Once nirvana is reached is there any connection to earth available?

There is some misconception floating around regarding nirvana. Nirvana doe NOT mean that one is free from the cycle of rebirth. It means that one is free from suffering in the cycle of rebirth.

Rebirth in Buddhism is inevitable and cannot be escaped from. This is because of the law of causality - since every moment we create causes, we must exprience the effects in later times in our lives and environment. These effects are created in the depths of one's life the moment a cause is made (through action, word and thoughts), but much of it may not be apparent till it manifests in real life. Such effects exist, but stay in latent form in the depths of our lives till a manifest cause brings them into the fore.

Active life is the manifestation of such effects - latent karma brought into action. Life is an expression of the law of causality. Death (or passive life) is the other manifestation. Since the law is constant, so is life and death, therefore the cycle of birth and rebirth is constant. There is no escape from it, I think its a misconception that nirvana means freedom from this cycle.

True freedom is not being free of problems - it is to be able to employ the power of Buddhism freely to overcome sufferings and create a truly happy life.

In the Lotus Sutra chapter "Immeasurable Life Span of the Thus Come One", Buddha states -

“You must listen carefully and hear of the thus come one’s secret and his transcendental powers. In all the worlds the heavenly and human beings and asuras all believe that the present Shakyamuni Buddha, after leaving the palace of the Shakyas, seated himself in the place of enlightenment not far from the city of Gaya and there attained supreme perfect enlightenment. But good men, it has been immeasurable, boundless hundreds, thousands, ten thousands, millions of nayutas of kalpas since I in fact attained buddhahood."

Further he states - At that time the Buddha said to the multitude of great bodhisattvas: “Good men, now I will state this to you clearly. Suppose all these worlds, whether they received a particle of dust or not, are once more reduced to dust. Let one particle represent one kalpa. The time that has passed since I attained buddhahood surpasses this by a hundred, a thousand, ten thousand, a million nayuta asamkhya kalpas. “Ever since then I have been constantly in this saha world, preaching the Law, teaching, and converting. And elsewhere I have led and benefited living beings in hundreds, thousands, ten thousands, millions of nayutas and asamkhyas of lands."

In other words, Shakyamuni Buddha states he had been enlightened since the remote past, unlike what people believed that he attained Buddhahood for the first time under the Bodhi tree. Since he attained Buddhahood, he had been preaching the Law to countless beings. That should be documentary proof enough that nirvana does not stop rebirth - even the Buddha is born time and again in order to preach the Great Law.

This should be a comment, But I can't comment yet since my points are less than 50 and below is as of my understanding.

You are in a wrong view called 'Sakkaya Ditti' in Pali. You always think there is person, and he will attain Nirvana. But it is wrong. What lord Buddha praeches is neither 'Sakkaya Ditti' nor a 'Uchcheda Ditti'. He didn't preach there is a person. and He didn't preach there is not a person. There is only connections between continuously changing things.

If we took a tower build by stones, actually there is nothing called 'tower' but set of stones. Like wise, if we consider a person, there is nothing but set of things. Lets say you are 40 years old now. What are the things you have in your body when you are 1 year old? Nothing right? But how you can be recognize now as same you in age 1? because of the connection between things changed.

Nirvana is ending of having these set of things (person). That means, there will not be 'a person' when you attain Nirvana. I suggest you to read more about 'Pattichcha Samudpaada'.