It's difficult to give an exact number for branches of Earth science, as the field is very broad and there's a lot of overlap between different areas of study.

Here's a breakdown of the major categories, with some examples within each:

1. Geology:

* Petrology: Study of rocks

* Mineralogy: Study of minerals

* Structural Geology: Study of Earth's structures and how they form

* Sedimentology: Study of sediments and sedimentary rocks

* Geomorphology: Study of landforms

* Paleontology: Study of ancient life

2. Oceanography:

* Physical Oceanography: Study of ocean currents, waves, and tides

* Chemical Oceanography: Study of the chemical composition of the ocean

* Biological Oceanography: Study of marine life

* Geological Oceanography: Study of the ocean floor

3. Meteorology:

* Synoptic Meteorology: Study of weather patterns

* Dynamic Meteorology: Study of the physics of weather

* Climatology: Study of climate and its changes

4. Atmospheric Science:

* Aerosol Science: Study of particles in the atmosphere

* Climate Modeling: Development of computer models to predict future climate

* Atmospheric Chemistry: Study of chemical reactions in the atmosphere

5. Hydrology:

* Surface Hydrology: Study of water on the Earth's surface

* Groundwater Hydrology: Study of water beneath the surface

* Hydrogeology: Study of the interaction between water and rocks

6. Geochemistry:

* Isotope Geochemistry: Study of the ratios of different isotopes in rocks and minerals

* Organic Geochemistry: Study of the chemistry of organic matter in the Earth

* Environmental Geochemistry: Study of the role of chemical processes in the environment

7. Geophysics:

* Seismology: Study of earthquakes

* Geodesy: Study of the Earth's shape and gravity field

* Geomagnetism: Study of the Earth's magnetic field

8. Space Science:

* Planetary Science: Study of planets and other celestial bodies

* Astrobiology: Study of the possibility of life on other planets

9. Environmental Science:

* Environmental Geology: Study of the interaction between humans and the Earth

* Environmental Chemistry: Study of the chemistry of the environment

* Environmental Biology: Study of the effects of environmental changes on living organisms

This is just a starting point. There are many other branches of Earth science, and new ones are constantly emerging.

In addition to the main categories, there are also many interdisciplinary fields that combine different branches of Earth science, such as:

* Earth System Science: Studies the Earth as a whole system

* Paleoclimatology: Studies past climates

* Biogeochemistry: Studies the interaction between biological, geological, and chemical processes

Ultimately, the "number of branches" of Earth science is not as important as the understanding that it is a vast and complex field with many different areas of study.