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.
Part 1: Orbital velocities of the planets

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.
  1. Does Jupiter move faster or slower than the Earth?
  2. How does orbital velocity vary with distance from the Sun?
  3. Graph orbital velocity v against distance from the Sun r. Is it a straight line?
  4. 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). Show Shapes of different orbits
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. Show Astronomical units
Part 2: Transfer orbits

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.
  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.


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