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The Sun's mass is 2.0 × 10³⁰ kg and the Earth's is 6.0 × 10²⁴ kg…
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's mass is and the Earth's is . Their centres are apart. How far from the Sun's centre is their centre of mass? The Sun's radius is : is the point inside the Sun?
Need a reminder? The key ideaShow
The centre of mass is the mass-weighted average position: , and the same for and . For a continuous body, . A hole can be treated as a negative mass.
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. Origin at the Sun, so only the Earth's term survives.
Step 1. .
Answer: About from the Sun's centre, deep inside the Sun.
Check. is tiny next to the Sun's radius, . The Earth barely makes the Sun wobble.
Watch out. The Earth's mass is so small that adding it to the Sun's in the bottom changes nothing you can see.
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