# How Long Could Gravitational Contraction Power the Sun?

• Tuugii
In summary, the gravitational potential energy of a self-gravitating sphere is dependent on the mass and radius of the sphere. For the Sun, this energy is calculated as -2G(M_sun)^2/R. The timescale for gravitational contraction to supply the Sun's current rate of power can be found using the equation t = -(1/2)(W_sun)/(L_sun), where L_sun is the Sun's luminosity. The hint provided is to simply plug in the value of L_sun into the equation to find the timescale.
Tuugii

## Homework Statement

The gravitational potential energy W of a self-gravitating sphere of mass M and radius R depends on the detailed distribution of mass within the sphere, but it is generally of order of magnitude -GM^2/R. For the Sun, W_sun = -2G(M_sun)^2/R. What is the timescale
t = -(1/2)(W_sun)/(L_sun) over which gravitational contraction could have supplied the power radiated by the sun at it's present rate?

please give some hints, thanks a lot.

what is L_sun ?

(iknow that it is Luminosity, but try to find the value)

malawi_glenn said:
what is L_sun ?

(iknow that it is Luminosity, but try to find the value)

thanks for the reply. But I didn't understand what was your hint... :)

Tuugii said:
thanks for the reply. But I didn't understand what was your hint... :)

I meant, have you tried just to plug in the value of L_sun into that eq?

## What is gravitational contraction Q?

Gravitational contraction Q is a measure of the amount of energy released through the contraction of a gravitationally bound system, such as a star or a planet.

## How does gravitational contraction Q occur?

Gravitational contraction Q occurs when the gravitational force between particles in a system causes them to move closer together, converting potential energy into kinetic energy and releasing it as heat.

## What factors affect the value of gravitational contraction Q?

The value of gravitational contraction Q is affected by the mass of the system, the initial radius of the system, and the composition of the system's materials.

## What is the relationship between gravitational contraction Q and the age of a system?

The larger the value of gravitational contraction Q, the younger the system is, as more energy is released during the contraction process in the earlier stages of a system's formation.

## How is gravitational contraction Q related to the formation of celestial bodies?

Gravitational contraction Q plays a significant role in the formation of celestial bodies, as it is responsible for heating up and shaping protoplanetary disks, causing them to eventually form planets and other objects in the universe.

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