In my story, the government is looking to get as many individuals as possible outside. Is there a way to convince the population that there will be an eclipse or some other astronomical event without people figuring out that the calculations don't add up?
I don't believe there is a way that a government could convince the population of an eclipse or significant astronomical event without a significant amount of collaborative material.
I would have said that the best way to get as many individuals outside as possible would be to stage some mass civil protest. Typically, such a protest would be against government, so the recipe would be for government to pass legislation intended to be massively unpopular and, very soon after, subtly to orchestrate a grass-roots counter movement to protest against it culminating in the people taking to the streets to show their solidarity.
It may be cynical, but I think people are more likely to take to the streets against their government rather than be convinced by them to take to the streets for some other reason.
It would be far easier to make an announcement Geological Service detected an alarming series of small (imperceptible by population) earthquakes apparently converging on [some city] National Guard (or whatever) will be arriving soon with tents and other facilities. It may be dangerous to remain anywhere near tall buildings...
We can map out eclipses centuries in advance. Here is a list in case any of these days would work for your story.
Other celestial events? Maybe.
Meteors and comets routinely pass by the Earth. Some of them are in known regular orbits, and some of them have never been seen prior to their approach.
NASA and other agencies have some telescopes looking for celestial bodies on a near-Earth trajectory. You could convince a lot of people if the entities with the most powerful telescopes predicted it. However, the object should become visible to weaker instruments as it comes closer so this may not remain credible for long.
Social events or disasters
Curiosity will get some people to watch an eclipse or a comet, but a lot more people will show up for a popular social event. And everyone will respond to a disaster.
If you go with a disaster, it could be the real deal or a fake announcement---and the fake news alerts could come from the anyone: government, conspiracy, hackers, etc.
As others said, eclipses are very predictable. Perhaps your government can time their nefarious scheme to happen during an actual eclipse. Lunar eclipses are better, since they are visible from everywhere, and at the same time. Solar eclipse is visible a fraction of earth surface, and it moves.
To get people outside, you can have government announce a harder to predict event, like incoming meteor shower (that can only be detected using a few radars or telescopes). Or you can have a man-made event like re-entry of a spaceship, deorbit of a space station, or deployment of a space mirror.
However, they could get a bunch of people outside at night by announcing a predicted visible supernova. They could even launch a satellite into LEO with the purpose of getting really bright for a short amount of time (enough time to draw people out of their homes).
Note that this only works if it is OK that people realize after they are outside that it is a hoax. That's because a satellite will move across the sky differently than a star. However, by the time they see that, they will be outside. Also, even if it is seen as a hoax in the few minutes that it is happening, people will probably head outside to try to figure out what is going on.