Introduction:

Every physics student has had a lot of experience with the force of gravity.

Unfortunately, this experience is limited to the interaction between a very large object, the

Earth, and much smaller objects that are very close to it. This is a

very limited range of the

possibilities. Software simulations of gravity allow physics students to explore a variety of other

gravitational interactions between objects. These activities are designed to be used with the

JAVA applet My Solar System that ca

n be found on the Physics Education Technology (PhET)

website at the University of Colorado at Boulder.

Procedure

:

Go to the My Solar System simulation on the PhET website and carefully follow the

instructions for each activity. Answer the questions and

record your results before going on to

the next activity. The simulation can be found at this URL:

http://phet.colorado.edu/sims/my

-

solar

-

system/my

-

solar

-

system.swf

Activity

A:

Look over the start screen. The simulations controls and settings are on the right and

simulation inputs are at the bottom. Click on Start to see the outputs in the center and lower

right. The paths of the objects in the simulation are displayed alon

g with elapsed time. Click

Stop and move the cursor over each object. Its current position and velocity are displayed

under the time.

Click the Show Grid box and make sure that System Centered and Show Traces are checked too.

Drag the slider bar all the w

ay to the left for the most accuracy. Click Reset, then change Body

1s mass to 500 and its and

position and velocity to 0. Change Body 2s mass to 30, its

position to 200, and position and

and

velocity to zero. Reset must always be clicked

before changing position and velocity of the current simulation. Write down your prediction for

the motion of both Bodies below before clicking Start to find out.

Body 1 (Yellow) motion:

Body 2 (Purple) motion:

1.

Were your predictions correct? How many d

istance units does one square of the grid

represent? Click and drag on the lower right corner of the window to make it 10 grids wide.

2.

Change Body 2s mass to 0.001. Click Start again. What is different about the result? Why

do you think this is?

3.

What sh

ould be the direction of Body 2s initial velocity so that it doesnt ever hit Body 1?

Project

Caliper

Gravity Simulations

Page

2

4.

Increase Body 2s

velocity by increments of 10 until it doesnt touch Body 1. At what

velocity does this first happen? What is the shape of the resulting orbit? Descr

ibe Body 2s

speed near Body 1 and when it is far from Body 1.

5.

Continue to increase Body 2s velocity until the orbit has a circular shape. Using the grid,

adjust it by increments of 1 until it is as close to a perfect circle as you can get. What

velocity

resulted in a circle? Is the speed of Body 2 constant? Stop it as it crosses the grid on

the opposite side and place the cursor over it to verify.

6.

Is the velocity of Body 2 constant? Explain.

Activity B:

Draw a free

-

body diagram of Body 2 in its circular orbit below. Using Newtons Second

Law, the Law of Gravity, and the equation for centripetal acceleration, derive an expression for

the Universal Gravitational Constant,

. Using the values from the simul

ation, solve for the

value of

used in the simulation. Show ALL of your work below. Verify your result with your

instructor before going on.

=

7.

Use your equation from above to derive an equation for the speed of an object in a circular

orbit. Using this equation and your value for

, solve for the speed required for a third body

to be in a circular orbit with a radius of 100. Show all of your wor

k and your final answer

below.

8.

Click Reset and change the

velocity of Body 2 to 250. What happens to Body 2? Why?

What shape is its trajectory?

9.

Using conservation of energy and the fact that a body moving at escape velocity has zero

kinetic energy f

ar from the other mass, find the escape velocity from a given mass at a given

radius, starting at rest. What would the escape velocity be for Body 2 using the value of

found in Q6

?