Day 4.2: Orbital Dynamics
1) Watch http://perimeterinstitute.ca/videos/alice-and-bob-wonderland-why-doesnt-moon-fall-down
The moon is moving very fast sideways. Gravity bends the velocity down and the direction of down
keeps changing so that it keeps falling down and never hitting.
If gravity were to suddenly disappear, then the Earth would
A) fall toward the sun B) fall away from the sun C) spiral into the sun D) something else
If there is no gravity, then there is no force and it will just keep moving in the same direction.
Instructions: Use the spacetime fabric or a ball on a string to demonstrate the effect gravity
disappearing. This is not easy to do, but worth the effort. It may seem like we are repeating the same
point, but misconceptions about circular motion are very deep seated.
Use the data below to answer the next four questions.
2) If the radius of orbit is larger, then the period is
a) larger
b) smaller
c) the same.
Compare any two bodies in the same system
3) If the mass of the orbiting body is larger, then the period of orbit is
a) larger
b) smaller
c) the same
Compare __ISS_____ and ___HST___
4) If the mass of the central body is larger, then the period of orbit is
a) larger
b) smaller
c) the same
Compare ___Moon ____ and ____Io
5) If the radius is doubled, then the period is
a) doubled b) tripled
c) quadrupled d) something else
Radius is roughly doubled but period is tripled.
Orbital Radius (x108 m)
579
1080
1490
2280
Planet
Mercury
Venus
Earth
Mars
Satellites of the Earth
ISS
Hubble Space Telescope
GPS Satellite
Moon
Moons of Jupiter
Io
Europa
Ganymede
Callisto
Mass (kg)
4.17x105
1.11x104
2.37x103
7.35x1022
Mass (x1022 kg)
8.93
4.80
14.8
10.8
Compare .Venus and Mars.
Orbital Period (days)
88
225
365
688
Orbital Radius (x108 m)
0.0673
0.0694
0.266
3.84
Orbital Radius (x108 m)
4.22
6.71
10.7
18.8
Orbital Period (days)
0.063
0.067
0.5
27.3
Orbital Period (days)
1.77
3.55
7.15
16.7
6) Use Newton`s universal law of gravity, his second law of motion and one of his laws of circular
acceleration to create formulas to explain the answers for questions 4 - 7 above.
G M m/r2 = m 4 r/T2
#3) The mass of the orbiting body, m, cancels out.
#4) The mass of the central body is given by M = 4 r3/GT2, bigger mass – smaller period.
#2, #5 The period is given by sqrt (4 r3/GM). So in the above questions when radius is double, period
should be root 2 cubed or 2.8 which is very close to 3.
7) Calculate the mass of one of the central bodies above.
The mass of the central body is given by M = 4 r3/GT2
8) Go to PhET http://phet.colorado.edu/sims/my-solar-system/my-solar-system_en.html
a) Run the standard settings. Double the mass of the smaller mass. What will happen?
Very little happens as we would expect from above, but you do see the larger mass wobble more.
b) Reset to Sun and planet and then double the larger mass. What will happen?
The period is shorter as expected. It is also no longer round. You can make it round by lengthening
the initial velocity vector by root two.
c) Reset to sun and planet and halve the radius. What will happen?
The force is now four times stronger and the period will be smaller. It won`t be as circular. You can
make it circular if you also increase the speed.
d) Select the sun, planet and moon. What will the moon`s orbit look like?
9) Galileo said that the Earth orbited the Sun. The Catholic Church made him recant and say that the Sun
orbits the Earth. What is the truth?
The Earth and sun orbit their common centre of mass which orbits the centre of the Milky Way galaxy
which orbits ..
10) You can easily see the ISS if you look at the right time. http://iss.astroviewer.net/observation.php We
must be in darkness but the ISS must be in light. At what angular speed will you see it move? Why do
we only see it for a few minutes?
The period is 0.063 days = 91 minutes. It covers 360 degrees in 91 minutes or about 4 degrees/minute.
We never see it for more than seven minutes according to the site. So we see less than 30 or 1/12th of an
orbit. This is because the orbit is so close to the Earth.
Textbook: 3.4
p. 147 # 1, 2, 6
p. 151 # 4, 5, 8