#$&*
course phy 231
Brief Gravitational Simulation circular orbits:Uses gravitational simulation Motion in the Gravitational Field of the Earth, may use TIMER.
See also Pictures of Gravitational Simulation
Starting at distance 2 with initial angular position 0 and initial direction 1.57, determine the initial velocity necessary to achieve a nearly-circular orbit, in which the speed of the satellite changes by less than 50 in a circuit of the planet.
Repeat for starting distances 1.1 and 1.6.
Report max and minimum speeds in each of the orbits.
****
Starting distance 2. 5600 initial, 5564 min, 5600 max
Starting distance 1.1. 7540 initial. 7534 min, 7542 max
Starting distance 1.6. 6250 initial, 6247 min, 6257 max
#$&*
Calculate the average kinetic energy for each, based on satellite mass 1 kg, and give your results:
****
Taking the integral of mv with limits being the max and min velocities given above gives me the following results.
Starting distance 2. Average KE of 200952 N
Starting distance 1.1. Average KE of 60304 N
Starting distance 1.6. Average KE of 62520 N
If you take the integral of m v with respect to v, your antiderivative is in fact 1/2 m v^2. Since an integral indicates the change in the value of an antiderivative, your integrals should indicate the change in 1/2 m v^2, i.e., the difference between max and min KE within the orbit.
However you were asked for the average KE, not the change in KE.
#$&*
What is the percent uncertainty in the average velocity you used to calculate the average kinetic energy?
****
Im confused about this one. I used the maximum and minimum with integration, I didn’t really use an average value
#$&*
What therefore is the percent uncertainty in your calculated result for the average kinetic energy?
You can answer these questions, but first see my note on your calculation. When asked for average KE you found the change in KE.
****
#$&*
"
Analysis:
What is the average KE of each orbit? (You might have already calculated this correctly in your original submission).
****
#$&*
By how much would your KE change if you were to move from the first circular orbit to the second? Does it increase or decrease?
****
#$&*
By how much does KE change from the second orbit to the third?
****
#$&*
By how much does the gravitational PE change from the first orbit to the second? University Physics students should answer by integrating the gravitational force from one orbital distance to the other. Others can use the formula for gravitational PE (which, in this context, is NOT m g h).
****
#$&*
By how much does gravitational PE change between the second orbit and the third?
****
#$&*
When going from the first orbit to the second, does the satellite speed up or slow down?
****
#$&*
If you're in the first orbit and slow down, what happens to your orbit? Does slowing down seem to be helpful in getting to the second orbit?
****
#$&*
When going from the first orbit to the second, does the satellite's gravitational PE increase or decrease?
****
#$&*
When going from the first orbit to the second, does the gravitational force do positive or negative work on the satellite?
****
#$&*
By how much does the total energy of the orbit (i.e., KE + PE) change between the first and the second orbit?
****
#$&*
Does a forward push from its engines do positive or negative work on the satellite? Does this increase or decrease our total energy? Does it increase or decrease our speed?
****
#$&*
So to get from the first orbit to the second, do we use a forward push or a backward push from our engines?
****
#$&*
See my note on your original calculations and be sure you correct anything that needs to be corrected.
Then proceed with the analysis, as appended above.
#$&*