The drawing (not to scale) shows one alignment of the sun, earth, and moon. The gravitational force SM that the sun exerts on the moon is perpendicular to the force EM that the earth exerts on the moon. The masses are: mass of sun = 1.99 1030 kg, mass of earth = 5.98 1024 kg, mass of moon = 7.35 1022 kg. The distances shown in the drawing are rSM = 1.5 1011 m and rEM = 3.85 108 m. Determine the magnitude of the net gravitational force on the moon.
To determine the magnitude of the net gravitational force on the moon, we need to consider the gravitational forces exerted by both the sun and the earth on the moon. The net gravitational force can be found by calculating the vector sum of these two forces.
The gravitational force between two objects can be calculated using Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (approximately 6.67 x 10^-11 Nm^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between their centers.
First, let's calculate the magnitude of the gravitational force between the moon and the sun:
F_SM = G * (mass of sun * mass of moon) / r_SM^2
Substituting the given values, we have:
F_SM = (6.67 x 10^-11 Nm^2/kg^2) * (1.99 x 10^30 kg * 7.35 x 10^22 kg) / (1.5 x 10^11 m)^2
Calculating this expression will give us the magnitude of the gravitational force between the sun and the moon, F_SM.
Similarly, let's calculate the magnitude of the gravitational force between the moon and the earth:
F_EM = G * (mass of earth * mass of moon) / r_EM^2
Substituting the given values, we have:
F_EM = (6.67 x 10^-11 Nm^2/kg^2) * (5.98 x 10^24 kg * 7.35 x 10^22 kg) / (3.85 x 10^8 m)^2
Calculating this expression will give us the magnitude of the gravitational force between the earth and the moon, F_EM.
Finally, to find the magnitude of the net gravitational force on the moon, we need to calculate the vector sum of F_SM and F_EM. Since the forces are perpendicular to each other, we can use the Pythagorean theorem:
F_net^2 = F_SM^2 + F_EM^2
Taking the square root of both sides will give us the magnitude of the net gravitational force on the moon, F_net.
Once you have calculated F_net using the given values and the equations mentioned above, you will have the required answer.