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Does NASA calculate orbital periods using Kepler's Laws, or do they measure and observe it in some way? If the latter, how do they do so?

Similarly, does NASA calculate the mass of bodies using Kepler's 3rd Law, or do they measure it some other way?

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  • $\begingroup$ There are a lot of objects in the solar system where the mass is not known. For example, Sedna is the largest transneptunian object not known to have a moon, and thus, its mass is not known. $\endgroup$ Commented Dec 3, 2021 at 4:18
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    $\begingroup$ As mentioned below, we normally don't use the mass $m$ of a celestial body in calculations, we use the standard gravitational parameter, $Gm$. It's really hard to measure $G$, so we only know it to 5 significant figures. But we have much more precise values of the gravitational parameter for many Solar System bodies. As well as that list on the Wikipedia page, the $Gm$ of a body is listed on its data page in Horizons. $\endgroup$
    – PM 2Ring
    Commented Dec 3, 2021 at 7:47

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I'll take a small exception to @JamesK's answer about what NASA does and doesn't do. The Jet Propulsion Laboratory is part of NASA and one of the many invaluable contributions they've made to spaceflight are JPL's development ephemerides.

Have a look at the most recent release in The JPL Planetary and Lunar Ephemerides DE440 and DE441. What's done here is a gathering of all possible data, both from NASA and other space agency spacecraft and NASA and other observations, including those with telescopes, some of which were built for NASA and some not, and laser ranging of the Moon and radar ranging of other celestial bodies like planets and asteroids, again some with NASA radars and some with other radars.

See for example:

  1. Observational Data Used for Computing DE440 and DE441

The observations that have been used to compute DE440 and DE441 are summarized in Tables 3–5 for each body.

Especially in Table 3 you can see many deep space spacecraft. When they perform flybys of planets and asteroids their precise positions and speeds are closely monitored by delay-doppler measurements using their on-board coherent transponders; Earth sends a signal with an encoded Gold code (analogous to what's in a GPS signal) and the spacecraft picks it up, amplifies it and broadcasts the same signal right back to Earth. By mathematically correlating the outgoing and returning signal they can measure the distances to the spacecraft to accuracies of tens of meters over hundreds of millions of kilometers, and speeds to accuracies of millimeters per second. One of the main uncertainties is actually the effects of the signal passing twice through Earth's atmosphere due to interaction with water and electrons in the ionosphere.

Then they run lots and lots of simulations to fit all of this data, extracting very accurate standard gravitational parameters (i.e. the mass of an object times the gravitational constant $G$ since it's really hard to measure one and not the other) as well as most accurate and predictive models of the orbits and trajectories of as many solar system bodies as possible.

We have to remember that gravity has a practically infinite reach, so everything affects everything. What that means includes:

  • you need a very good computer program and lots and lots of data to get a handle on what's happening
  • in reality there are no exact periods, the semimajor axis of an orbit isn't even constant over one orbit, and no orbit is really exactly Keplerian to begin with.

Keplerian orbits are great starting points for understanding solar system motion, but they are not "right". Yes, NASA does provide periods in their planetary fact sheets and these are pretty close, but if you really want to know accurately where an object will be, you need a detailed ephemeris computed in this way, using all available data.

As far as masses or standard gravitational parameters are concerned, these come from several main sources.

For planets, they originally came from historical observations of satellite positions over time. Since the satellites are so much less massive than the planets they orbit (unlike our system) their positions and periods can be used to calculate the standard gravitational parameters.

Once astronomers learned to model the effects of the planet's perturbations on each other, they could further refine this.

Interestingly, the masses of some asteroids were determined by their tiny perturbations on each others' orbits!

But the big breakthrough came when there started to be spacecraft flybys of planets as mentioned above and in table 3 of the linked JPL paper.

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    $\begingroup$ Taking very slight exception to your answer: While flybys are indeed helpful, they aren't nearly as helpful as is putting a satellite in orbit about another planet or solar system body. We know a lot more about the gravitational parameters and orbits of Mercury, Venus, Mars, Jupiter, and Saturn (and also several smaller bodies) than is known about other objects in the solar system because space agencies have placed probes in orbit about them. This, by the way, is an excellent answer. $\endgroup$ Commented Dec 3, 2021 at 9:01
  • $\begingroup$ @DavidHammen thanks very much! I started out writing a short answer then realized it wasn't going to be short and ran out of time. I'll fine tune based on your comments soon. $\endgroup$
    – uhoh
    Commented Dec 3, 2021 at 9:45
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    $\begingroup$ GPS is even used to wrangle down Ionosphere noise! $\endgroup$ Commented Dec 3, 2021 at 13:51
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    $\begingroup$ Some background on the creation of the JPL ephemerides and orbit fitting and the fitted observational data for planets are available on the JPL site. $\endgroup$ Commented Dec 3, 2021 at 21:32
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Yes, NASA uses indeed Kepler's 3rd law to calculate the orbital periods of planets and other objects in the solar system. If you go to NASA's Horizons Website and generate orbital data for a planet in the 'Osculating Orbital Elements' format, you find that the orbital periods (PR) have been calculated from the semi-major axis (A) via Kepler's 3rd law (as the data are consistent with this to the last printed digit). As you can also see, these values are not strictly constant with time but show slight variations due to the sun-planet motion being perturbed by other objects. The classical Kepler elements are therefore only applicable as momentary approximations at a certain time instant. They are obtained by converting the so called 'state vector' (the measured Cartesian position and velocity vectors at a certain time) to a Kepler orbit that would reproduce the measurements of the object at this moment.

All the data (including the masses) are hereby obtained from numerous different observations (optical RA/DEC angles, VLBI, lunar laser ranging, radar delay and Doppler, occultation/transit timing, and spacecraft in-situ tracking) via a least squares fit. This is all done in the 'state vector' representation of the orbits though (i.e. using Cartesian position and velocity vectors). The final result is then only converted into the classical 'Osculating Orbital Elements' for those applications that require such a representation or benefit from it.

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"Nasa" does have an interest in astronomy, but the measurement of the planets was done long before Nasa existed.

The positions of the planets can be directly observed. You can literally see where the planets are and measure their positions. With this you can tell exactly how long it takes to make one complete orbit.

You can tell the mass of a planet by observing its gravitational effects on other bodies. It is most convenient to measure the orbit of the planet's moons.

Kepler's third law can't be used to find mass. Kepler's laws say that orbital period is dependent on the distance, not the mass.

So both the orbital period and the planet's masses can be measured. While simple observations of the planet's position can determine the orbital period. More exact measurements with radar can exactly locate the position and motion of a planet with very high accuracy.

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    $\begingroup$ While individual masses cannot be measure by keplers law, you can find the combined mass through the Newtonian version of Kepler’s 3rd law, namely $$P^2=4\pi^2a^3/(G(M_1+M_2))$$ and as you can see by this, mass does affect orbital periods. It’s worth mentioning that for the non-Newtonian version, AU and years are used, while here SI units are used $\endgroup$
    – Justin T
    Commented Dec 2, 2021 at 23:02
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    $\begingroup$ Kepler’s non-Newtonian law works without masses for our solar system because the combined mass of the sun and any given planet is about the same since the sun is so much more massive than any object. $\endgroup$
    – Justin T
    Commented Dec 2, 2021 at 23:10
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    $\begingroup$ Re The positions of the planets can be directly observed. No, they can't. A single observation by a telescope gives a rather lousy estimate of right ascension and declination. At least three (and preferably a lot more than three) such measurements are needed. Re With this you can tell exactly how long it takes to make one complete orbit. This too is incorrect. Nothing is exact. Please don't use the word "exactly". You used that word twice in this answer. There is much in this answer that is incorrect. $\endgroup$ Commented Dec 3, 2021 at 9:17
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    $\begingroup$ "The positions of the planets can be directly observed". Yes they can. Sure you need several measurements over a period of time, but this doesn't change the fact that the postions can be observed. $\endgroup$
    – James K
    Commented Dec 3, 2021 at 22:00
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    $\begingroup$ Radar is mostly not used for planet positions. Gas giants don't give strong signals, and solid bodies more distant than Saturn don't give strong signals. Radar is mostly used for asteroids. $\endgroup$
    – Mark
    Commented Dec 3, 2021 at 22:01

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