# How Does a Massive Planet's Orbit Around the Sun Appear?

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• pruthvi
pruthvi
consider a giant planet have a 3/4 mass of it sun and with the distance of 50AU from the sun.
does the planet revolve around in a elliptical orbit because the mass of the planet is high so there barycenter is half the distance between them so it look like binary star system but the question is as per Kepler rules the plant should revolve around the sun in a elliptical orbit. How it is possible in this case to say that the planet is in elliptical orbit ?

Kepler’s laws were empirically determined for planets with much smaller mass than the primary. They are not directly applicable to the case where the masses are similar.

However, the two body problem may be reformulated as a Kepler problem for the reduced mass in a central gravitational potential given by the same expression as for the two-body problem. This means that Kepler’s laws do hold true, albeit with a different mass relation. In particular, the orbit is indeed elliptical, but relative to the barycenter.

topsquark, russ_watters, PeroK and 1 other person
pruthvi said:
consider a giant planet have a 3/4 mass of it sun and with the distance of 50AU from the sun.
That would make a binary star. It would rotate about a barycenter somewhere near the middle.
pruthvi said:
How it is possible in this case to say that the planet is in elliptical orbit ?
It would not be considered to be a planet.

topsquark, BillTre and PeroK
Every planet orbits around it's barycenter with the Sun. In most cases, this barycenter is close enough the center of the Sun to make little difference. The Jupiter-Sun barycenter is actually just above the surface of the Sun. There is no real difference between Earth orbiting the Sun and Jupiter other than the size of the Sun's orbit around the respective barycenters. Kepler's Laws reflected a pattern he derived via observation, and of course, were limited by those observations. The small variation due to planets orbiting barycenters rather than the Sun proper were more than likely within the error bars of his observations. Remember, he produced these laws before Newton came up with the theory of gravity which explained them.

topsquark, BillTre and russ_watters
We cannot see the barycenter of a binary star. It is an unmarked dark spot in empty sky between the stars. If you want to find out the actual location of the barycenter of the binary star, you must make great precision measurement of large angles from the binary star to fixed points in the sky... over a long, long time!
If you simply measure the separation between the stars and their position angle then both stars follow elliptical orbits - of equal size, because you have only one separation. And the stars are NOT required to be at the focus (because the orbit can have any inclination!).

Measuring these large angles is useful, though, if you can. You need to track the proper motion, too. Because if you find a position along the separation which follows a straight proper motion while the stars have wavy proper motion then this is the barycenter. And what it gives to you is the ratio of lever arms - the ratio of the masses of the components.

Janus said:
Every planet orbits around it's barycenter with the Sun.
In most cases the difference is negligible to the extent that other effects, such as the jovian influence on the orbit, have a larger impact. In the case of Jupite it is relatively accurate.

For the interested, there is a telling image on Wikipedia:

This displays the motion of the solar system barycenter relative to the Sun.

DaveC426913
Easy way to visualise it is for Earth/Moon system, whose barycentre, around which both components have elliptical orbits, is located on average 4,671 km (2,902 mi) from Earth's centre, which is 75% of Earth's radius of 6,378 km (3,963 mi).
https://en.wikipedia.org/wiki/Barycenter_(astronomy)

Note that solar 'tides', plus the gravitational effects of Jupiter, Venus etc etc do nudge / perturb the orbits, though the 'dominant' factor is 'receding' Moon due momentum exchange via tidal dissipation...

## 1. How does the orbit of a massive planet differ from that of a smaller planet?

The orbit of a massive planet around the Sun follows the same elliptical path as smaller planets, as described by Kepler's laws of planetary motion. However, due to its larger mass, the gravitational interactions with the Sun and other celestial bodies may be more pronounced, potentially leading to more noticeable perturbations in its orbit.

## 2. Does the mass of a planet affect the shape of its orbit around the Sun?

No, the mass of a planet does not affect the shape of its orbit. According to Kepler's first law, all planets, regardless of their mass, follow elliptical orbits with the Sun at one of the foci. The shape of the orbit is determined by the planet's velocity and its distance from the Sun, not its mass.

## 3. How does a massive planet's gravitational influence affect its orbit?

A massive planet's strong gravitational influence can affect its orbit by causing more significant perturbations due to interactions with other celestial bodies. For instance, a massive planet may experience gravitational tugs from nearby planets or moons, leading to variations in its orbital path over time.

## 4. Can a massive planet's orbit around the Sun be perfectly circular?

While it is theoretically possible for a massive planet to have a perfectly circular orbit, in practice, most planetary orbits are slightly elliptical. A perfectly circular orbit would require a very specific set of initial conditions, which are rare in the dynamic environment of a solar system.

## 5. How do astronomers measure the orbit of a massive planet around the Sun?

Astronomers measure the orbit of a massive planet using a variety of methods, including direct observation through telescopes, tracking the planet's position over time, and analyzing the gravitational effects on nearby objects. Data from space missions and advanced techniques like astrometry and radial velocity measurements also help in accurately determining the planet's orbital parameters.

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