While "What's your sign?" has become a popular way to gauge compatibility, in actuality it is only a small piece in a very large astrological compatibility puzzle. The Sun in our natal charts represents our outward personality, identity, and how we want to be seen in the world. While the way we present ourselves and how we want to be seen is a part of it, there are many other facets to pay attention to when it comes to relating and compatibility. Though to me, looking only at the Sun (or Moon), leaves a lot to be desired in my book of love.
What is compatibility between two people? That is the ultimate question. Compatibility comes from the same Latin root as "compassion" and "com-" meaning "with, together" and living in harmony. Of course this applies to all relationships...romantic, familial, work, and friendships.
Of course there are many theories, here are a few of my favorites and how I see them relating to particular planets/ asteroids in the natal astrology chart:
In astrology I orient harmony together as related to a blend of our love language, attachment, communication styles, passion, feeling seen. These areas of life reveal themselves in certain archetypal patterns in the natal charts or synastry between two people or composite charts. These patterns, or in this case planets, give us a better understanding of the lessons or healing between two people whether that be romantic partnerships, business partners, or even family members. I also believe there are "types of soulmates" that reveal patterns of these relating.
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I pay the most attention to personal planets or asteroids because they are closest to us in the solar system and also move the fastest. There are also several "sex" or erotic asteroids I utilize in chart comparisons, but I don't go into that here. It's also of utmost importance to focus on these factors in your own chart before thinking about others'. Astrology is not a tool to diagnose to try to figure someone else out, it can be helpful most as a self-awareness tool.
Here are the main things I look at between two charts (synastry) and in the composite (a combined chart of two people). They point to places of ease in relating versus more difficulty. Though none of these are deal breakers!
Moon :: unconsciousness needs, attachment style, home life important to know when living with someone, internal rhythms and sense of self
Example: You have a fire sign moon, such as Aries, and tend to lean more towards optimism or sometimes even emotional avoidance. However, one of your best friends has a water sign moon, such as Cancer, and is often overwhelmed by emotions and moves through how she feels more quickly. Knowing the needs of your own chart can be helpful to give yourself and others more compassion around their emotional process. (Read more about Moon compatibility on Elite Daily)
2. Sun :: outward personality and identity, how you want to be seen in the world, do your identities match or is there a clash of ego? Read more on Bustle about why dating an "incompatibility zodiac" sign doesn't really matter.
Example: Your Gemini sun partner is really extroverted, even though she has a Pisces Moon which makes her sensitive. Out in the world she may present one way, but may feel differently or overwhelmed when in large groups.
3. Mercury :: communication style, intellectual stimulation, can you hear each other and communicate easily
Example: Your sister has a Mercury in Leo and speaks with a fiery clarity and purpose, while your Mercury is in retrograde in Cancer and communicates more with feelings and intuition. Communication styles are different but doesn't mean they can't work together to find mutual understanding.
4. Venus :: love language, love style, feelings of compatibility and harmony
Example: Your mother has a Venus in Libra and loves relating one-on-one and loves giving you gifts. You have a Venus in Virgo and tend to show your love through doing nice things and acts of service.
5. Mars :: conflict style, turn on, or how you move in the world
Example: Your business partner has Mars in Scorpio and tends to take his time in decision making needing to uncover as much information as possible, while you have Mars in Sagittarius that keeps the big picture in mind but tends to move more quickly.
6. Juno :: what motivates you to be in partnership, what is non-negotiable (read more here) Juno applies most to romantic and business partners.
Example: Your Juno in Capricorn craves stability and security in romantic relationships and values a good partner based on their ability to be this. Your romantic partner has Juno in Pisces and prefers less structure and more flowing relationship style that may not need commitment based on other parts of their chart, such as the descendant.
Descendant :: type of relationship/container, what you want a relationship to feel like, ideal relationship
Example: Your partner has Aquarius descendant and craves novelty and non-traditional relationships, and you have Taurus and depending on other parts of your chart you may be an adventurous person but prefer tradition when it comes to your relationships.
I'm not going to tell you all my secrets about what I look for within these, but am hoping this can showcase more of the complexity of relating..for that it makes sense to schedule a personal reading or other session.;)