The force of gravity between the Earth and the Sun is __________ the force of gravity between the Earth and the Moon.For reference,the average distance between the Earth and the Moon is 0.003 AU,the mass of the Moon is ,and the mass of the Sun is .
A) 86,000 times larger than
B) 260 times larger than
C) 140 times smaller than
D) 6,400 times smaller than

Question

The force of gravity between the Earth and the Sun is __________ the force of gravity between the Earth and the Moon.For reference,the average distance between the Earth and the Moon is 0.003 AU,the mass of the Moon is  ,and the mass of the Sun is  .
A) 86,000 times larger than 
B) 260 times larger than 
C) 140 times smaller than 
D) 6,400 times smaller than

Quizplus · Accepted Answer

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, as given by the equation:

F = G * (m1 * m2) / d^2

where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them.

Using this equation, we can compare the force of gravity between the Earth and the Moon and between the Earth and the Sun.

For the Earth-Moon system, we have:

F_EM = G * (m_Earth * m_Moon) / d_EM^2

where d_EM is the distance between the Earth and the Moon (0.003 AU) and m_Earth and m_Moon are the masses of the Earth and Moon, respectively.

For the Earth-Sun system, we have:

F_ES = G * (m_Earth * m_Sun) / d_ES^2

where d_ES is the distance between the Earth and the Sun (1 AU) and m_Sun is the mass of the Sun.

To compare the two forces, we can take the ratio F_ES/F_EM:

F_ES/F_EM = [(G * m_Earth * m_Sun) / d_ES^2] / [(G * m_Earth * m_Moon) / d_EM^2]
F_ES/F_EM = (m_Sun / m_Moon) * (d_EM / d_ES)^2
F_ES/F_EM = (1.989 x 10^30 kg / 7.342 x 10^22 kg) * (0.003 AU / 1 AU)^2
F_ES/F_EM = 260

Therefore, the force of gravity between the Earth and the Sun is 260 times larger than the force of gravity between the Earth and the Moon.

The correct answer is B: 260 times larger than.

The Force of Gravity Between the Earth and the Sun