In 1969, the Solar and Heliospheric Observatory (SOHO) was \"parked\" in an orbi
ID: 1700681 • Letter: I
Question
In 1969, the Solar and Heliospheric Observatory (SOHO) was "parked" in an orbit slighlty inside earth's orbit, as shown in Figure CP12.72. The Satelite's period in this orbit is exactly one year, so it remains fixed relative to the earth. At this point, called Lagrange point, the light from the sun is never blocked by the earth, yet the satelite remains "nearby" so that data are easily transmitted to earth. What is SOHO's distance from earth?
Hint: Use R_e = 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 m_sun, m_earth, R_e, and d
Explanation / Answer
we have that. mw*2*r=GMm/r^2. w^2r^3=GM -------- so the sun earth system we have. w1^2*r_e^3=GM_sun. w2^2*d^3=GM_earth. because w1=w2. so r_e^3/d^3=M_sun/M_earth. do d=r_e*(M_earth/M_sun)^1/3