In 1996, the Solar and Heliospheric Observatory (SOHO) was \"parked\" in an orbi
ID: 2244781 • Letter: I
Question
In 1996, the Solar and Heliospheric Observatory (SOHO) was "parked" in an orbit slightly inside the earth's orbit. The satellite's period in this orbit is exactly one year, so it remains fixed relative to the earth. At this point, called a Lagrange point, the light from the sun is never blocked by the earth, yet the satellite remains "nearby" so that data are easily transmitted to earth. What is SOHO's distance from the earth.
Use Re = sun to earth distance, r = sun to SOHO, d = SOHO to earth. Use Newton's second law for circular motion. Obtain a single equation with msun, mearth, Re, and d only. Yes, you can eliminate r, G, v, and T if you work hard enough. Use a binomial expansion, a solver, or guess and check to find d. Explain why this cannot be solved analytically without the binomial expansion
Explanation / Answer
Let f = the fraction of the distance from the earth to the sun of the Lagrange point.Equating the 2 gravitational forces ?
(1 - Ms/Me)*f
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