Planet Mass and Orbital Radius ? - Help Needed.

[rust]

While it is normally not easy to drive me into a state of confusion, one of
the players now managed to do it. :shock:

Until his monologue on star systems I was convinced that the mass of a
planet is important for the calculation of its orbital period (= year), but
has no influence on its orbital radius.

Well, I am still convinced that this is the case, but the player in question
insists that the mass of a planet also determines its orbital radius, and I
do not want to rule out that my brain has a malfunction today.

Could someone please tell me which one of the ideas is the right one ?

Thank you.

 

[DFW]

How EXACTLY did he say it effects the orbital radius?

Earth is more massive than both Venus & Mars yet, its orbital radius is larger than one and smaller than the other...

 

[Rick]

Unless he means that in very general terms, all the big gas giants are on the outer part of the system, no. :?

 

[rust]

Thank you for your answers.

How EXACTLY did he say it effects the orbital radius?

Unfortunately he did not remember how exactly it was supposed to work,
only the fact that it did. :?

 

[far-trader]

Actually, to further confuse you rust I don't think the mass of the planet has any bearing on either the orbital period or radius. In most cases of the definition of planet/star/orbit.

I could be misremembering but it is the mass of the central body that determines the orbit. And it is the speed of the orbiting body that determines both the orbit's radius and period (as well as it's eccentricity). Changing the mass of the orbiting body does not change the orbit.

Unless the two bodies are close to the same mass in which case it is a two body orbit problem (each orbits the other around a "central" point). For most planet/star orbits (and planet/moon orbits) the masses are so different as to not factor (the orbit center is deep inside the body of the larger - causing the larger body to wobble a bit).

Earth/Moon for example is almost or practically a two body system because the masses are close. The orbital "center" is still within the body of the Earth but only just, or it would be unarguably a two body system.

 

[rust]

Actually, to further confuse you rust I don't think the mass of the planet has any bearing on either the orbital period or radius. In most cases of the definition of planet/star/orbit.

Yep, I am aware that the influence is only a minimal one, and negligible
when there is a huge difference between the two bodies. I would not at-
tempt to use it as a factor when calculating the orbital period of Earth,
but I would probably consider it when calculating the orbital period of
Jupiter.

 

[BP]

Ah, well, this can be a confusing subject...

Kepler set forth 3 'laws' that describe elliptical orbits (due to center of mass actually) - and they approximately hold for planets since he based them on numerical observations - without knowing masses. But this is a simple geometry equation. (Basically the cube of the orbital distance from the sun is proportional to the square of the period, at least for the major planets.)

Later, Newton came along and (using Kepler's data, mind you) established that orbits are dependent on gravity and more accurately derivable from such (and using conics...). In the simple case of two bodies, the size of an orbit is inversely proportional to their masses - and they revolve about their mutual center of mass. His use of conics also accounted for non-planetary orbits...

Einstein then came along and fixed this by establishing that gravity is a feature/function of the curvature of space-time. Newton had to require that the force of gravity be propagated instantaneously for the conic sections - Einstein's theories correct this and our reality matches his theories within measurable accuracies.

So there are three levels of approximation (ignoring pre-Kepler when orbits where assumed to be circular) - the crudest of which does not, directly, use mass.

For many practical purposes, Keplers laws work for planets (as the Sun is so much more massive than the planets) to a limited degree of precision. Newtonian laws are required for everything else - especially as orbital ellipses slowly rotate (apsidal precession - sp?) - and they are based on mass.

However, Newton's laws aren't good enough for certain situations - notably Mercury's precession. In everyday life, the GPS depends on taking into account relativistic effects.

Ok - now your head's probably spinning (and I am not a teacher by trade - so you can blame me for some of that and not just the nature of the subject)... and I'm extremely hungry (i.e. need some mass!).

 

[rust]

Meanwhile I tried to sort this out with the player in question, and it seems
he somehow mistook Bode's (so called) Law for a law describing the orbits
of planets based upon their mass. The existence of "hot jupiters" in very
close orbits around their stars finally convinced him that my new setting's
planetary system does not violate the natural order ... :lol:

... and I'm extremely hungry (i.e. need some mass!).

BP, as a former Catholic I have to tell you the bad news you that a mass,
especially a long one, has a tendency to cause hunger, not to end it.

 

[far-trader]

I don't think anyone has much regarded Bode's Law as at all valid for a long time. It's been suspect since shortly after it was proposed and that was a long time ago. Misunderstanding it aside

 

[BP]

Ah - perhaps you need to establish Rust's Law!

And, perhaps your player needs food too! Tidus-Bode's 'law' is just a unit free equation, not a prayer of mass figuring into that! :shock:

P.S. - as a child I discovered there is no frequency limit on communion, though one gets funny looks when seen re-entering the line...

 

[SSWarlock]

P.S. - as a child I discovered there is no frequency limit on communion, though one gets funny looks when seen re-entering the line...

Just don't ask the priest for the "salsa cup" (hey, it was my sister's idea, not mine).

 

[rust]

Ah - perhaps you need to establish Rust's Law!

According to the players I already did that, their interpretation of my Law
of Roleplaying is "MacGyver beats Rambo".

 

[GypsyComet]

I don't think anyone has much regarded Bode's Law as at all valid for a long time. It's been suspect since shortly after it was proposed and that was a long time ago. Misunderstanding it aside

Right. Traveller uses it in prior editions to set the orbital distances for simplicity sake more than anything else.

 

[BP]

Ah - perhaps you need to establish Rust's Law!

According to the players I already did that, their interpretation of my Law
of Roleplaying is "MacGyver beats Rambo".

:lol:

So... cheesy American Sitcoms and Movies are well known in Germany?

Please accept my sincerest apologizes, on behalf of my peoples!

 

[rust]

Please accept my sincerest apologizes, on behalf of my peoples!

Well, we exported Roland Emmerich ...

 

[BP]

Yeah - that was uncalled for! :evil:

But, at least neither of our prestigious countries have to take credit for John Woo!

 

[GypsyComet]

Meanwhile I tried to sort this out with the player in question, and it seems he somehow mistook Bode's (so called) Law for a law describing the orbits of planets based upon their mass. The existence of "hot jupiters" in very close orbits around their stars finally convinced him that my new setting's planetary system does not violate the natural order ... :lol:

While the mass is a factor, it is a small one, relatively speaking.
Gravitational "attraction" between two bodies is based on their distance from one another and their masses. The closer together or larger they are, the more they attract each other. In the case of the Sun and its planets, this attraction is manifested entirely (for all intents and purposes) by the smaller mass, which will get sucked into the unmoving star.

To avoid that fate the attraction must be balanced by something else. Nature's way of doing this is the orbit. If the smaller body has exactly enough sideways velocity to balance the inward attraction, the resulting motion is a stable orbit. If that mass is larger, the attraction that must be countered is larger, and the orbital velocity must therefore be higher.

So while orbital distance is NOT directly related to mass, the orbital distance, masses, and orbital velocity ARE all related. Set any two of them and the third shakes out by necessity.

 

[locarno24]

Mass tends to be largely irrelevant in pure gravity situations (daft as that sounds);

Your acceleration depends on the ratio of your mass and the force experienced.

But since the force experienced also varies with your mass, it's always pretty much proportional.

As long as the 'centrepoint' (in this case star) is sufficiently heavier than anything orbiting it not to have to worry about its acceleration, or interaction between planets, then you can all but ignore mass from the system unless you're trying to be really, really accurate.