Measuring the speed of the moon

[bobsmith76]

I tried 5 times to get this problem, so I'm sort of heavily invested in it.

Homework Statement

How fast is the moon moving as it orbits Earth at a distance of 3.84 × 10^5 km?

Homework Equations

I'm using the kinematic equation: v = Δd/Δt

Here distance will be 2∏r (I know that the moon's orbit is elliptical but I think my textbook is simplifying to circular)

So that equation will come to:

2. v = (2∏r)/ΔtI then use the Kepler equation:

(G * M)/r = (4∏²r²)/T²

I put the equation in terms of T, this is probably where I messed up:

3. √((G*M)/4∏²r³

I then divide equation 2 by 3

M = mass of Earth or 5.98 * 10²⁴
r = radius of Moon's orbit 3.84 *10⁸

The Attempt at a Solution

When you plug in all the numbers, you get the following equation seen at this screen shot using this calculator

http://web2.0calc.com/

That number comes to 5.7 * 10^15

The correct answer is 1.02 * 10^3

 

[bobsmith76]

Ok, I tried another strategy.

I used this equation

(G*M₁M₂)/r²=(M₂v²)/r

which simplifies to

√((G * M₁)/r) = v

And I got .052 which is closer to 1030 m/s but not quite.

 

[ehild]

Show that calculation in detail. I get the given result.


ehild

 

[bobsmith76]

Thanks for your help but your answer is a little vague. Does given result refer to my answer on the first thread, second thread or the answer supplied by the book? As for calculation does that refer to my first calculation or second?

In any case, I've found the answer with a new equation

v = ((2πGM)/T)^1/3

But I would like to know why those two equations that I tried first do not work.

 

[ehild]

But I would like to know why those two equations that I tried first do not work.

The formula 3 in your first post was not an equation, and I did not understand what you wrote in the spoiler.

ehild

 

[bobsmith76]

there are some errors in the 3rd equation but based on the image i have posted you should be able to figure it out.

i don't know what a spoiler is.

 

[SammyS]

Thanks for your help but your answer is a little vague. Does given result refer to my answer on the first thread, second thread or the answer supplied by the book? As for calculation does that refer to my first calculation or second?

In any case, I've found the answer with a new equation

v = ((2πGM)/T)^1/3

But I would like to know why those two equations that I tried first do not work.

Using √((G * M₁)/r) = v , I get v = 1.019×10³ m/s .

In your original post, if you divide equation 2 by equation 3 (What you have for (3) is not an equation. No '=' sign.) you are finding v/t. That's not velocity.

If you look carefully at what you have for "equation" 3, you have solved for 1/T, not T.

The expression in your screen shot can be greatly simplified and is actually equal to 1/v .

 

[bobsmith76]

Hi Sammy,

Thanks for your help