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Rearranging of formulas

  • Thread starter dukg08
  • Start date
  • #1
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Homework Statement



(i)
Combine Equations A and B to give a single equation for v and substitute this in place of v in Equation C.
(ii)
Rearrange your answer to part (i) to make r the subject of the equation.


Homework Equations



Equation A
z = Δλ/λ0

Equation B
v = zc

For a planet such as the one orbiting Gliese, the speed v is linked to the mass of the star M and the planet’s orbital radius, by Equation C:

Equation C
v2 = GM/r

G is Newton’s universal constant of gravitation.

The Attempt at a Solution



(i) v = (Δλ/λ0)c -> (Δλ/λ0)c2 = GM/r
(ii) this is where I'm not sure, is the above correct? I always get roots confused.
 
Last edited:

Answers and Replies

  • #2
Ouabache
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Are you sure about your result for [itex]v^2[/itex] in equ. (i)?
It looks like you only squared part of your expression for [itex]v[/itex].
 
  • #3
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((Δλ/λ0)c)2 = GM/r
 
  • #4
Ouabache
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That looks good to me, now they ask you to rearrange your expression
to make r the subject of the equation. Shall we interpret this to mean solving for r ?
 
Last edited:
  • #5
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((Δλ/λ0)c)2 = GM/r

So do I multiply the r to both sides now or remove the root?

(Δλ/λ0)c = √(GM/r) or ((Δλ/λ0)c)2/r = GM
 
Last edited:
  • #6
Ouabache
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what are you solving for? that will help you decide which direction to take.
 
  • #7
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I'm trying to make r the subject.

((Δλ/λ0)c)2/r = GM

r = ((Δλ/λ0)c)2xGM
 
  • #8
Ouabache
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Your algebra doesn't look quite right.
To this expression: ((Δλ/λ0)c)2 = GM/r

are you sure you multiplied both sides by r ??
 
  • #9
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((Δλ/λ0)c)2 = GM/r

((Δλ/λ0)c)2 x r = GM

totally not sure
 
  • #10
Ouabache
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Looks good, you're almost there now.
 
  • #11
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so then:

r = GM/((Δλ/λ0)c)2
 
  • #12
Ouabache
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well done :approve:
 

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