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ehild
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It looks good. What did you get for t?
Yes, it was easy to make mistakes, but I got the same results as you at the end. The initial conditions were different. The first method assumed zero initial speed, negative total energy. The second one assumed zero total energy, but that meant nonzero initial speed. As you noticed, the asteroid gains speed very slowly at the beginning. That can cause the difference between the times.Crush1986 said:I get 12.3 years from that. I had 29 years the other way. But the other way was much more mistake prone.
I see. If we made crude approximations that the P.E. at this distance is zero, and assumed the asteroid had zero speed at it's beginning. Method 2 would be ok, right?ehild said:Yes, it was easy to make mistakes, but I got the same results as you at the end. The initial conditions were different. The first method assumed zero initial speed, negative total energy. The second one assumed zero total energy, but that meant nonzero initial speed. As you noticed, the asteroid gains speed very slowly at the beginning. That can cause the difference between the times.
Both methods have sense. The complicated one assumed that the asteroid had zero speed, so its energy was negative. The simple method assumed zero total energy, which meant it got some initial speed towards the Sun.Crush1986 said:I see. If we made crude approximations that the P.E. at this distance is zero, and assumed the asteroid had zero speed at it's beginning. Method 2 would be ok, right?