While the Earth is traveling in orbit around the sun at a speed and the solar system is traveling at a speed inside the galaxy as our galaxy travels at a speed toward other places, then how can we be sure how fast we are going and how does this effect how we measure the speeds of things?
Relativity. Simply put the only way we can tell the speed of any object in constant motion is by comparing it to something else. How fast we are moving is dependent on where we measure it from. Say a truck is traveling at you at 30 mph, the driver of the car would see you going towards him at 30 mph because relative to him, he isn't moving anywhere; things are just flying past him. Nor you or the truck driver would agree on the speed you two were traveling but you both are equally right. So to answer your question, we can be sure how fast we are moving relative to some other object like the floor, or the earth or a truck by dividing the distance traveled over the time elapsed but there is no final universal answer to your speed because as I've stated, everything is relative.
thank you , I liked the anlogy of the truck funny thing is I was going to just use the truck analogy instead of the galaxy, my son asked me the question about a truck driving on a train that was moving moving the same direction as the truck at a certain speed and of course the train some how was on a fast moving bridge while there was a hypothetical man closed in the back of the semitrucks trailor boasting that he could throw his ball at 50mph and no one was there to explain it to the hypothetical man that his ball was going much faster. thanks for a good answer.
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