# Question #50cc1

Feb 23, 2017

See below.

#### Explanation:

First of all, the same amount of time almost exactly would "go by" on each planet, ie 24 hours. Even though the planets are moving at terrifying speeds, and gravity is over double on Jupiter, I don't think there are any relativistic effects worth noting here.

Also, a simple pendulum has approximate period:

$T = 2 \pi \sqrt{\frac{l}{g}}$

On Earth that means the pendulum has, as your post suggests, a period of:

${T}_{e} = 2 \pi \sqrt{\frac{0.25}{9.81}} \approx 1 s$

On Jupiter, that becomes:

${T}_{j} = 2 \pi \sqrt{\frac{0.25}{24}} = 0.641 s$

So it seems that if you assume that every oscillation on Jupiter was still 1 second, you would be fooled into thinking that 24 hours had passed, when in fact only $0.641 \cdot 24 = 15.4$ hours had passed.

I hope I haven't misunderstood you :(