<p>Gas giants can be found very close to their suns. The closest ones are then called <a href="https://en.wikipedia.org/wiki/Hot_Jupiter" rel="nofollow noreferrer">Hot Jupiters</a>.<br />
But not with a orbital period of 30 years. Everything that orbits a star with one solar mass at 1 AU will also have an orbital period of 1 year, according to <a href="https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion#Third_law_of_Kepler" rel="nofollow noreferrer">Keplers 3rd law</a>:</p>
<p><span class="math-container">$$
T^{2}=\frac{4 \pi^{2}}{G M} a^{3}.
$$</span></p>

CC BY-SA 4.0
2019-12-13T11:18:09.807Z
OK. That fits with Ethereal Mechanics as well. The model where the aether moves around stars (and galaxies, planets), and planets move with the aether. Explaining Michelson–Morley experiment giving null result. In EM, the orbital period is equivalent to the speed of the aether, and like in a hurricane, decreases with distance.
orbus
CC BY-SA 4.0
2019-12-13T11:56:46.743Z
@orbus For a 30 year period at 1 AU, the combined mass of the planet & star equals 1/900 solar masses. But for a planet with the mass of Saturn, the "star" mass is just under 2.9 times the mass of Saturn, which is far too small for a star: it's actually lighter than Jupiter.
PM 2Ring
CC BY-SA 4.0
2019-12-13T12:02:31.587Z
@PM2Ring The exact context of the question was, despite that it contradicts the scientific consensus, I was looking at if Sirius B could be an exoplanet, and, much closer to Sirius than assumed. Just wanted to know if, in theory, a similar arrangement was possible. It is proven that the object called Sirius B orbits with a 50 year period. Do you see any arrangement where that object could be much closer to Sirius, 1 AU, or, 1-5 AU?
orbus
CC BY-SA 4.0
2019-12-13T12:08:45.603Z
@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
CC BY-SA 4.0
2019-12-13T12:28:14.703Z
Thanks. Feeding in 4pi^2*5.2^3/(G(mass of sun + mass of Jupiter))

 (39.4784176*5.2^3)/((6.673×10^-11)(1.989 × 10^30 + 1.898 × 10^27 kg)) gives a value that seems completely wrong for T^2. 

The comments are not for discussion, but, do you see what I'm missing? T^2 should be 12^2, I guess, Jupiter's orbital period.
orbus
CC BY-SA 4.0
2019-12-13T12:45:26.907Z
@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
CC BY-SA 4.0
2019-12-13T12:52:36.907Z
OK. Thanks. With seconds and meters it fit.
orbus
CC BY-SA 4.0
2019-12-13T14:28:12.470Z
@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
CC BY-SA 4.0
2019-12-13T10:54:28.183Z
2019-12-13T10:54:28.183Z
2020-06-17T09:47:40.653Z
SpaceCore
<p>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?</p>

<exoplanet><orbital-mechanics><newtonian-gravity>
Could a gas giant orbit a star with a 30 year period at a distance of just 1 AU?
orbus
# Could a gas giant orbit a star with a 30 year period at a distance of just 1 AU?

(Asked by: username_0 on 2019-12-13)

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?

**Tags:** exoplanet, orbital-mechanics, newtonian-gravity


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## 1 answers

### Answer by username_1 on 2019-12-13. Score: 2

Gas giants can be found very close to their suns. The closest ones are then called [Hot Jupiters](https://en.wikipedia.org/wiki/Hot_Jupiter).  
But not with a orbital period of 30 years. Everything that orbits a star with one solar mass at 1 AU will also have an orbital period of 1 year, according to [Keplers 3rd law](https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion#Third_law_of_Kepler):

$$
T^{2}=\frac{4 \pi^{2}}{G M} a^{3}.
$$

> **Comments:**
> **username_0**: OK. That fits with Ethereal Mechanics as well. The model where the aether moves around stars (and galaxies, planets), and planets move with the aether. Explaining Michelson–Morley experiment giving null result. In EM, the orbital period is equivalent to the speed of the aether, and like in a hurricane, decreases with distance.  
> **username_2**: @username_0 For a 30 year period at 1 AU, the combined mass of the planet & star equals 1/900 solar masses. But for a planet with the mass of Saturn, the "star" mass is just under 2.9 times the mass of Saturn, which is far too small for a star: it's actually lighter than Jupiter.  
> **username_0**: @PM2Ring The exact context of the question was, despite that it contradicts the scientific consensus, I was looking at if Sirius B could be an exoplanet, and, much closer to Sirius than assumed. Just wanted to know if, in theory, a similar arrangement was possible. It is proven that the object called Sirius B orbits with a 50 year period. Do you see any arrangement where that object could be much closer to Sirius, 1 AU, or, 1-5 AU?  
> **username_3**: @username_0 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…  
> **username_0**: Thanks. Feeding in 4pi^2*5.2^3/(G(mass of sun + mass of Jupiter))   (39.4784176*5.2^3)/((6.673×10^-11)(1.989 × 10^30 + 1.898 × 10^27 kg)) gives a value that seems completely wrong for T^2.   The comments are not for discussion, but, do you see what I'm missing? T^2 should be 12^2, I guess, Jupiter's orbital period.  
> **username_4**: @username_0 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.  
> **username_0**: OK. Thanks. With seconds and meters it fit.  
> **username_3**: @username_0 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!  

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