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Lauching of Artificial Satellites into Orbit and Measuring their Angular Velocity

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Author: Janice VanCleave

A natural satellite is a celestial body that orbits another, such as the Moon, which orbits Earth. An artificial satellite is a man-made object that orbits Earth. Artificial satellites are raised to a desired height above Earth and launched by rockets parallel to Earth's surface. This forward velocity and the force of gravity keep the satellite in otbit around Earth.

In this project, you will learn about launching speed and its effect on a man-made satellite's orbit. You will discover the best times to see satellites and how to measure their angular velocity. You will also find out why satellites are launched in different directions.

Getting Started

Purpose: To model how a satellite is launched into orbit.

Materials

  • 2 equal-size books, each about 10 inches (25 cm) long
  • index card
  • transparent tape
  • 3 rulers—2 must be identical and have a groove down the center
  • walnut-size piece of modeling clay
  • bath towel
  • marble

Procedure

  1. Lay the books end to end on a table.
  2. Lay the index card on the end of the books farther from the edge of the table.
  3. Tape the grooved rulers together end to end. Tape only on the ungrooved side. This is your launcher.
  4. Lay the launcher on the books so that one end is on the index card. Raise that end 2 inches (5 cm) above the book. Put the clay under the end for support Let the other end of the launcher extend over the end of the books.
  5. Adjust the books so that the extended end of the launcher is 4 inches (10 cm) from the edge of the table.
  6. Lay the towel on the floor near the edge of the table. The towel will help stop the marble when it hits the floor.
  7. Position the marble on the raised end of the launcher, then release it (see Figure 30.1). The marble should land on the towel.
  8. Observe the path of the marble after it leaves the launcher.

Artificial Satellites: Man-made Orbiters

Results

The marble's path curves after it leaves the launcher.

Why?

In this model, the table represents Earth. The top of the books is a position above Earth's surface where the "marble satellite" is launched horizontally, parallel to Earth's surface. After it separates from its launcher, the satellite moves in a curved path. The curve results from the satellite's forward horizontal velocity (speed in a specific direction) and the downward pull of gravity. A real satellite would continue in a curved path and return to its launching point.

Try New Approaches

If the horizontal velocity of the marble satellite is great enough, the gravity pulls it into a curved path past the edge of the table. Demonstrate the effect of different horizontal velocities on the path of the satellite by repeating the experiment, raising the end of the launcher to different heights.

Design Your Own Experiment

  1.  
    1. Earth's surface curves away from a line tangent (touching at a single point) to its surface at a rate of 33/50 miles (4.9 km) for every 5 miles (8 km). So, near Earth's surface, an object traveling at 5 miles (8 km) per second would maintain its altitude and move in a circular path around Earth. Draw a diagram to represent the effect of launching speeds greater than, less than, and equal to 5 miles (8 km) per second.
    2. A satellite's horizontal speed depends on its distance above Earth, which affects the strength of gravity acting on the satellite. The gravity at a certain distance from the center of Earth can be calculated by using this equation:
        g1/g2= r22/r12
    3. where g1 = 9.8 m/s2, gravity at distance equal to the radius of earth (at surface)

        r1 = 12,757 Km, radius of Earth
        g2 = gravity at distance r2
        r2 = distance from center of Earth to satellite's orbit

      The least velocity a satellite must have to orbit Earth is determined by this equation:

      where V = the velocity of the satellite

        g = the acceleration of gravity at distance r from the center of Earth
        r = the average radius of the satellite's orbit from the center of Earth

      Satellites that stay above one place on Earth as they orbit are called geosynchronous statellites. These satellites orbit at an altitude of 22,300 miles (13,938 km). Use these formulas to determine the velocity of a geosynchronous satellite and the gravity acting on it. Science Fair Hint: Prepare a diagram showing satellites at different distances from Earth's surfaces, the calculations used to determine their velocity, and the gravity acting on them. For more information, look up satellite velocity in a physics text.

  2. Satellites look like slow-moving stars. Those in orbits at an altitude of 300 miles (480 km) or less are visible to the naked eye. Determine when satellites are most visible. Observe satellites at different times of the night and during different seasons. For more information on satellite motion, see Terence Dickinson, Night Watch (Willowdale, Ontario: Firefly Books, 1999), p. 35.
  3. Determine the angular velocity (angular displacement per unit time of an object moving in a curved path) of satellites by measuring the angular distance traveled during a measured amount of time. Find out which satellites are visible on a certain date from sources such as Sky and Telescope magazine or from web sites such as www.skyandtelescope.com. (See Chapter 2, "Angular Separation" for information about measuring angular distance.)

Get the Facts

Most satellites are launched from west to east, but some are launched to orbit Earth from pole to pole. Why is a launch into a polar orbit more difficult? What are satellites used for? For information, see Dinah Moche, Astronomy Today (New York: Random House, 1995), pp. 20–21.

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