Can we stop or prevent the effects planets and stars have on our life?

Every particle in this Creation is related to us and our life. 
It is said that the whole Creation, right from the smallest atom to the subtlest Mahat Tattva (a fundamental principle of existence said to be far subtler than the Ego) are all connected and strung together by a single thread.
Scientists today say, that when a butterfly in South America flutters its wings, it affects the clouds hovering over China (implying a deep level of inter-connectedness). So, in this way, the whole world is one.

Our ancestors and Rishis (wise sages) also used to say that when you perform a Yagna (sacred fire ritual) here, the vibrations and effects will reach everywhere. When you pray, your prayers have the power to move the whole world.

This is true. But do not misunderstand this and take a fatalist view of everything around you, thinking that everything is already pre-destined and you have no choice but to endure your fate. Do not think that you have no freedom. Life is a combination of destiny and free will. There are some things we can change through our actions, and there are some things that we just cannot change and we have to accept them the way they are.
For example, after the age of 17-20 years, your height cannot increase any further. If you are five feet tall at that age, then that is what your height is going to be. But your weight can increase or decrease. So if you have gained 100 kilos in weight, you cannot say, “Oh, this is my destiny. What can I do?” Of course you can reduce your weight. But you cannot change your height. The same with life also.

There are many things we can change, and many things that we cannot change. The planets and stars definitely do have their effects on our life, but we can stop or even prevent that. This is why the unique number of 108 has been prescribed when it comes to chanting.
There are nine planets and twelve zodiac constellations. When these nine planets move through the twelve zodiac signs, they can create 108 different kinds of effects in our lives. In order to save ourselves from any ill effects of those vibrations, we chant Om Namaha Shivaya.

When we chant Om Namaha Shivaya, a protective shield is formed around us which saves us from these effects.