The Sun is 3.33 × 10⁵ times as heavy as the Earth, and their centres are 1.5 × 10¹¹ m apart.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The Sun is times as heavy as the Earth, and their centres are apart. At what distance from the Earth, on the line between them, is the net gravitational force on a small body zero?
Need a reminder? The key ideaShow
Newton's law of gravitation: , with and between the centres. The pulls on the two bodies are equal and opposite; for several bodies they add as vectors.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Set the two pulls equal; the body's mass cancels.
Step 1. , so .
Step 2. .
Answer: About from the Earth, closer than the Moon.
Check. The point lies near the far lighter body, as it must for the pulls to match.
Watch out. Take the square root of the mass ratio: the pulls fall as distance squared.
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