<p>Yes, the change in Jupiter's mean orbital radius due to the Voyager flybys is literally subatomic.</p>
<p>We can make a rough estimate using the law of conservation of energy: Jupiter's orbital energy loss equals Voyager's orbital energy gain. But Jupiter's mass is ~<span class="math-container">$10^{24}$</span> times Voyager's mass, so the effect on Jupiter's orbit is correspondingly tiny.</p>
<p>The orbital energy of a body is the sum of its potential energy and its kinetic energy. I have the details and equations in my answer to <a href="https://astronomy.stackexchange.com/q/58419/16685">In theory, could an object like &#39;Oumuamua have been captured by a three-body interaction with the sun and planets?</a></p>
<p>Note that there are two Voyagers. You didn't specify which Voyager you're interested in, so I chose Voyager 2. We can calculate its specific orbital energy at various points in time using the trajectory data on JPL <a href="https://ssd.jpl.nasa.gov/horizons/" rel="noreferrer">Horizons</a>. There's some info about its trajectory on its <a href="https://ssd.jpl.nasa.gov/api/horizons.api?format=text&amp;MAKE_EPHEM=NO&amp;COMMAND=-32" rel="noreferrer">body data page</a>, including the dates of its flybys. That page mentions that Voyager 2 performed 24 impulsive maneuvers. I expect that it did a burn at the time of its closest approach to Jupiter, but I can't find any official data on that. So in my calculations I assume that the Voyager speed boost at Jupiter was purely gravitational. If Voyager did do a burn at Jupiter then it would have had an even smaller effect on Jupiter's orbit for the same change in speed.</p>
<p>In a comment, <a href="https://astronomy.stackexchange.com/users/23872/heopps">Heopps</a> states that there was no burn during the flyby.</p>
<blockquote>
<p>All the burns were for aiming. [...] Powered GA [gravity assist] can be beneficial, but it's less robust. A small error in the attitude or duration of the burn can result in a huge error in the trajectory.</p>
</blockquote>
<p>As I said in the linked page, the orbital energy of a gravitationally bound body is negative: you have to add energy to unbind it. The Voyager 2 flyby of Jupiter was on 1979-Jul-19. Here's a Horizons plot of its specific orbital energy (orbital energy per kilogram) around that time.</p>
<p><a href="https://i.sstatic.net/B61gOfzu.png" rel="noreferrer"><img src="https://i.sstatic.net/B61gOfzu.png" alt="Voyager 2 orbital energy, 1979-May-1 to 1979-Oct" /></a></p>
<p>We can see that it picked up enough energy during the flyby to become unbound from the Sun.</p>
<p>Here are a few more plots with more detail so we can estimate the change in orbital energy.</p>
<p><a href="https://i.sstatic.net/gwXsyxDI.png" rel="noreferrer"><img src="https://i.sstatic.net/gwXsyxDI.png" alt="Voyager orbital energy, May" /></a></p>
<p><a href="https://i.sstatic.net/AMFR1E8J.png" rel="noreferrer"><img src="https://i.sstatic.net/AMFR1E8J.png" alt="Voyager orbital energy, July" /></a></p>
<p><a href="https://i.sstatic.net/tLE7cVyf.png" rel="noreferrer"><img src="https://i.sstatic.net/tLE7cVyf.png" alt="Voyager orbital energy, Sept" /></a></p>
<p>So its specific energy increased from (approximately) <span class="math-container">$-121.4\,\rm{km^2/s^2}$</span> to <span class="math-container">$29.9\,\rm{km^2/s^2}$</span>, a change of <span class="math-container">$151.3\,\rm{km^2/s^2}$</span>. To find the change in Jupiter's specific orbital energy we have to multiply that by their mass ratio. I don't know what Voyager 2's mass was at the Jupiter flyby, so I just used its launch mass. This gives a mass ratio of <span class="math-container">$\frac{721.9\,\rm{kg}}{1.89813×10^{27}\,\rm{kg}}$</span>.</p>
<p>That gives a change to Jupiter's specific orbital energy of ~ <span class="math-container">$-5.7543×10^{-23}  \,\rm{km^2/s^2}$</span>.</p>
<p>Jupiter's orbit is not simple. Its mean eccentricity is ~<span class="math-container">$0.0487$</span> roughly <span class="math-container">$3$</span> times larger than Earth's. But it is strongly affected by the other giant planets, especially Saturn, both because it's the closest and because it's in a roughly resonant pattern with Saturn: in <span class="math-container">$60$</span> years, Jupiter does roughly <span class="math-container">$5$</span> orbits while Saturn does roughly <span class="math-container">$2$</span> orbits. Here's a plot of Jupiter's specific orbital energy spanning 60 years, roughly centred on the time of the Voyager flybys.</p>
<p><a href="https://i.sstatic.net/A9IlCt8J.png" rel="noreferrer"><img src="https://i.sstatic.net/A9IlCt8J.png" alt="Jupiter orbital energy, 1950 to 2010" /></a></p>
<p>For our calculation, we can ignore that mess, and just use the mean value of the specific orbital energy, <span class="math-container">$-85.17\,\rm{km^2/s^2}$</span>.</p>
<p>Rearranging
<span class="math-container">$$\varepsilon = -\frac{\mu}{2a}$$</span></p>
<p>we get an estimate of the change in Jupiter's semi-major axis of ~<span class="math-container">$-5.2×10^{-13}$</span> m, that is ~<span class="math-container">$-0.52$</span> picometres, which is smaller than a hydrogen atom, but larger than a proton (<span class="math-container">$0.833$</span> fm).</p>

CC BY-SA 4.0
2024-11-22T06:38:10.447Z
It's very good answer, but about one moment: Voyagers definitely didn't burn during Jupiter fllyby. All the burns were for aiming. Interplanetary probes have never performed "powered gravity assist" yet, AFAIK. Powered GA can be benefitial, but it's less robust. A small error in the attitude or duration of the burn can result in a huge error in the trajectory. But passive gravity assist is very precise, because the pre-assist trajectory of a spacecraft can be measured by radio communication using Doppler effect and corrected for the best aiming.
Heopps
CC BY-SA 4.0
2024-11-22T07:53:07.677Z
Thanks, @Heopps. I've added that info to my answer.
PM 2Ring
CC BY-SA 4.0
2024-11-22T22:36:52.557Z
FWIW, that's on the order of $10^{22}$ planck lengths (10 billion trillion planck lengths)
James K
CC BY-SA 4.0
2024-11-21T09:25:11.510Z
2024-11-22T07:50:36.773Z
2024-11-22T07:50:36.773Z
PM 2Ring
<p>I know that a planetary flyby craft gains more energy than it had because when Voyager swung around Jupiter, Jupiter slowed down and fell slightly closer toward the sun.</p>
<p>Assuming it had a perfectly circular orbit before the flyby, how much closer is it's new orbit to the sun? It must be unimaginably small. A micron? A nanometer? Jupiter is so huge and Voyager so small, that I'd be surprised if it was even  the Planck length.</p>
<p>I imagine that depending on the direction that Voyager approached Jupiter, it's effect on the orbit would change. It would become more elliptical, right?</p>
<p>So assume that voyager approaches from exactly the opposite direction that Jupiter is moving (tangent to its orbit). That way, Jupiter would just drop closer to the sun without its orbit becoming more eccentric.</p>
<p>So how much closer to the sun does Jupiter orbit because Voyager flew past it?</p>

CC BY-SA 4.0
2024-11-21T09:46:47.087Z
_"I'd be surprised if it was even the Planck length"_ — well, it cannot be less if our current understanding is correct.
doubleunary
<orbit><gravity><orbital-mechanics>
How much closer is Jupiter's orbit to the sun after Voyager did a gravity assist fly by?
Miss Understands
# How much closer is Jupiter's orbit to the sun after Voyager did a gravity assist fly by?

(Asked by: username_0 on 2024-11-18)

I know that a planetary flyby craft gains more energy than it had because when Voyager swung around Jupiter, Jupiter slowed down and fell slightly closer toward the sun.

Assuming it had a perfectly circular orbit before the flyby, how much closer is it's new orbit to the sun? It must be unimaginably small. A micron? A nanometer? Jupiter is so huge and Voyager so small, that I'd be surprised if it was even the Planck length.

I imagine that depending on the direction that Voyager approached Jupiter, it's effect on the orbit would change. It would become more elliptical, right?

So assume that voyager approaches from exactly the opposite direction that Jupiter is moving (tangent to its orbit). That way, Jupiter would just drop closer to the sun without its orbit becoming more eccentric.

So how much closer to the sun does Jupiter orbit because Voyager flew past it?

**Tags:** orbit, gravity, orbital-mechanics
> **Comments:**
> **username_1**: _"I'd be surprised if it was even the Planck length"_ — well, it cannot be less if our current understanding is correct.  

---

## 1 answers

### Answer by username_2 on 2024-11-21. Score: 14

Yes, the change in Jupiter's mean orbital radius due to the Voyager flybys is literally subatomic.

We can make a rough estimate using the law of conservation of energy: Jupiter's orbital energy loss equals Voyager's orbital energy gain. But Jupiter's mass is ~$10^{24}$ times Voyager's mass, so the effect on Jupiter's orbit is correspondingly tiny.

The orbital energy of a body is the sum of its potential energy and its kinetic energy. I have the details and equations in my answer to [In theory, could an object like 'Oumuamua have been captured by a three-body interaction with the sun and planets?](https://astronomy.stackexchange.com/q/58419/16685)

Note that there are two Voyagers. You didn't specify which Voyager you're interested in, so I chose Voyager 2. We can calculate its specific orbital energy at various points in time using the trajectory data on JPL [Horizons](https://ssd.jpl.nasa.gov/horizons/). There's some info about its trajectory on its [body data page](https://ssd.jpl.nasa.gov/api/horizons.api?format=text&MAKE_EPHEM=NO&COMMAND=-32), including the dates of its flybys. That page mentions that Voyager 2 performed 24 impulsive maneuvers. I expect that it did a burn at the time of its closest approach to Jupiter, but I can't find any official data on that. So in my calculations I assume that the Voyager speed boost at Jupiter was purely gravitational. If Voyager did do a burn at Jupiter then it would have had an even smaller effect on Jupiter's orbit for the same change in speed.

In a comment, [Heopps](https://astronomy.stackexchange.com/users/23872/heopps) states that there was no burn during the flyby.

> All the burns were for aiming. [...] Powered GA [gravity assist] can be beneficial, but it's less robust. A small error in the attitude or duration of the burn can result in a huge error in the trajectory.

As I said in the linked page, the orbital energy of a gravitationally bound body is negative: you have to add energy to unbind it. The Voyager 2 flyby of Jupiter was on 1979-Jul-19. Here's a Horizons plot of its specific orbital energy (orbital energy per kilogram) around that time.

[![Voyager 2 orbital energy, 1979-May-1 to 1979-Oct](https://i.sstatic.net/B61gOfzu.png)](https://i.sstatic.net/B61gOfzu.png)

We can see that it picked up enough energy during the flyby to become unbound from the Sun.

Here are a few more plots with more detail so we can estimate the change in orbital energy.

[![Voyager orbital energy, May](https://i.sstatic.net/gwXsyxDI.png)](https://i.sstatic.net/gwXsyxDI.png)

[![Voyager orbital energy, July](https://i.sstatic.net/AMFR1E8J.png)](https://i.sstatic.net/AMFR1E8J.png)

[![Voyager orbital energy, Sept](https://i.sstatic.net/tLE7cVyf.png)](https://i.sstatic.net/tLE7cVyf.png)

So its specific energy increased from (approximately) $-121.4\,\rm{km^2/s^2}$ to $29.9\,\rm{km^2/s^2}$, a change of $151.3\,\rm{km^2/s^2}$. To find the change in Jupiter's specific orbital energy we have to multiply that by their mass ratio. I don't know what Voyager 2's mass was at the Jupiter flyby, so I just used its launch mass. This gives a mass ratio of $\frac{721.9\,\rm{kg}}{1.89813×10^{27}\,\rm{kg}}$.

That gives a change to Jupiter's specific orbital energy of ~ $-5.7543×10^{-23} \,\rm{km^2/s^2}$.

Jupiter's orbit is not simple. Its mean eccentricity is ~$0.0487$ roughly $3$ times larger than Earth's. But it is strongly affected by the other giant planets, especially Saturn, both because it's the closest and because it's in a roughly resonant pattern with Saturn: in $60$ years, Jupiter does roughly $5$ orbits while Saturn does roughly $2$ orbits. Here's a plot of Jupiter's specific orbital energy spanning 60 years, roughly centred on the time of the Voyager flybys.

[![Jupiter orbital energy, 1950 to 2010](https://i.sstatic.net/A9IlCt8J.png)](https://i.sstatic.net/A9IlCt8J.png)

For our calculation, we can ignore that mess, and just use the mean value of the specific orbital energy, $-85.17\,\rm{km^2/s^2}$.

Rearranging
$$\varepsilon = -\frac{\mu}{2a}$$

we get an estimate of the change in Jupiter's semi-major axis of ~$-5.2×10^{-13}$ m, that is ~$-0.52$ picometres, which is smaller than a hydrogen atom, but larger than a proton ($0.833$ fm).

> **Comments:**
> **username_3**: It's very good answer, but about one moment: Voyagers definitely didn't burn during Jupiter fllyby. All the burns were for aiming. Interplanetary probes have never performed "powered gravity assist" yet, AFAIK. Powered GA can be benefitial, but it's less robust. A small error in the attitude or duration of the burn can result in a huge error in the trajectory. But passive gravity assist is very precise, because the pre-assist trajectory of a spacecraft can be measured by radio communication using Doppler effect and corrected for the best aiming.  
> **username_2**: Thanks, @Heopps. I've added that info to my answer.  
> **username_4**: FWIW, that's on the order of $10^{22}$ planck lengths (10 billion trillion planck lengths)  

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