Question Why is GGRAV set to 6.67259e-11 in Orbiter?

[ADSWNJ]

I was reviewing some orbital constants with my new astrophysics buddy Keith Gelling, and I was surprised to see that Orbiter's gravitational constant was different to the current official value:

GGRAV: 6.67259E-11 N·(m/kg)2
Official: 6.673889 × 10−11 N·(m/kg)2

Actually - I was more surprised to see that the official value has varied over time, and appears to have an oscillation to it, per this: http://phys.org/news/2015-04-gravitational-constant-vary.html

For modeling gravity in Orbiter's sysem, is it safe to assume that the best gravitational constant we have is that set by GGRAV, or is there a better resolution constant inside the Orbiter core?

 

[Urwumpe]

The official 2014 CODATA value is 6.67408E-11 right now.

 

[RisingFury]

We've been lied to!!! :O

 

[martins]

I suspect that it is more important to pick the celestial body masses compatible with the value of G you are using than getting the absolute value of G correct. We can measure mu = GM more precisely than either G or M, so as long as the resulting mu is correct, there is a bit of leeway between G and M. Or in other words, if I adjusted G every time it is updated, I would also have to adjust the celestial body masses, which might cause more compatibility problems than it is worth.

 

[ADSWNJ]

I suspect that it is more important to pick the celestial body masses compatible with the value of G you are using than getting the absolute value of G correct. We can measure nu = GM more precisely than either G or M, so as long as the resulting nu is correct, there is a bit of leeway between G and M. Or in other words, if I adjusted G every time it is updated, I would also have to adjust the celestial body masses, which might cause more compatibility problems than it is worth.

Thanks Martin - so can I take it that the most accurate GM value for a body is oapiGetMass() * GGRAV?

(Assume so!)

 

[ADSWNJ]

We can measure mu = GM more precisely than either G or M, so as long as the resulting mu is correct, there is a bit of leeway between G and M.

Asking another way ... what's the most accurate to get GM values for the celestial objects? Do you have a lookup table of constants, or is the most accurate estimate just the orbiter mass times the GGRAV constant? I just want to get the best baseline data before running the 4th order integrator.

 

[Keithth G]

Because of the sensitivity of dynamics near collinear Lagrange points, precise estimation of gravitational parameters - GM - for Orbiter's gravitating bodies is important for precision trajectory planning in the vicinity of those points (particularly when approach speeds to a Lagrange points ia low.)

In the absence of simply being told by 'martins' how Orbiter calculates the gravitational parameters from .cfg data and other system parameters, I propose that the most expedient way to obtain a high precision estimate of GM for, say, the Earth, the Moon and the Sun is to conduct a numerical experiment. That numerical experiment would work something like this:

1. Place a spacecraft in low orbit around, say, the Earth. Use a Lua script to Let the simulation run for a suitably long period of time, 24 hours say, and sample the system state vectors every 24 hours.

2. Using a separate high precision integrator - with n assumed value for Earth's GM and starting with the same initial conditions - integrate forward for a 24 hour period. Again sample state vectors every 24 hours.

3. Take differences of the state vectors of the two time series and construct a summed of squares of those differences. Now, repeat step 2 by changing GM until one minimises the value of sum of squares. The resulting value of GM should provide an accurate estimate Earth's GM.

4. Repeat this exercise for other gravitating bodies in Orbiter.

Because Orbiter provides very high precision state vector information, even relatively short time series in this least-squares estimation method should provide a correspondingly precise estimate of GM. And it isn't that hard to implement.

But, obviously, it would simply be easier just to be told what the GM values are.

 

[Thorsten]

I was reviewing some orbital constants with my new astrophysics buddy Keith Gelling, and I was surprised to see that Orbiter's gravitational constant was different to the current official value:

Actually, in reality many celestial bodies are not perfect spheres - their rotation tends to elongate the radius along the equator, Jupiter would be a good example with 3000 km difference between equatorial and polar radius.

That however means that their gravity field is not really that of a point mass, and that means that quoting GM is always an approximation to the real field which is then not spherically symmetric.

Not sure how much of that would be implemented - but nature sure knows, and the Jupiter missions actually measured the deviation from point mass gravity during flybys to get a handle on the actual mass distribution of several moons.

 

[ADSWNJ]

Actually, in reality many celestial bodies are not perfect spheres - their rotation tends to elongate the radius along the equator, Jupiter would be a good example with 3000 km difference between equatorial and polar radius.

That however means that their gravity field is not really that of a point mass, and that means that quoting GM is always an approximation to the real field which is then not spherically symmetric.

Regardless of the oblateness of the body, I would assume it still has a center of gravity, no?

I would certainly expect that the barycenter of the whole solar system wobbles around, e.g. with Jupiter exerting influence on the center of the Sun. It's easy to calculate exactly what this looks like, in meters offset from the Sun's CoG.

 

[Thorsten]

Regardless of the oblateness of the body, I would assume it still has a center of gravity, no?

Well, not in the sense that you can represent the gravity field by a point mass sitting in that center.

The field has rotational symmetry along xy axes and a discrete mirror symmetry along the z-axis (where z is the rotation axis), and in that sense you can still define a center.

And if you're sufficiently far away, all the higher moments drop out and you're left with something very close to a point mass field sitting in the center - but for instance in low Earth orbit, point mass gravity isn't really good. If you compute an inclination from the local state vector assuming point mass field, you see it wobble by a small fraction of a degree during an orbit for instance.

 

[martins]

Unless you untick the "Nonspherical gravity sources" option in the Parameters tab, Orbiter doesn't assume point sources.

 

[martins]

If there is a general consensus, I'd be happy to update the values of G and the celestial body masses to more recent/more precise values. What source do you recommend that provides consistent values for both G and M for all celestial bodies supported in Orbiter?

 

[Keithth G]

If there is a general consensus, I'd be happy to update the values of G and the celestial body masses to more recent/more precise values. What source do you recommend that provides consistent values for both G and M for all celestial bodies supported in Orbiter?

To the extent that Orbiter is 'a world unto itself', there is no need to update values of G and celestial body masses. For most users, most of the time, the differences between current and possible updated values would be too small to observe differences in the resulting trajectories.

And to the extent that users wish to execute trajectories devised in third-party mission planning software from, say, NASA and the ESA, if the product GM values needs updating then this can be done by the user by simply making a systematic change to gravitating body masses in the .cfg files.

On the other hand, real GM values are moving targets, and it may do no harm to update fundamental constants in the model every five to ten years or so.

 

[indy91]

I think to get a fine grasp how relevant the point mass vs. perturbations topic is at different points in space, an explanation how the Apollo Guidance Computer handles it might help.

Low Earth Orbit:

-Earth with nonspherical gravity perturbations, taking into account the J2-J4 harmonics

High Earth Orbit:

-Earth point mass, Sun and Moon as disturbing forces

High Lunar Orbit:

-Moon point mass, Sun and Earth as disturbing forces

Low Lunar Orbit:

-Moon with nonspherical gravity perturbations, taking into account the J2-J4 harmonics and asymmetry about the polar axis (J22). The later lunar missions had an even more complex gravity model onboard.

It's not too much of a problem for NASSP, because J22 is small and these other perturbations are in the erasable memory of the AGC and can be set to 0. And the normal J2-J4 are supported by Orbiter and can be defined in the Moon config. I mean, I wouldn't mind if the nonspherical gravity model of Orbiter would support perturbations around each axis, but we can live without it. :thumbup:

 

[martins]

On the other hand, real GM values are moving targets, and it may do no harm to update fundamental constants in the model every five to ten years or so. If updating, constants that support JPL's most recent ephemeris would probably be the place to shop.

However, Orbiter still depends heavily on the VSOP87 series expansion coefficients for its ephemeris calculation. Those will have been generated with the constants available at the time (and the observational data that led to them). If I update the values in Orbiter to more modern ones, there is a good chance that they will be further away from the 87 data, making the model less rather than more consistent. Maybe we should actually go back to the 1987 data. In any case, while the VSOP87 model is in place, any discussion of the finer points of G is probably moot.

Obviously the better solution would be to regenerate the series approximation with modern data. I remember there was a discussion about building a solar system gravity simulator that could be used for such a purpose. I'm not sure if there has been any progress on that. Whether we could make this sufficiently accurate for the variation in G to make any significant change I don't know. It would be a cool project though. It would also give us more options, such as adding more celestial objects, or building custom solar systems.

 

[Artlav]

Speaking of progress, was VSOP87 compared to the observations over the last 30 years?
Does the lack of updates mean that they are still precise enough, or just that no one bothered to?

 

[Keithth G]

However, Orbiter still depends heavily on the VSOP87 series expansion coefficients for its ephemeris calculation. Those will have been generated with the constants available at the time (and the observational data that led to them). If I update the values in Orbiter to more modern ones, there is a good chance that they will be further away from the 87 data, making the model less rather than more consistent. Maybe we should actually go back to the 1987 data. In any case, while the VSOP87 model is in place, any discussion of the finer points of G is probably moot

Yes, I quite agree. For me, the issue has been knowing 'how' Orbiter forms the product 'GM' and not so much the 'what' the values of 'G' and 'M' actually are.

It is probably worthwhile just reflecting on the magnitude of this non-problem. Although, Orbiter's value of 'G' differs markedly from the most recent value, the product 'GM' - for the Sun and other gravitating bodies - does not. Let's take the Sun as example: if we use Orbiter parameter values and calculate the product 'GM' we get

GM_Sun (Orbiter) = 1.32712439955 x 10^20

And if we look at Wikipedia, say (https://en.wikipedia.org/wiki/Standard_gravitational_parameter

GM_Sun (Wikipedia) = 1.32712440018 x 10^20

This is an absolute difference of 6.3 x 10^10 - i.e., a relative error of around 4.7 x 10^-10. For the Earth orbiting the Sun at around 1 AU, the change in orbital period implied by this is 0.015 seconds. Significant? Methinks not.

 

[ADSWNJ]

If we changed GGRAV and then corrected the celestial masses, I wonder how many MFD's would break? Aerobrake, IMFD, TransX, etc? I'm with Keith - so long as GM is consistent, then it's all good.

I would love to read a blog from Mr Schweiger though, on the propagation model in the Orbiter engine, and how much each body is calculated w.r.t. each other one. E.g. I assume the orbit of Earth is calculated w.r.t. the Sun, and at least all the planets or to Saturn? We live in awe of this computational engine, and the occasional peek behind the curtain is enthralling!

 

[Linguofreak]

However, Orbiter still depends heavily on the VSOP87 series expansion coefficients for its ephemeris calculation. Those will have been generated with the constants available at the time (and the observational data that led to them). If I update the values in Orbiter to more modern ones, there is a good chance that they will be further away from the 87 data, making the model less rather than more consistent. Maybe we should actually go back to the 1987 data. In any case, while the VSOP87 model is in place, any discussion of the finer points of G is probably moot.

What units does VSOP87 use? Given that G is known so imprecisely, I'd think they'd be using AU/Msun/Day or AU/Msun/Year units instead of m/kg/s. If it's AU/Msun/Year, couldn't we just use those units in the sim for celestial bodies and define G=4pi^2? IIRC the sim uses m/kg/s currently. Since the ratio of the meter to the AU and the year to the second is known to great precision (in fact I think the meter/AU ratio is now set by definition), the uncertainty of G would then become an uncertainty in the mass of kg-scale objects (that is, spacecraft). Since spacecraft are not gravitational sources in-sim, and, AFAICT, do not transfer momentum to celestial bodies even in direct collisions (which is to say, the sim assumes them to have zero mass as far as interactions of any kind with celestial bodies are concerned), and as no sane spacecraft will be massive enough to cause significant inaccuracies in the simulation due to the above (Death Star, anyone?), I'd say that an uncertainty in the in-sim value of the kg is acceptable.

Of course, for all I know, changing units would require a complete rewrite of Orbiter.

Obviously the better solution would be to regenerate the series approximation with modern data. I remember there was a discussion about building a solar system gravity simulator that could be used for such a purpose. I'm not sure if there has been any progress on that. Whether we could make this sufficiently accurate for the variation in G to make any significant change I don't know. It would be a cool project though. It would also give us more options, such as adding more celestial objects, or building custom solar systems.

IIRC, I had once brought up the possibility of generating ephemeris dlls for custom systems from output from a specific, existing external program. I'd also suggested a dll to deal with certain special cases like Trojan and horseshoe orbits.

 

[martins]

I'm not quite sure I am following. Your proposed model is

1) Msun := 1
2) yr := 1
3) AU := 1
4) G = 4pi^2 AU^3 yr^-2 Msun^-1 = 4pi^2

1), 2), 3) are definitions. Obviously you can define your units as whatever seems convenient. It doesn't change the underlying physics.

4) Is where the actual physics comes in. In this case, from Kepler's third law for an unperturbed 2-body orbit. Isn't the error you induce with this assumption already much higher than any uncertainty we have for G?

Edit: Incidentally, 1AU is not the semi-major axis of Earth's orbit. It is defined completely independently of any astronomical reference, as 149597870700 metres. So you are back to a metre-based unit.