# Rearranging of formulas

1. May 27, 2009

### dukg08

1. The problem statement, all variables and given/known data

(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.

2. Relevant 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.

3. 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: May 27, 2009
2. May 27, 2009

### Ouabache

Are you sure about your result for $v^2$ in equ. (i)?
It looks like you only squared part of your expression for $v$.

3. May 27, 2009

### dukg08

((Δλ/λ0)c)2 = GM/r

4. May 27, 2009

### Ouabache

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: May 27, 2009
5. May 27, 2009

### dukg08

((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: May 27, 2009
6. May 27, 2009

### Ouabache

what are you solving for? that will help you decide which direction to take.

7. May 27, 2009

### dukg08

I'm trying to make r the subject.

((Δλ/λ0)c)2/r = GM

r = ((Δλ/λ0)c)2xGM

8. May 27, 2009

### Ouabache

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. May 27, 2009

### dukg08

((Δλ/λ0)c)2 = GM/r

((Δλ/λ0)c)2 x r = GM

totally not sure

10. May 27, 2009

### Ouabache

Looks good, you're almost there now.

11. May 27, 2009

### dukg08

so then:

r = GM/((Δλ/λ0)c)2

12. May 27, 2009

well done