My Solar System Lab

Physics

HS/Science

Unit: 05 Lesson: 01

My Solar System Lab

Introduction:

Every physics student has had experience with the force of gravity. For most, 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 possibilities. Software simulations of gravity allow physics students to explore a variety of other gravitational interactions between objects. This lab utilizes the simulation “My Solar System” developed by the Physics Education Technology (PhET) group at the University of Colorado at Boulder. The URL is: http://phet.colorado.edu/sims/my-solar-system/my-solar-system.swf.

This simulation does not use conventional units for distance, velocity, or G (the universal gravitational constant), but is realistic in the behavior of gravity. In this simulation, the value of G can be taken to be 10,000, and the units should be disregarded in calculations. For familiarity, we will refer to the force unit as a Newton and the time units in seconds, but the units of the simulation do not justify this convention.

Procedure:

Go to the “My Solar System” simulation on the PhET website, and carefully follow the instructions below for each activity. Answer the questions, and record your results before going on to the next activity.

Activity 1: Get familiar with the simulation

Look over the start screen. The simulation controls and settings are on the right, and the 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 simulation are displayed along with elapsed time.

· Click Stop, and move the cursor over each object. Its current position and velocity are displayed under the time display.

· With the trace and grid displayed, determine the grid distance, satellite velocity, time for one period, and the radius of the orbit.

Distance for grid block ______units

Time for one period ______s

Radius of orbit ______units

Speed of orbiting object ______units

Activity 2: Free Fall Observations

· Click Reset, and then move the Sun to -200 units and planet to +200 units. Set the speed of the planet to zero.

· Find the time for the planet to fall to the Sun and final location of the Sun after the collision. (Remember, you place the hand on the Sun, and its values appear under the time.) M = 200,

m = 10

Time for fall ______s

Location of combined mass ______units

Comment on the movement of the larger mass ______

· Change the mass of the Sun to 2000, and determine the values again. M = 2000, m = 10

Time for fall ______s

Location of combined mass ______units

Comment on the movement of the larger mass______

· Change the mass of the Sun to 2000 and the mass of the planet to .001. Run again. M = 2000, m = .001

Time for fall ______s

Location of combined mass ______units

Summarize how the smaller mass accelerates toward the larger mass depending upon the two masses involved. Include the movement of the larger mass.

Activity 3: Types of Orbits

· Reset the simulation to the original situation by selecting the preset 2-body simulation.

· Set the velocity of the planet to zero, and observe its fall into the Sun. Reset and increase its speed until it misses the Sun. This is an elliptical orbit.

Value of lowest speed producing an elliptical orbit ______units

· Set the velocity of the planet to 50, and give the time for a complete orbit ______s.

· Comment on the speed of the planet as it gets nearer and farther away from the Sun:

· Set the velocity of the planet to 100. Describe this orbit:

Activity 4: Circular Orbits and the Mass of the Planet

While the original setup for two bodies presents a nearly circular orbit for the planet, a close examination of the orbit parameters with the tape measure will verify that it is slightly elliptical. In addition, the relatively equal masses create a significant wobble in the Sun-like inner body. In this portion of the lab, we want to minimize the wobble and get orbits as circular as possible within the limits of the simulation- two significant figure calculations.

· Reset the simulation to the original situation by selecting the preset 2-body simulation.

· Change the mass of the orbiting planet to 0.1, and set the velocity to 116. Verify that the orbit is very close to circular using the tape measure. Find the time for one rotation.

Period for one orbit = ______s with mass of 0.1 units

· Change the mass of the orbiting planet to .001mass units, and find the period.

Period for one orbit = ______s with mass of 0.001units

· Kepler’s laws predict that the period depends only on the mass of the Sun and satellite distance.

Do you agree?______(yes/no)

Activity 5: Orbital Radius and Velocity Correlation

Kepler’s laws indicate that a lower orbit (smaller radius) satellite will move faster and have a smaller period. Newton’s gravity law indicates that the inner planets will have larger gravity acceleration and, thus, a larger centripetal acceleration. The purpose of this activity is to check out these ideas using the simulation. The masses of the orbiting planets are set to be very small, so that they do not influence each other to any significant degree. The orbiting masses will be 0.001, and the Sun’s mass will be held at 200 units.

· Reset the simulation to three bodies, and alter the radii and speeds in the following manner.

o Set the inner planet radius to 75 units and its speed to 164 units. Set the mass to 0.001.

o Set the outer planet radius to 150 units and its speed to 116 units. Set the mass to 0.001.

· Verify that both planets travel in circular orbits, and measure the periods of revolution for each.

Period for inner planet = ______s

Period for outer planet = ______s

Do you agree with Kepler that the inner planets move faster and take less time to orbit? ______(yes/no)

· Newton’s laws give an equation for the gravitational acceleration as g = GM/r2, where M is the mass of the inner body and r is the radius of the orbit. Newton also gave an expression for the centripetal acceleration as ac = v2/r for objects moving in circular orbits. Since gravity is the source of the centripetal acceleration, these two numbers should be the same. In the spaces below, calculate the values of the gravitational acceleration and centripetal acceleration for the two planets. Recall that the value of G for this simulation is G=10,000 units and that value should be used in the calculations.

Activity 6: View of Planetary Orbits from Different Locations

Early astronomers viewed the motions of the heavens from the Earth and thought that it was the center of the universe. The motion of the planets was complicated with planets, sometimes moving in one direction and then looping back on the path. This is known as retrograde motion. From the perspective of the Sun, this apparent motion is a result of planets moving at different rates and sometimes passing each other. In this activity, the motion of the Moon is viewed from the Sun’s perspective.

· Reset the motion, select the preset Sun, planet, and Moon simulation, and play it. Observe the path of the Moon, and imagine its path as viewed from the Earth. Describe the motion of the Moon from both perspectives.

Activity 7: Interaction of Satellites – Slingshot and other** (as time permits)

In sending a probe to Saturn, it was necessary to slingshot the probe off planets to gain energy. View the preselected simulation Slingshot. As time permits, view other simulations and try to imagine what is happening.