Artificial Satellites (page 2)

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

   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. Artificial satellites that stay above one place on Earth as they orbit are called geosynchronous satellites. These satellites orbit above Earth at an altitude (height above a surface) 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 (force of attraction between all objects in the universe) 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's 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 Part II, Chapter 4, "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's Astronomy Today (New York: Random House, 1995), pp. 20–21.

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