Assuming you are using radio to communicate back to earth, then earth's replies to us have already given away earth position to the locals. the cat is very much out of the bag, they know where earth is, and they know earth is communicating with someone at their end, and it isn't them.
There are steps that can be taken to minimise the 'damage'.
frequency hopping and encryption can be used to make a radio signal very hard to detect, if you don't have the key. Although, making it work across the distances involved, with the added complexity of everything being in disparate orbits, moving in different directions at different speeds will make things a bit tricky.
you can probably mask you approach by slingshoting around various bodies in the target solar system, only making significant engine burns when you are shielded from the inhabited planet by aforementioned bodies. the slingshot manoeuvre's are an efficient use of fuel anyway. but the shielding prohibition may may be impractical.
when your deceleration burn lights up an entire hemisphere of a planet like Jupiter or Saturn, which someone is probably looking at through a telescope, they're probably going to pay attention.
Given all of that, If they're beaming signals at me, the best option is probably a brief reply to indicate that we are intelligent, and then to back off a LONG way, and observe, and minimally communicate. |