Stationary point between sun and earth

There is a special point between Sun and Earth where a spacecraft can be parked, so that it always remains directly between them, at a fixed distance \(x\) from Earth, as Earth rotates around the Sun. A spacecraft can remain at this point without using any thrust.

What is the distance \(x\) of this point from the Earth in gigameters? \(\big(1\text{ gigameter}=10^6\text{ km}\big)\)

Details and Assumptions:

  • The masses of the Earth and the Sun have a ratio of \(1: 333,000.\)
  • The distance between the Earth and the Sun is \(a \approx 150 \cdot 10^6 \text{ km}.\)
  • The radii of the Earth and the Sun are negligibly small.
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