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Gravitational self-energy
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Energy needed to assemble a sphere of mass.
U = −3GM²/5RAssembling a uniform sphere from dust requires binding energy U = −3GM²/5R. It powers the early heating of stars and planets.
The Sun's self-energy ≈ −2.3×10⁴¹ J.
Compare to the Sun's total luminosity over time.
In more detail
Gravitational self-energy is the energy needed to assemble a body from its parts, and it is negative. It is the gravitational binding energy of planets and stars.
Real-world uses
- Estimating the energy released when a planet or star formed.
- Calculating the energy needed to disassemble a star.
- Astrophysicists estimate the energy released when a planet or star forms by gravitational collapse.
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Frequently asked questions
Why is it negative?
Because gravity is attractive, so bound systems have lower energy than separated parts.
How big is it for Earth?
Earth's gravitational binding energy is about 2.5 × 10³² joules.
Why is the self-energy negative?
Assembling the sphere from distant pieces releases energy, so the bound state has lower energy than the scattered pieces.
Related topics in Gravitation & Orbits
Neutron stars and white dwarfs · Dark matter evidence · Newton's shell theorem · Inertial vs gravitational mass · Equivalence principle · Orbital precession