Jupiter Ascending

Classical Mechanics Level 3

Two moons of Jupiter, Callisto and Europa of masses m C m_C and m E m_E are orbiting in circular paths of radius r C r_C and r E r_E respectively about Jupiter. The radii are measured from the Jupiter’s centre of mass and the respective moons’ centre of masses.

What is the ratio of their velocities v C v E \dfrac{v_C}{v_E} in terms of the given variables?

m C r E m E r C \frac{m_C r_E}{m_E r_C} r C r E \sqrt{\frac{r_C}{r_E}} r E r C \frac{r_E}{r_C} r E r C \sqrt{\frac{r_E}{r_C}}

View wiki
Wee Xian Bin by Wee Xian Bin , 25, Singapore

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

We shall assume that Callisto and Europa are in uniform circular motion. Then, we know that the centripetal acceleration is equals to the acceleration due to gravity. So, we have the equation: m v 2 r = G m m j u p i t e r r 2 v = G m j u p i t e r r \frac{mv^2}{r}=\frac{Gmm_{jupiter}}{r^2}\\v=\sqrt{\frac{Gm_{jupiter}}{r}}

Thus, v C v E = 1 r C 1 r E = r E r C \frac{v_C}{v_E}=\frac{\sqrt{\frac{1}{r_C}}}{\sqrt{\frac{1}{r_E}}}=\sqrt{\frac{r_E}{r_C}}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...