When the Earth, Moon, and Sun form a right triangle, with the Moon located at the right angle, the Moon is in its third-quarter phase.

Find the magnitude of the net force exerted on the Sun.

Find the direction of the net force exerted on the Sun. Give the direction relative to the line connecting the Sun and the Moon.

To find the magnitude and direction of the net force exerted on the Sun in this scenario, we need to consider the gravitational forces between the Earth, Moon, and Sun.

1. Magnitude of the net force:
The gravitational force between two objects can be determined using Newton's law of universal gravitation:

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

Where:
F is the gravitational force between the two objects,
G is the gravitational constant (approximately 6.67430 x 10^-11 N m^2/kg^2),
m1 and m2 are the masses of the two objects in question, and
r is the distance between the centers of the two objects.

We can consider the Earth-Moon system as a single object and calculate the gravitational force between this system and the Sun. The net force on the Sun will be equal in magnitude but opposite in direction to the force exerted by the Sun on the Earth-Moon system.

The mass of the Earth is approximately 5.972 × 10^24 kg, while the mass of the Moon is approximately 7.348 × 10^22 kg. The average distance from the Earth to the Moon is roughly 384,400 km (approximately 3.844 × 10^8 m).

Using these values, we can calculate the gravitational force between the Earth-Moon system and the Sun as follows:

F = G * ((m_Earth + m_Moon) * m_Sun) / r^2

Substituting the known values:

F = (6.67430 x 10^-11 N m^2/kg^2) * ((5.972 × 10^24 kg + 7.348 × 10^22 kg) * m_Sun) / (3.844 × 10^8 m)^2

2. Direction of the net force:
The direction of the net force is opposite to the direction of the force exerted by the Sun on the Earth-Moon system. Since the Moon is located at the right angle of the right triangle formed, the direction of the net force will be perpendicular to the line connecting the Sun and the Moon.

To determine the specific direction, we can consider the line connecting the Sun and the Moon as a reference line. The net force will be directed either towards the Sun or away from it, depending on the relative magnitudes of the gravitational forces involved.

To know the exact direction, we need to know the mass of the Sun (m_Sun). Once we have this information, we can calculate the magnitude and direction of the net force exerted on the Sun using the equations and principles described above.