocity the rocket can be made to travel almost all the way across the screen before being captures and accelerated back towards the planet. The student is then asked to calculate G using the formula vo is the initial velocity, Ro is the initial distance between the planet and the rocket and R1 is the distance between the planet and the farthest position of the rocket along the x-axis. This value of G is compared to the value computed in the first experiment.

3. The third experiment is to create a planet of mass 2m at the center of the screen and two satellites of mass m located along the x axis at positions x and -x. One satellite is given a velocicty of vy and the other is given a velocity - vy . The numerical value of the velocity is adjusted until both satellites travel in the same circular orbit. Under these circumstances, v is given by the formula

The student confirms this formula by substituting values of G (=5), m and R taken from their plot and computing a value for v. This value is compared to the value they had to use to get the satellites to travel in the same circular orbit.

4. The fourth experiment is to use the program to test the validity of Kepler's third law relating the period of an elliptical orbit to the semi-major axis of the orbit.

Introductory

#### Equipment

 Number of set-ups available: 1 Per lab station: 1 Macintosh SE/30/dust cover, mouse pad and rolling cart 1 Turbonet connector 1 4 wire phone cable 1 network printer 1 Gravitation software on Mac 1 network port

#### Notes

 Last Update: Site contact: largent@Dartmouth.EDU