Gravity and Orbital Motion
Name ______________
1) You will be using a large sheet of stretchy fabric to form a gravity well. The fabric can be pulled down
in the center by a large weight or by a person pulling underneath. Your challenge is to roll a ball on the
fabric so that it orbits as many times as possible. You may not move the fabric to keep it going.
a) Predict and Explain: How can you get the ball to orbit many times?
b) Observe and Explain: What else did you need to do to get the ball to orbit many times?
2) How does the radius of an orbit affect the period of the orbit?
a) What did you notice with the fabric?
b) What do you notice about the planets in the data below?
Orbital radius
Orbital period
9
Mercury
58 x 10 m
88 days
Venus
108 x 109 m
225 days
Earth
149 x 109 m
365 days
9
Mars
228 x 10 m
688 days
3) How does mass affect the orbital period of the orbit?
a) What did you notice with the fabric? Which mass affected the period the most - the mass of the
orbiting ball or the ‘mass’ pulling down in the centre? Try rolling two balls at a time.
b) Which data below shows that the period of the orbit is not affected by the mass of the orbiting object?
(Hint: Choose two orbits with almost the same radius but very different orbiting objects.)
c) Which two orbits show that the period of the orbit is affected by the central mass?
Jupiter’s Four Largest Moons
Orbital radius
Io
0.422 x 109 m
Europa
0.671 x 109 m
Ganeymede
1.07 x 109 m
Callisto
1.883 x 109 m
Orbital Period
1.769 days
3.551 days
7.154 days
16.689 days
Earth’s Artificial Satellites and the Moon
Orbital radius
Space Station
0.0067 x 109 m
Weather satellite
0.0072 x 109 m
Geostationary satellite 0.0421 x 109 m
Moon
0.38
x 109 m
Orbital Period
0.0632 days (91 minutes)
0.0701 days (101 minutes)
1 day
27.3 days
4) You and a group of students are going to act out the motion of the planets around the Sun. Make the
motion as accurate as you can. In what direction do the planets move? How do their speeds compare?
5) The mass of Earth, Jupiter and the Sun are 5.98 x 1024 kg, 1.90 x 1027 kg and 1.99 x 1030 kg. Your
parents wonder how astronomers can find the mass of an astronomical object. Explain it to them.
6) Your grandparents are wondering why the moon doesn’t fall down. Explain it to them.
Answers and extra information for teachers
The activities allow the students to explore orbital motion with as many different learning styles as possible.
In a senior physics class you can also add mathematical problem solving.
1) The fabric that works best is stretchy in all directions and is fairly thick. It can be found at any large
fabric store and may be called swimwear or active wear or four-way stretch. You need a piece that is as
large as possible and as wide as it is long. It will cost from $10 to $20 dollars depending on the quality.
Attach a small marble in the centre to provide grip.
Be sure to have the students predict and explain and write their ideas down before having them explore.
This encourages the building of strong mental models instead of random playing.
The students may take a while to be successful. Give them time to work it out as a cooperative group
investigation. Eventually they will realize that the ball needs to be launched sideways and at just the
right speed. To work well, you need to hold the edges level and the fabric taut. The student pulling down
should form as deep a well as possible to maximize potential energy available. The orbiting ball should
be dense – to reduce the effects of air resistance – and light enough that it doesn’t deform the fabric
much as it orbits.
2) It should be very clear, that the smaller radii have shorter periods. The can also be seen with the
planetary data and further down with the satellite data – as long as you stay within one system.
Something however, changes from system to system and that is the focus of the next questions.
3) They should be able to notice that the mass of the orbiting ball doesn`t matter - much. A glass marble
and a small super ball can have the same orbits even though one has ten times the mass of the others.
You can demonstrate this by launching the two balls at the same time.
The space station is much more massive than a weather satellite, but their radii and periods are about the
same. The mass of the orbiting body doesn’t matter. This is similar to how objects fall at the same rate.
Our moon has an orbital radius similar to Jupiter`s Io, but a much greater period. The difference in
period is caused by the difference in mass of the central body.
4) This exercise has the students apply their understanding of how mass and radius affect orbital period.
The benefit of a role playing exercise is in the discussions between students before the performance
rather than the performance itself. The orbits nearer the Earth should have shorter periods than those
farther away. The orbits should be circular – they are only very slightly elliptical – and in the same
direction. You might also want to supplement these activities with a computer simulation of orbital
motion. Two very good ones are provided by Physics Education Technology (PhET).
http://phet.colorado.edu/en/simulation/gravity-and-orbits is of objects orbiting Earth and
http://phet.colorado.edu/en/simulation/my-solar-system is of objects orbiting the Sun.
5) Astronomers measure the radius and period of the orbit of satellites and use a formula to calculate the
mass. Senior physics students should be able to develop the formula from Newton’s law of gravity and a
formula for circular motion to get M = sqrt (4 r3/GT2), where r is the radius, T is the time for one orbit
and G is the universal gravitational constant 6.67 x 10-11 N m2/kg2.
6) This is a hard concept to explain clearly and concisely. You might have them look at this one-minute
video exploring the same question.
http://www.perimeterinstitute.ca/Outreach/Alice_and_Bob_in_Wonderland/Alice_and_Bob_in_Wonderland/