Steven Hoaglund, a 15 year old male from the Internet asks on May 25, 1999,Galileo said, "in a vacuum, all objects fall at the same speed." Well, I have an idea that might prove him wrong. My idea goes as follows: Take a bowling ball, and a golf ball and drop them off of a high point, say, a cliff. Now, the bowling ball has its own gravity, which may be small, but does exist. And the golf ball has its own gravity as well. And of course, the earth has its own gravity. When you drop the objects at the same time, gravity from the earth is pulling them towards the surface, while at the same time the gravity from the objects are pulling the earth towards them. Theoretically, wouldn't the object with the larger gravity hit the earth first? It may be just a fraction of a second, but wouldn't it hit the surface first? Please respond as my friend and I have had many heated discussions on this topic!
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You are quite right, both the Earth and the bowling/golf ball are falling toward their common centre of gravity, which for the bowling ball is a tiny bit closer to the bowling ball, so it will hit a tiny bit sooner. However I think the difference is short compared to the length of time it takes light to cross a nucleus.
Probably you are also correct in believing that Galileo would not have thought of this correction (although he might have - one of Galileo's strengths lay in his ability to ignore the details to highlight the fundamentals). However, Newton would have certainly recognized this effect immediately.
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