I have heard that we will soon lose track of the Tesla Roadster launched with the Falcon Heavy test launch. Yet, we know where Voyager is out beyond the Solar System and we followed other satellites to the outer planets. Why the difference?
Is it possible to track an item of that size? Does it require that it transmit some type of signal to be tracked?
An object as small as the Tesla Roadster will not be trackable all the way out beyond the orbit of Mars. The Tesla is too small, or space is too big, or both. The fact that the booster is still attached and that it's all pretty bright makes things a little easier, so we might be able to track it for quite a while yet (although you may have a hard time convincing to get valuable Hubble time to point it at the Roadster-booster, there's cheaper telescopes on Earth where you might have better luck). See uhohs excellent answer for a more detailed analysis.
Why the difference?
Voyager is actively aiming an antenna at Earth and transmitting to the best of its ability. We aim some of our largest receiving antennas in the direction of Voyager and listen to the best of our ability. We get a handful of bytes through per second (if not per hour). Without such efforts, we would never locate it.
The other answer makes good points about Voyager actively transmitting - but there is something else to keep in mind.
Telescopes are designed to view things very far away - telescopes in space even more so. They are built to view extremely distant objects and have a difficult time seeing near objects clearly (obligatory xkcd). Because they are designed to view very distant objects, they can only view a tiny portion of the sky at a time (angular distance): and there is a lot of sky.
However, we have a pretty good idea of where the Roadster is going, so we can at least narrow down the area. Over time I would expect Earth and Mars to perturb its orbit and make it more unpredictable, but for the next couple of years, we should be able to figure out its general location.
Knowing that, we could point telescopes in its general area and search. However, this is worse than the needle-in-a-haystack problem. It would be more like dropping a haystack the size of Texas on the moon, with a needle placed somewhere on top. You can only search 10m2 at a time, and Texas has a lot of m2. Even if the needle is in the telescope's view, you might not realize it unless the Sun or another bright body is hitting it at the right angle to reflect in your direction. It gives off no light of its own.
Your question mentioned "the" Roadster but also appears to be more generally-applicable to objects the size of "a" Roadster. A similar problem would be tracking J002E3, widely speculated to be an old Apollo rocket. We know it is out there, and every once in a while we catch a glimpse, but it is both notoriously difficult to track and far closer than the Roadster is to Earth. It also gives off no light nor does it transmit anything. It is close enough to the size of a car and is in the same order of magnitude distance from Earth to provide a good real-world example of how difficult this can be.
If Elon wanted to know where his car is at all times, he would have been better off equipping it with an RTG (or solar panels) and high-gain antenna.
tl;dr: When the Roadster is about 1 AU away from both the Earth and the Sun, it will have an apparent magnitude $m$ equal to its absolute magnitude $M$ or +28. According to Wikipedia Hubble's limiting magnitude is +31, and for large Earth-bound observatories which need to contend with skyglow the limiting magnitude is in the ballpark of +24 to +26, depending on aperture, conditions, adaptive optics, exposure time, etc. So Roadster will certainly be theoretically trackable optically for at least a month or two, if not many more!
Thanks to the (presumably) still attached 2nd stage rocket body, starting point near Earth, and mild eccentricity, Roadster will be trackable for quite a while in fact!
above: From this answer, originally from here.
I'm going to characterize the 8 x 3.6 meter white 2nd stage as a 6 meter diffuse sphere(ical cow) with albedo 0.3 for order of magnitude estimation.
The expression for absolute magnitude $M_{Abs}$ by rearranging the equation here is:
$$M_{Abs} = 5 \left(\log_{10}(1329) -\frac{1}{2}\log_{10}(\text{albedo}) -\log_{10}(D_{km})\right)$$
For the "spherical cow" spacecraft that turns out to be an absolute magnitude of +28. You get the same answer if you start with the Sun at magnitude -27, then knowing that a 6 meter circle at 1 AU from the sun intercepts 1E-22 of its sunshine, -27 + 2.5*22 = +28!
Knowing the absolute magnitude of an object, you calculate the apparent magnitude $m$ using:
$$ m = M_{Abs} + 2.5 \log_{10}\left(\frac{d_{SR} \ d_{RE}}{1 \ \text{AU}^2 O(1)}\right), $$
where $d_{SR}$ and $d_{RE}$ are the Sun-Roadster and Roadster-Earth distances, each normalized by 1 AU, and the factor $O(1)$ is the phase integral, of order unity, taking into account the angular difference between the direction of illumination and the direction of viewing. In an order of magnitude calculation, this only becomes really significant when the body moves between the Sun and the viewer. See https://en.wikipedia.org/wiki/Absolute_magnitude#Solar_System_bodies_(H).
So for example when the Roadster is about 1 AU away from both the Earth and the Sun, it will have an apparent magnitude $m$ equal to its absolute magnitude $M$ or +28. According to Wikipedia Hubble's limiting magnitude is +31, and for large Earth-bound observatories which need to contend with skyglow the limiting magnitude is in the ballpark of +24 to +26, depending on aperture, conditions, adaptive optics, exposure time, etc. So Roadster will certainly be theoretically trackable optically for at least a month or two, if not many more!
above: Top: Distance data from JPL's Horizons plotted using Python from here. Bottom: Estimated apparent magnitude using distances from Horizons plus math shown here in the text. Your milage may vary, but probably within +/-2 magnitudes of "official" predictions when they come out. NOTE: This answer shows that Horizons predicts +21 at 30 days, 4 magnitudes brighter than what I have here.
Here are some of the first optical sighting of Roadster. With these, the orbit can be refined, making it much easier for telescopes with much larger apertures to pinpoint its positing in the future as it gets farther and farther away from Earth, needing the light-collecting power of larger aperture telescopes.
A really cool GIF can be seen in the Space.com article Observatory Spots Elon Musk's Tesla Roadster Zooming Through Space (Video). It is over 7 MB so I can't add it here. However, here are ten frames from somewhere in the middle. Still, you should go see the whole thing.
DEMIOS image below, from here as also tweeted by Jonathan McDowell. The little dot near the center moving to the right and up is Roadster in reflected sunlight, probably mostly from the white FH 2nd stage still attached.
This morning at 6:09 AM local time from the South of Spain, Elecnor Deimos Space Surveillance & Tracking Centre captured a moving object at a distance of 520.000 km and at only 20 arcmin from the predicted position of the Starman-driven Tesla Roadster, which was launched towards Mars by SpaceX’s Falcon Heavy vehicle during a historic event on the 6th of February 2018. Whether the object observed is the Tesla vehicle itself or the upper stage of the launcher is yet to be confirmed. (emphasis added)
Later:
Elecnor Deimos Space Surveillance and Tracking Centre, Deimos Sky Survey (DeSS), has obtained new images of the Spaceman-driven Tesla Roadster on its way to Mars. It has been confirmed that the vehicle is still attached to the upper stage of SpaceX’s Falcon Heavy launcher.
The images, which captured the vehicle at a distance of 720.000 km from Earth (almost twice the distance of the Moon), show a flickering effect that suggests that the Tesla Roadster is spinning fast.
Annotated/cropped:
Original GIF showing moving spacecraft with variable brightness as it rotates:
below: Deimos Sky Survey (DeSS) is a project aimed at the detection and tracking of near-Earth space objects. From here.
The Roadster itself? No. Asteroid surveys aren't really set up to track things that small.
However, the Roadster is still attached to the upper stage of the Falcon Heavy. The full assembly is roughly the same size and brightness as an Apollo upper stage, and as the detection of "asteroid" J002E3 shows, it's likely to appear in sky surveys from time to time. Expect it to start picking up provisional asteroid identifiers in a few years.
