Question

Q|C Assume dark matter exists throughout space with a uniform density of 6.00 × 10⁻²⁸kg / m³

Answer 1

(b) By Gauss’s law, the dark matter would create a gravitational field acting on the Earth to accelerate it toward the Sun. It would

shorten the duration of the year in the same way that 8.41× $10^{6}$kg of extra material in the Sun would.

This has the fractional effect of

$\frac{8.41*10^{6}kg }{1.99*10^{30}kg } = 4.23*10^{-24}$of the mass of the Sun.

No. It is only the fraction 4.23×$10^{-24}$ of the mass of the Sun.

Which Gauss law governs gravity?

• According to Gauss's law of gravity, gravitational flux through any closed surface is proportional to the enclosed mass.

• Gauss's law for gravity, also known as Gauss' flux theorem for gravity, is a physical law that is equivalent to Newton's law of universal gravitation.
• Carl Friedrich Gauss inspired the name. The flux (surface integral) of the gravitational field over any closed surface is equal to the mass enclosed, according to this formula. Gauss' law of gravity is frequently more convenient to work with than Newton's law.

• Gauss's law for gravity has a mathematically similar form to Gauss's law for electrostatics, which is one of Maxwell's equations. Gauss' law of gravity has the same mathematical relationship to Newton's law as Gauss' law of electrostatics does to Coulomb's law.
• This is due to the fact that both Newton's law and Coulomb's law describe inverse-square interaction in three dimensions.

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