In 1996, the Solar and Heliospheric Observatory (SOHO) was \"parked\" in an orbi

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 force from the sun and the force from the earth combine to give the satellite the same period of revolution as the earth. Calculate SOHO's distance from the earth. (Hint: You will need the binomial approximation. SOHO's distance from earth is very small compared to the earth's distance from the sun.)

Explanation / Answer

This image of the solar corona was acquired on 23 December 1996 by the LASCO instrument on the SOHO spacecraft. It shows the inner streamer belt along the Sun's equator, where the low latitude solar wind originates and is accelerated. Over the polar regions, one sees the polar plumes all the way out to the edge of the field of view. The field of view of this coronagraph encompasses 8.4 million kilometers (5.25 million miles) of the inner heliosphere. The frame was selected to show Comet SOHO-6, one of seven sungrazers discovered so far by LASCO, as its head enters the equatorial solar wind region. It eventually plunged into the Sun. (Courtesy ESA/NASA)

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