You can simply lie to them.
You can lie in different ways:
Tell them that there's only enough resources for them and their family.
You can embellish if they press. You can come up with very elaborate scientific reasons involving weight, rocket fuel, time constraints, etc. This won't fool the more educated engineers who are well versed in space faring science and determined to do the mathematics themselves, but it will fool most of the people who are coming on the trip.
There's a few other less scientific ones that might involve food rations or something like that, but very determined people will insist that they can survive on less to bring one more person. You'd have to combine these lies and make them hard/difficult to disprove.
Tell them that more ships will be made for other people.
No one has to know that only ten are made, and it would be hard to disprove this lie. Google Earth updates its satellite imagery every one to three years, so over the course of waiting the average person won't be able to do their own satellite sleuthing.
If they believe that the people will be saved anyway, they're not going to want to insist that they come, especially if this lie is combined with the previous one.
In part of the onboarding process, keep them in a secure location.
In whatever process is made to process the right people and confirm that they are valid candidates for traveling to Mars, don't allow them to leave after the process is done. 500
They'll think they'll go home but they won't be able to. Your government agencies can retrieve their stuff for them, and their distant family/neighbours don't have to really know what's going on.
Once in a secure location, they're stuck there until you're ready to go to Mars.
Lie about their destination or purpose of leaving. - Thanks to <PERSON>.
You can tell them that they're under arrest. You have some powerful people at play so forging enough documentation to convince the person that the evidence is sufficient for a peaceful arrest without the usage of force is very realistic.
You could also tell them that it's a very exotic dream trip or some desired reason based on the research and information you have on them, but some things you say might be suspicious to them, since many appealing trips are often used in scams.
You can also offer payment in tandem with this. You could give an initial payment with a promise of a higher payment later in order to gain the person's trust. 821