If you haven’t started the simulation already click here to start the simulation.
Then answer the questions below. Please insert your answers to each question in the gray boxes immediately after the question to make it clear to the grader which question you are answering.
I After the simulation loads click Start.
Describe what you see in this simple sun-planet system.
Specifically, what happens to the central object (the Sun)?
The sun begins to move
Can you explain why the central object moves?
HINT: Is gravitational attraction only the star pulling on the planet?
Gravitational forces between it and the planet are pulling it.
Does the planet orbit in a perfect circle? Is the sun at the center?
It orbits in an elliptical and the sun is off to the side.
Why don’t the objects move in a straight line as described in Newton’s first law?
II Make it so
Set the “Position x” of body 2 to be a value between 30 and 300 and move the “Accurate/Fast” bar to the far left. Through trial and error experimentation, determine the minimum initial speed (Velocity y) that will allow body 2 to get around the sun (rather than crashing into it). You must click the reset button to change the velocity each time. Record that minimum speed and the position you chose in the box below. minimum speed = position =
Click reset and then set the “Position x” of body 2 to a value between 30 and 300 (your choice!). This will be the radius r, of your circular orbit. Through trial and error experimentation, determine the initial speed (Velocity y) that will allow the planet to sustain a circular orbit at your chosen r. You will find the tape measure useful here. Place the tape measure at the starting point of the planet. Now click the “free” end of the tape and stretch it horizontally through the sun so that the end of the tape is 2r from planet. So if your given radius were 75, the far end of the tape would be 150 to the left of the launch point. If the launched planet passes through the end of the tape, the orbit is circular. Record the given radius you chose and the correct speed you discovered. radius = speed for circular orbit =
Now, compare your data to Newton’s law of universal gravitation in the form of Kepler’s third law. A quick remind is in order. Recall that Newton’s law of universal gravitation is:
Force=G (m〖∙m〗_1)/r^2
And that for objects traveling in a circle, Force=(m_1 v^2)/r (this is size of centripetal force keeping planets, stars, or galaxies from moving in a straight line as described by Newton). Because the gravitational force is the centripetal force in this case we can set the two equations equal to each other:
G (m〖∙m〗_1)/r^2 =(m_1 v^2)/r
Now cancel the common terms, m1 and one of the r’s:
G m/r=v^2 and multiply both sides by r and divide by m:
G=〖r∙v〗^2/m
Take your values for r, v, and m (of body 1 – actually the sum of the two masses is more correct) and calculate G and place your value in the box below. Note this value is very different from the one given in your book – the programmers decided to use their own units!
G =
III Click Stop and then select 3 bodies. Then Start
Follow a complete cycle (orbit)
Watch the new object closely
What is it doing? Describe and explain.
The moon begins to orbit the planet that is orbiting the sun.
Could this be the Earth/Moon/Sun system? (Try unchecking Show Traces.) yes Explain what you think is the difference in the moon’s path when it is on the right side of the Sun compared to on the left side? (Turn Traces back on.)
The end points curve more on the right due to the speed of the planet increasing when it is closer to the sun.
IV Click Stop and then select 2 bodies again. Change the mass of the ‘planet’ to 100 units and then Start. Explain how the motion is different from Part I. Ever hear of a binary star?
Repeat with both bodies at 200 units of mass.
V Click Stop and then select 3 bodies again. Change the masses of bodies 2 and 3 to 5 units each and Start. Watch for several orbits and explain what’s happening.
VI Describe what you’ve seen here in terms of Newton’s law of universal gravitation.
Submit this document with your answers on BlackBoard.
