Gravitational Binding Energy?
A binary system consisting of two stars, each with a mass of 2 × 10^30 kg, is in a circular orbit around their common center of mass. If the orbital speed of each star is 1.5 × 10^6 m/s, calculate the gravitational binding energy of the system. Explain why this energy is crucial for the system's stability.
1 Answer
📌 CONCEPT: Gravitational binding energy is the energy required to separate two objects in a binary system, such as stars, by an infinite distance, making them non-interacting.
📐 RULE / FORMULA: The gravitational binding energy (E) of a binary system with masses m1 and m2, at a distance r, is given by the formula: E = -G × (m1 × m2) / r
💡 WORKED EXAMPLE: For the given binary system, we have m1 = m2 = 2 × 10^30 kg, and r is the radius of their circular orbit. We can calculate the gravitational potential energy of one star, then multiply it by 2. The orbital speed (v) is given by the formula v^2 = G × (m1 + m2) / r. After finding r, we substitute the values into the gravitational binding energy formula.
⚠️ COMMON MISTAKE: Students often confuse gravitational potential energy with gravitational binding energy, forgetting that the latter involves the energy required to completely separate the two objects.
29 Jun 26
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