2.3 
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Interactive Simulations   Position and displacement in one dimension    Displacement and position in two dimensions    Solve v=dx/dt for dt    Velocity, position, and time (basic version)    Velocity, position, and time (more advanced version)    Acceleration (basic version)    Acceleration (more advanced version)    Static equilibrium    Static equilibrium and the lever    Newton's second law (basic version)    Newton's second law (more advanced version)    Circular motion interactive simulation    Orbits of the planets and dwarf planets    Orbits simulation Interactive Calculators   Speed calculator    Velocity calculator    Acceleration calculator    Velocity in accelerated motion    Average velocity calculator    Hooke's law calculator    Torque calculator    Rotational equilibrium and torque    Newton's second law calculator    Momentum calculator    Angular velocity    Linear velocity and angular velocity    Centripetal acceleration    Centripetal force    Law of universal gravitation calculator
1 - Science of Physics
2 - Forces and Motion      Chapter 2 at a glance      2.1 - Motion      2.2 - Force, momentum, and Newton's laws      2.3 - Circular motion      2.4 - Solving harder physics problems      2.5 - Chapter review3 - Energy Transformations4 - Waves and Sound
5 - Electricity and Magnetism
6 - Light and Optics
7 - The Atom
8 - Linear Motion
9 - Vectors and Forces
10 - Forces
11 - Newton's Laws and Gravitation
12 - Circular Motion and Gravitation
13 - Torque and Static Equilibrium
14 - Momentum and Collisions
15 - Angular momentum
16 - Power and Machines
17 - Harmonic Motion
18 - Waves
19 - Sound
20 - Electricity
21 - Electric and Magnetic Fields
22 - Electromagnetism and Induction
23 - Light and Color
24 - Geometrical Optics
25 - Electromagnetic Radiation
26 - The Properties of Matter
27 - Thermodynamics and Heat Transfer
28 - The Atom
29 - The Quantum Theory
30 - TBD
31 - TBD
32 - TBD
33 - TBD
34 - TBD
35 - TBD
36 - TBD
37 - The atomic nucleus and radioactivity
38 - Nuclear reactions
39 - Relativity
40 - Particle physics and the standard model
41 - Electronics (semiconductors)
42 - Nuclear technology
43 - Lasers and photonics
44 - Metals, alloys and materials science
45 - Communications technology
46 - Buildings and structures
47 - Energy technology
48 - Biophysics
49 - Matter and Energy, Space and Time
50 - Energy Transformations
51 - Nanotechnology
52 - Website Videos
53 - ExtraStuff
55 - Modeling Motion, Friction, and Center of Mass
56 - Work and the Conservation of Energy
2G: Orbits
How does velocity relate to a planet's orbital radius?
How do you send a satellite from Earth to another planet's orbit?
The planets in the Solar System orbit the Sun in ellipses—elongated circles—although many of the planets have nearly-circular orbits. As a planet is placed further from the Sun, it experiences a smaller acceleration due to the Sun's gravity and hence travels with a different orbital velocity. In this investigation you will determine the velocities of different planetary bodies in the Solar System and correlate that with their distance from the Sun.

Doing the Investigation
In this interactive simulation, you will create orbits for the planets, dwarf planets, and other Trans-Neptunian objects (TNOs). When you select a particular planet, its true orbit will be plotted in the simulation. You will adjust the initial orbital velocity—in particular, you are varying the velocity at its closest approach, known as the perihelion velocity vperi—in order to get the best match to its true orbit.
How to use the orbits simulation
  1. In the interactive simulation, select the planet Earth.
  2. Vary the orbital velocity v to find your best match for the Earth's true orbit. Also record the average distance from the Sun (the semi-major axis).
  3. Repeat for the other seven planets.
Analysis
  1. Graph orbital velocity v against distance from the Sun r. Is it a straight line?
  2. Devise a new graph of v against a different quantity derived from r that will be a straight line. Measure its slope (including its units).
Assess Your Knowledge
  1. Does Jupiter move faster or slower than the Earth?
  2. How does orbital velocity vary with distance from the Sun?

Part 2: Transfer orbits
Doing the Investigation
Use the simulation above to do this part.
Transfer orbit from Earth to Mars In order to send a satellite from one planet to another, it is necessary to change the satellite's velocity. These trajectories are called transfer orbits.
  1. Select Earth. Determine the initial velocity necessary to propel a satellite initially from Earth's orbit to just barely reach Mars's orbit.
Assess Your Knowledge
  1. Compare the average velocity for Earth's orbit (from part 1) with the velocity necessary to reach Mars's orbit. How much does it need to change?
  2. What provides this change in velocity of the satellite?
  3. How much “elapsed time” does it take for this satellite to reach Mars? Compare this length of time to typical missions of the Space Shuttle and International Space Station.

Part 3: Dwarf planets and Trans-Neptunian objects
Doing the Investigation
Use the above simulation to do this part.
The Solar System has eight planets and five known dwarf planets—planetary objects that are massive enough to be spherical in shape, but not massive enough to clear their orbits of other small objects. Two other objects, Quaoar and Sedna, are also included in the simulation.
  1. Find the orbital velocities for the remaining seven objects.
Assess Your Knowledge
  1. Is there a similarity in location for all or most of these objects?
  2. Which ones do you think are called Trans-Neptunian objects? Why?
  3. What kind of object is Ceres, based on its location?
  4. Which object has the most unusual orbit? What is the period of its orbit?
Going Further
  1. With the exception of Pluto and Ceres, these TNOs have been discovered since the year 2000. Research and write a one-page essay about who has discovered most of these TNOs and what their method has been to find them.
  2. The International Astronomical Union defined a new category of Solar System object in 2006 called the “dwarf planet.” Research and write a one-page essay either in support or opposition to their decision to reclassify Pluto as a dwarf planet.

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