- #1
Buffu
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Homework Statement
Question :-
Two stars, each of a solar mass and radius ##10^7 m## are at a distance of ##10^{12} m## from each other. Find the speed of each star before collision if initial speed is negligible.
Homework Equations
$$V(r) = {-G Mm \over r}$$
The Attempt at a Solution
Initial total energy of a star would be $${-G m^2 \over 10^{26}}$$
and final energy would be $${-G m^2 \over 10^{14}} + {1 \over 2 }mv^2$$
use conservation of energy i got
$${-G m^2 \over 10^{26}} = {-G m^2 \over 10^{14}} + {1 \over 2 }mv^2$$
Solving for ##v## i got, ##3.6 \times 10^6 m/s##. But, the given answer is ##2.6 \times 10^6 m/s##.
Now i can get the given answer by solving of ##v## in equation $${-G m^2 \over 10^{26}} = {-G m^2 \over 10^{14}} + mv^2$$
I am not getting the concept that why i should drop the half from equation ? Please help me.