How Does the Sun's Gravitational Pull on the Moon Compare to Earth's?

[girl_saint86]

Homework Statement

What is the ratio of the gravitationalpull of the sun on the moon to that of the Earth on the moon?(Assume the distance of the moon from the suncan be approximated by the distance of the Earth from the sun.)

Homework Equations

F$$_{g}$$ = (Gm$$_{1}$$m$$_{2}$$)/r^{2}

The Attempt at a Solution

What i got from the question the surface to surface distance is the same and to calculate F_{g} so using the orbital distance of the Earth from moon i found out theorbital disrance of sun to moon but my answer s totally different from the aI am to get


Thanks for any help possible

 

[yourdadonapogostick]

What i got from the question the surface to surface distance is the same and to calculate F_{g} so using the orbital distance of the Earth from moon i found out theorbital disrance of sun to moon

The question said to use the distance between the Sun and the Earth as the distance between the Sun and the Moon.

 

[Moetasim]

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As a scientist, it is important to approach this question with precision and accuracy. The ratio of the gravitational pull of the sun on the moon to that of the Earth on the moon can be calculated using Newton's Law of Gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Using this equation, we can calculate the gravitational pull of the sun on the moon (F_s) and the gravitational pull of the Earth on the moon (F_e) by plugging in the respective masses and distances.

F_s = (G*m_s*m_m)/(r_{sm})^2
F_e = (G*m_e*m_m)/(r_{em})^2

Where G is the gravitational constant (6.67 x 10^-11 N*m^2/kg^2), m_s is the mass of the sun (1.99 x 10^30 kg), m_e is the mass of the Earth (5.97 x 10^24 kg), m_m is the mass of the moon (7.35 x 10^22 kg), r_{sm} is the distance between the sun and the moon (1 AU = 1.5 x 10^11 m), and r_{em} is the distance between the Earth and the moon (3.84 x 10^8 m).

Plugging in these values, we get F_s = 4.46 x 10^20 N and F_e = 1.98 x 10^20 N.

Therefore, the ratio of the gravitational pull of the sun on the moon to that of the Earth on the moon is F_s/F_e = 4.46 x 10^20 N/1.98 x 10^20 N = 2.25.

This means that the gravitational pull of the sun on the moon is about 2.25 times stronger than the gravitational pull of the Earth on the moon.

It is important to note that this is a simplified calculation and does not take into account other factors such as the gravitational pull of other planets, the moon's orbit around the Earth, or the Earth's orbit around the sun. However, it gives us a good approximation of the ratio between these two gravitational forces.