# Length of one day on another planet

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1. Apr 10, 2016

### Balsam

1. The problem statement, all variables and given/known data
Imagine another planet with an acceleration of 10m/s^2 at its equator when ignoring the rotation of the planet. The radius of the planet is 6.2 x 10^6m. An object dropped at the equator yields an acceleration of 9.70m/s^2. Determine the length of one day on this planet.
r=6.2x10^6m
g=9.70m/s^2
a=10m/s^2--> I don't know why we were given the first acceleration, I don't think it's equal to ac.

2. Relevant equations
I used Fc=4pi^2mr/T^2 and isolated for T.

3. The attempt at a solution
I used the above equation, plugging in mg for Fc because I think the force of gravity is the centripetal force. The 'm' variables cancelled out since I just divided them out. Then, I plugged all of my other given values in and solved for T. Since T is the time it takes in seconds to complete one revolution, I divided my result by 3600 to get the time it takes in hours to complete one revolution. My final answer was about 1.3hours. However, the book's answer is 7.9hours. I don't know where I went wrong

2. Apr 10, 2016

### BvU

Fgravity does more than keep a person in a cicular orbit. It also keeps his feet on the ground .... with a given force mg.

3. Apr 10, 2016

### Balsam

But the formula I used just asked for Fc

4. Apr 10, 2016

### BvU

So ?

5. Apr 10, 2016

### BvU

If a person with a mass of 80 kg stands on a scale, the scale will show 80 x 9.7 kg, so the scale will push up with 776 N. Where does that force come from ?

6. Apr 10, 2016

### Balsam

It's the force of gravity, but how is that important in centripetal acceleration?

7. Apr 11, 2016

### BvU

If the planet wouldn't rotate, what would the scale indicate ?

8. Apr 13, 2016

### Balsam

Apparently you have to subtract the acceleration of the dropped object from the acceleration of the planet

9. Apr 14, 2016

### BvU

Is that understandable ?

10. Apr 27, 2016

### Balsam

I don't understand why you're supposed to do that, but that's what my teacher said