Orbital Motion of Satellites 13'1

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Orbital Motion of Satellites (13.1)

• Satellites move in circular (or more generally,
  elliptical) orbits
• Compute their period and speed by applying
  Newtons 2nd Law in the radial direction

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m
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M
Orbital speed
Orbital period
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Example
Venus rotates slowly about its axis, the period
being 243 days. The mass of Venus is 4.87 x 1024
kg. Determine the radius for a synchronous
satellite in orbit about Venus. Solution Given
MV 4.87 x1024 kg, TV 243 days Recognize
Synchronous means that the period of the
satellite equals the period of Venus,
TsTV Convert TV to seconds and find rs
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Compare this to the radius of Venus 6.05x106 m
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Section 13.4 Keplers Laws of Orbital Motion

• 1st Law - planets follow elliptical orbits with
  the Sun at one focus of the ellipse
• 2nd Law - the radius vector from the Sun to the
  planet sweeps out equal areas in equal time
• 3rd Law - the orbital period of a planet is
  proportional to the radius to the 3/2 power
  (derived for circular orbit just replace r by a)

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Example Problem 13.47

• The Solar and Heliospheric Observatory (SOHO)
  spacecraft has a special orbit such that it
  always has a view of the Sun, but is close to the
  Earth. It moves in a nearly-circular orbit around
  the Sun that is smaller than the Earths orbit.
  Its period is equal to 1 year! It is always
  located between the Sun and the Earth along a
  line joining them. Show that SOHOs distance from
  the Earth is between 1.47x109 m and 1.48x109 m.
  MS 1.991x1030 kg, ME 5.983x1024 kg, and rE
  1.496x1011 m.

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SOHO was launched Feb. 14, 1996.
See http//sohowww.nascom.nasa.gov/