# SOHO spacecraft problem

1. Nov 16, 2005

### Kenny Lee

Anyone of you heard of this problem before? Its from my textbook (serway & Jewett), pg. 417, if anyone you got it, then probably easier to look it up there.
The question asks: what is the satellite orbit's distance from the earth, if it is always on the line connecting the sun and the earth; and has exactly a time period of one year (same as the earth).
Question concerns the SOHO spacecraft, which acts as an observatory for the sun.
Could someone please check if my approach is right?
So I said:
• fixed distance of x from earth
• period of one year
• consider the gravitational pull of earth as well
So I set up a simple centripetal force equation for the spacecraft: mv^2/(Re - x), expressing v in terms of its time period (which we know).
Then I said that since the spacecraft is always on the line connecting earth and sun, the resultant centripetal force is given by the difference of the sun's pull and the earth's pull. I put this in an equation and tried to solve.
I can't solve the equation so I don't know if its right.
The answer is around 1.47 X 10^9, and it says to use the earth mass value of 5.983 X 10^24.