The force of attraction of the Earth to the sun is 1.6 times less than the force of attraction of Venus to the Sun

| March 1, 2021 | education

The force of attraction of the Earth to the sun is 1.6 times less than the force of attraction of Venus to the Sun. How many times is the distance between Venus and the Sun less than the distance between the Earth and the Sun, if the mass of Venus is 0.8 Earth masses.

Fvs / Fzs = 1.6
mw = 0.8 * m3 = (4 * 5) * mz.
Rzs / Rvs -?
According to the law of universal gravitation, the force of attraction is determined by the formula:
Fвс = G * mв * mс / Rвс ^ 2, where Fвс is the gravitational force of Venus and the Sun, G is the gravitational constant, mв is the mass of Venus, ms is the mass of the sun, Rвс is the distance between Venus and the Sun.
Fzs = G * mz * mc / Rzs ^ 2, where Fzs is the gravitational force of the Earth and the Sun, G is the gravitational constant, mz is the mass of the Earth, mc is the mass of the sun, Rzs is the distance between the Earth and the Sun.
Rvs ^ 2 = G * mv * mc / Fvs.
Rvs = √ (G * mv * mc / Fvs).
Rzs ^ 2 = G * mz * mc / Fzs.
Rzs = √ (G * mz * mc / Fzs).
Rzs / Rvs = √ (G * mw * mw / Fzs) / √ (G * mw * mw / Fws) = √ (mz * Fws / Fzs * mw) = √ (1.6 * 5/4) = √2 = 1.4.
Answer: 1.4 times the distance between Venus and the Sun is less than the distance between the Earth and the Sun.



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