Gravity and Kepler's Laws Simulation

Open this link: http://www.jjdebenedictis.com/Gravity-and-Keplers-Laws/

1. Once you have opened the simulation, drag the pointer all the way over to the left on the "fast - accurate" scale so that the results you get are as accurate as possible. Turn on the grid as well by using the checkbox.
2. Ensure that the number of bodies is selected at 2 and populate the mass/position/velocity table as so: body 1: Mass 500; position -300x, 0y; velocity 0x, 0y AND body 2: Mass 1; position 200x, 0y; velocity 0x, 0y

Question 1) Click "Start" to run the simulation and notice what happens. The pink planet will begin to fall toward the yellow planet (the "sun"), and a timer will begin to run. Click the "Stop" button as soon as the pink planet crashes into the Sun (you will see it flash). Record the time it took the took the pink planet to crash into the Sun.

Question 2) If you are to repeat the trial, what would you expect? (choose one of the following multiple choice below)

a. That the time will get longer in the next trial

b.That the time will get shorter in the next trial

c. That the time should remain relatively the same (within a reaction time value of give-or-take 0.15).

Question 3) Click "Reset" and measure the time it takes the pink planet to fall into the sun 2 more times, then average the 3 time trials together to get 1 average time, and enter that below. Record your answer.

Question 4) If you double the mass of the pink planet, what do you predict will be the effect on the time it takes to fall into the sun? (choose one of the following multiple choice below)

a. The time will stay the same because the force and acceleration don't change appreciably

b. The time will get longer because the force and acceleration decrease

c. The time will get shorter because the force and acceleration increase

Question 5) Select "Reset" and change the mass of the pink planet from 1 to 2. Click "Start" and measure the time it takes for the pink planet to hit the sun. Was your prediction correct or not? Why do you think the time turned out the way it did? Record your answer.

Question 6) What do you predict will happen to the time if the mass of the pink planet is doubled again? (choose one of the following multiple choice below)

a. The time remains the same because the force and acceleration don't change appreciably

b. The time gets shorter because the force and acceleration increase

c. The time gets longer because the force and acceleration decrease

Question 7) Click "Reset" and double the mass of the pink planet again from 2 to 4. Run the simulation and record the time for the pink planet to hit the sun. Record your answer.

Question 8) Why do you think that you saw the results you observed in this part of the simulation? Explain why changing the mass from 2 to 4 gave the results you observed?

Question 9) If the sun's mass was to double, what would happen to the time for the pink planet to collide with it? (choose one of the following multiple choice below)

a. The time will get longer because the force and acceleration decrease

b. The time will get shorter because the force and acceleration increase

c. The time will remain the same as when the sun was mass 500 and the planet mass 1. The force and acceleration aren't appreciably different

Question 10) Click "Reset" and adjust the table so that again there are no velocities, but make the sun's mass 1000 (double the original 500) and make the pink planet's mass 1 again. Run the simulation and time how long it takes for the planet to hit the sun. Record your answer.

Question 11) Explain why your timing changed with the increased sun mass, but not with the increased planet mass

Question 12) If the sun's mass was to double again, all other variables being the same, what would be the effect on the time? (choose one of the following multiple choice below)

a. The time will increase because the force and acceleration decrease

b. The time will decrease because the force and acceleration increase

c. The time will remain the same because the force and acceleration do not change noticeably

Question 13) Click "Reset" and double the mass of the sun again from 1000 to 2000, keeping all other variables the same. Run the simulation and time how long for the collision to occur. Record your value.

Question 14) Earlier, we looked at the time it took for a collision when the sun's mass was 500 and the planet's mass was 1, 2 and 4. If we followed that trend even higher so that the mass of the planet was doubled 5 more times, will that trend continue? (choose one of the following multiple choice below)

a. The times will still be the same as the 500/4 scenario since the acceleration and force will not change in any noticeable way

b. The times should decrease because the force and acceleration increase substantially

c. The times should increase because the force and acceleration decrease substantially

Question 15) Click "Reset" and change the values in the simulation so that there are still no velocities, but now the sun's mass is set to the original value of 500, and the planet's mass is doubled 5 times from its last value of 4 to its new mass of 128. Run the simulation and record the time.

Question 16) Was your prediction correct? Why or why not? What changed with this scenario as compared to when the masses were 500 and 4?

Question 17) If we double the planet mass again from 128 to 256, what do you predict will happen to the time? (choose one of the following multiple choice below)

a. The time should decrease because the gravitational force increases significantly

b. The time should increase because the gravitational force decreases significantly

c. It will remain the same because the force and acceleration will not change in any noticeable way

Question 18) Click "Reset" and double the planet's mass one more time (to 256), keeping the sun's mass at 500 and all other variables remaining constant. Run the simulation and record the time it takes for the collision to happen.

Question 19) Based on all your results from the lab so far, if you timed how long a bowling ball and a loonie both took to fall to the earth from the top of a large building, which would have the lower time? (choose one of the following multiple choice below)

a. They will both hit the ground at the same time, having the same time of fall.

b. The loonie will hit first/have the lowest time of fall

c. The bowling ball will hit first/have the lowest time of fall

Question 20) Explain why you answered as you did in the previous question. Which scenario best fits the situation of the bowling ball and loonie falling to the earth [large sun mass and small planet masses; increasing the sun's mass; large sun mass and large planet masses]? Why?

i) Now we'll begin a new set of studies. Start by clicking "Reset" ("Reset" must always be clicked before changing position and velocity of the current simulation).

Set the number of bodies to 2 and fill in the data table as follows:

body 1: Mass 500; position 0x, 0y; velocity 0x, 0y

body 2: Mass 0.001; position 200x, 0y; velocity 0x, 0y

Question 21) If you were to collect the data now, what do you predict will happen to the planet? (choose one of the following multiple choice below)

a. The planet will begin to orbit the sun in a counterclockwise direction

b. The planet will accelerate towards the sun as before

c. The planet will begin to orbit the sun in a clockwise direction

Question 22) What should the direction of the pink planet's velocity be so that it doesn't hit the sun but travels around it instead? (choose one of the following multiple choice below)

a. Right (+x)

b. Down (-y)

c. Left (-x)

d. Up (+y)

i) Test to see which direction(s) give you the proper results by changing the planet's velocity values in turn to +100y, -100y, +100x, -100x. Which one(s) make the planet orbit rather than collide with the sun?

Question 23) With your x-velocities set to 0 and your y-velocity Increasing (we suggest through increments of 10, starting at +10 or -10), keep increasing the velocity until you have found the minimum velocity that allows for the planet to orbit completely around the sun, without touching the sun at any point on the orbit. What is your minimum velocity?

Question 24) Keep increasing the planet's y-velocity until the orbit has a circular shape with the sun at the center. Once you get close, adjust the velocity 1 at a time instead of increments of 10 to get as precise an answer as possible.

Note! Your orbit is circular only when the orbit passes through EXACTLY the same point on the opposite side of the sun as it started from, i.e. if the planet starts out 2 grid-steps away from the sun on the right, then its orbit is only circular when the orbit passes through the point 2 grid-steps away from the sun on the left also.

What is the precise value (no decimal places) of the velocity which produces a perfect circular orbit?

Question 25) Is the velocity of the pink planet constant throughout the circular orbit? (choose one of the following multiple choice below)

a.No

b.Yes

Question 26) Once you have found the velocity for a circular orbit, keep increasing the y-velocity in increments of 10, leaving the x-velocity at 0. What happens to the shape of the orbit? (choose one of the following multiple choice below)

a.It stays circular

b.It becomes rectangular

c.It becomes more square/diamond shaped

d.It becomes elliptical or oval shaped

Question 27) If you were to add another planet into the system with half the orbital radius as the first (i.e. the new planet starts off closer to the sun), but it had the same velocity as the circular velocity of our original planet, what would the shape of the new planet's orbit be? (choose one of the following multiple choice below)

a.Square

b.Elliptical

c.Sinusoidal/wavy shaped

d.Rectangular

e.Circular

i) Click "Reset" and change the number of bodies from 2 to 3.

Give the new planet the following settings:

Blue planet (body 3): mass 0.001; position 100x, 0y; velocity 0x, y=Vc

...where Vc is the orbital velocity you discovered previously that led to a perfectly circular velocity for the outer (pink) planet.

The other bodies will have the same values as before:

Sun (body 1): mass 500; position 0x, 0y; velocity 0x, 0y

Pink planet (body 2): mass 0.001; position 200x, 0y; velocity 0x, y=Vc)

Question 28) Run the simulation. Was your previous prediction about the shape of the blue planet (body 3) correct? Why or why not?

Question 29) Should the y-velocity of the blue planet increase or decrease to move towards a circular orbit? (choose one of the following multiple choice below)

a.Decrease

b.Increase

Question 30) Test your prediction by changing the y-velocity (leaving the x-velocity at 0) of the blue planet in increments of 10 at first, and by increments of 1 as you get close to the correct value, until you can produce a perfectly circular orbit for your blue planet. (Remember, its orbit is circular only when it passes through exactly 100x on the opposite side of the sun; pay attention to the grid.)

What is the y-velocity that yielded a circular orbit for the blue planet?

Question 31) How does the velocity of the blue planet with a perfectly circular orbit compare to the velocity of the pink planet with a perfectly circular orbit? (choose one of the following multiple choice below)

a.The closer blue planet has a higher velocity than the pink planet

b.They are the same

c.The closer blue planet has a lower velocity than the pink planet

Question 32) If you keep increasing the y-velocity of the blue planet, what should happen to the shape of the orbit? (choose one of the following multiple choice below)

a.It should stay circular

b.It should become more rectangular

c.It should become more elliptical

d.It should become more square/diamond shaped

e.It should become sinusoidal/wavy

Question 33) Which is more common: circular orbits or elliptical/oval shaped orbits? Discuss using your previous observations to back up your answer.

i) Click "Reset" and switch the system back to 2 bodies. Make the mass of body 1 200 this time instead of 500. All of body 1's position and velocity values should again be 0.

Make body 2 have a mass of 0.001 as before, but make its position 50x this time and its y-velocity +150. All other values should be 0. This means that body 2 has an orbital radius, a, of 50.

Because we are, next, going to be finding circular orbits for a variety of planet positions that don't necessarily overlap with the grid, we will need to use the tape measure to help determine when our planet's orbit is exactly circular.

Make the tape measure visible by clicking the box for it.

You can drag the tape measure around on the screen by "grabbing" the end of it that has a yellow dot (a sun) with your mouse.

Put the cross-hairs (the small red x) of the yellow dot/sun end of the tape measure on top of your pink planet.

Now drag the opposite (non-sun) end of the tape measure directly across to the other side of the sun. Keep stretching the tape measure until it is exactly 2 times the radius of the pink planet. Because the pink planet's radius is 50 right now, that means the tape measure's length should be set to (2x50) = 100.

The tape measure should be as horizontal as possible.

Question 34) When you run the simulation, the orbit will be circular if the planet passes through the end of the tape measure positioned at -50. If it doesn't pass through, then you will need to adjust the y-velocity until it does pass through. Keep trying until you find the y-velocity that will produce a circular orbit (leaving the x-velocity at 0). What y-velocity gives a circular orbit for a planet radius of 50?

i) In your notebook, construct the following table. For each of the orbital radii of 50, 75, 100, 125, 150, 175, and 200, find the orbital velocity, Vy, that will produce a circular orbit. Record your data in the table in your notebook.

Orbital Radius (a) and Orbital Velocity (v)

Orbital Radius, a Orbital Velocity, v

(Position x) (Velocity y)

50

75

100

125

150

175

200

Using graph paper, make a graph with the orbital radius, a, placed on the y-axis, and orbital velocity, Vy, placed on the x-axis. Select scales that will allow you to fill the majority of the graph page with data.

Draw a best fit line for the data (a single curve or straight line, whichever fits your data better).

Question 35) Based upon your results and graph, does the pink planet obey Newton's version of Kepler's third law? Discuss your reasons for or against, making sure to reference your graph as evidence supporting your claim.

Answer the question and be sure to attach your graph and data table