What is Jeans mass ? Derive its expression stating your assumptions
Jeans mass is a fundamental concept in astronomy and astrophysics that helps us understand the conditions under which gravitational collapse occurs in a molecular cloud, leading to the formation of stars and other celestial objects. To comprehend the Jeans mass, let's delve into its derivation and the underlying assumptions.
Assumptions:
1. Isothermal Gas: Consider a cloud of gas in hydrostatic equilibrium, which means it's stable and not collapsing or expanding significantly.
2. Gravity: Gravity is the dominant force governing the behavior of the gas cloud.
3. Thermal Pressure: The gas exerts pressure due to its temperature, and this pressure opposes gravitational collapse.
4. Static Environment: We assume the cloud is not perturbed or undergoing any major external influences.
Derivation:
1. Equilibrium between Gravitational Force and Pressure:
At any point within the gas cloud, the gravitational force pulling inward is balanced by the
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