Proportion Problem Dealing with Moon's Period

[PeachBanana]

Homework Statement

18. If the moon were four times the distance from the Earth than it currently is, the amount of time it would take to go around the Earth would be roughly (the current orbital period of the moon is about four weeks)

A. 8 weeks
B. 11 Weeks
C. 16 Weeks
D. 32 Weeks
E. 64 Weeks

Homework Equations

T is directly proportional to (r)^3/2

The Attempt at a Solution

I absolutely am awful at problems that deal strictly with proportions.

T = (4)^(3/2)
(4)^(3/2) = 8 weeks

Since the coefficient in front of "T" is "one," should I multiply four by eight since the problem states the period of the moon is about four weeks long?

Also, is there a maximum number of times a person can post in one day? I feel like I post a lot.

 

[gash789]

I have no idea about a maximum number of votes, but who cares anyway!

Proportions are okay if you think about them in a good way (as with most things). Personally I like to introduce a constant so the statement "T is directly proportional to (r)^3/2" I would write as
$T \propto r^{3/2}$
then
$T = C r^{3/2}$

then you also have an equation for when the distance changes, using primes

$T' = C r'^{3/2}$

Now you are left with two coupled equations (see that C remains the same!) and a relation

$r'=4r$

By solving for T' you will see some cancellation which will you an answer.

I think doing it the method you have tried is possible. I get 32 if that helps.

 

[gneill]

You might find it easier to set up your ratios as an equation. If T is proportional to r^3/2, then ignoring constants of proportionality write:

$T^2 \propto r^3$

Then if you have initial and final values (one or more of which may be unknowns), then you might write:

$T1^2 \propto r1^3$
$T2^2 \propto r2^3$

Dividing one relation by the other:

$\frac{T1^2}{T2^2} = \frac{r1^3}{r2^3}$

Substitute in the things you know and solve for what you want.

 

[PeachBanana]

I have no idea about a maximum number of votes, but who cares anyway!

Proportions are okay if you think about them in a good way (as with most things). Personally I like to introduce a constant so the statement "T is directly proportional to (r)^3/2" I would write as
$T \propto r^{3/2}$
then
$T = C r^{3/2}$

then you also have an equation for when the distance changes, using primes

$T' = C r'^{3/2}$

Now you are left with two coupled equations (see that C remains the same!) and a relation

$r'=4r$

By solving for T' you will see some cancellation which will you an answer.

I think doing it the method you have tried is possible. I get 32 if that helps.

Do you mind explicitly explaining how you went from $T' = C r'^{3/2}$

to $r'=4r$ ? I also got 32, which is the correct answer, but I'm still just a tad bit confused.

 

[asteriatic]

As a scientist, it is important to approach problems with a systematic and logical approach. In this case, we can use the equation T is directly proportional to (r)^3/2, where T represents the orbital period and r represents the distance from the Earth to the moon.

If the moon were four times the current distance from the Earth, we can set up a proportion:

(T1) / (T2) = (r1)^3/2 / (r2)^3/2

Where T1 is the current orbital period of the moon (4 weeks), T2 is the unknown orbital period at four times the distance, r1 is the current distance, and r2 is four times the current distance.

Substituting in the values, we get:

(4 weeks) / (T2) = (1)^3/2 / (4)^3/2

Solving for T2, we get approximately 16 weeks. Therefore, the correct answer is C. 16 weeks.

In terms of posting multiple times in one day, there is no set limit but it is important to consider if your posts are contributing meaningful and relevant content to the discussion. It may be helpful to take a break and come back to the discussion later with a fresh perspective.