# Could a gas giant orbit a star with a 30 year period at a distance of just 1 AU?

Assuming a star with similar properties to our sun, could a gas giant orbit it with an orbital period similar to that of Saturn, but, at a much closer orbital distance, more similar to 1 AU?

$$T^{2}=\frac{4 \pi^{2}}{G M} a^{3}.$$
• @orbus The exact Kepler's law is $T^2 = 4\pi^2a^3/G(M+m)$, where $m$ is usually neglected if it's much smaller than $M$. You can play around with values of $T$, $a$, $M$, and $m$ to see if any values fulfil your scenario. For Sirius, I think you're out of luck, though… – pela Dec 13 '19 at 12:08
• @orbus You are using $a$ in AU but the rest of the quantities in SI units. Using multiple systems of units in a calculation often makes the answer difficult to interpret. If you want a form that's easier to use, $$T^{2}=\frac{a^{3}}{M+m}$$ works for $T$ in years, $a$ in AU, and $M,m$ in solar masses. – MathIsFun7225 Dec 13 '19 at 12:45
• @orbus Do you know Python? With the module astropy you can do calculations with units, so that you don't have to think about that. I love it! – pela Dec 13 '19 at 14:28