- #1
matpo39
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I am having a little trouble with this problem it is as follows:
consider the tidal force #(F_tid=-G*M*m[(d_unit vector/d^2)-(d_0 unit vector/d_0^2)]) on a mass m at the position P. write d as (d_0-R(radius of earth))=d_0*(1-R/d_0) and use binomial approximation to show that F_tid= -(2*G*M*m*R/d_0^3)x_unit vector.
sorry i can't get the picture up but all it is is the Earth with center at (0,0) and point P is located all the way to the left edge of the Earth on the x-axis and and 0 on the y axis. the moon is to the left of the Earth and is also on the x axis. which is why it is easy to see that the force will be in the -x direction.
first i used the binomial expansion and got d_0(1+2*R/d_0) and i replaced d in equation # with that value anf got this
-G*M*m[d_unit vector/(d_0(1+2R/d_0))^2 - d_0_unit vector/(d_0^2)]
I have been fiddleing with it all day and can't get it to match the force they said it should, I am pretty sure that my problem is coming from not really knowing how to handle the d,d_0 unit vectors.
thanks for the help
consider the tidal force #(F_tid=-G*M*m[(d_unit vector/d^2)-(d_0 unit vector/d_0^2)]) on a mass m at the position P. write d as (d_0-R(radius of earth))=d_0*(1-R/d_0) and use binomial approximation to show that F_tid= -(2*G*M*m*R/d_0^3)x_unit vector.
sorry i can't get the picture up but all it is is the Earth with center at (0,0) and point P is located all the way to the left edge of the Earth on the x-axis and and 0 on the y axis. the moon is to the left of the Earth and is also on the x axis. which is why it is easy to see that the force will be in the -x direction.
first i used the binomial expansion and got d_0(1+2*R/d_0) and i replaced d in equation # with that value anf got this
-G*M*m[d_unit vector/(d_0(1+2R/d_0))^2 - d_0_unit vector/(d_0^2)]
I have been fiddleing with it all day and can't get it to match the force they said it should, I am pretty sure that my problem is coming from not really knowing how to handle the d,d_0 unit vectors.
thanks for the help