The gravitational force that the sun exerts on the moon is perpendicular to the force 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 = 1.50 × 1011 m and rEM = 3.85 × 108 m. Determine the magnitude of the net gravitational force on the moon.
Well, it is a right angle.
force=sqrt[(GMs (Mm/rEM^2)^2 + (Me/rSM^2)^2 ]
There is a little math here.
To determine the magnitude of the net gravitational force on the moon, we need to calculate the individual gravitational forces exerted by the sun and the earth on the moon, and then find the vector sum of these forces.
The gravitational force between two bodies can be calculated using Newton's law of universal gravitation, which states that the force is given by the equation:
F = G * (m1 * m2) / r^2
Where F is the gravitational force between the two objects, G is the gravitational constant (approximately 6.67 x 10^-11 Nm^2/kg^2), m1 and m2 are the masses of the objects, and r is the distance between their centers of mass.
Let's start by calculating the gravitational force exerted by the sun on the moon:
F_SM = G * (m_sun * m_moon) / r_SM^2
Substituting the given values:
m_sun = 1.99 x 10^30 kg
m_moon = 7.35 x 10^22 kg
r_SM = 1.50 x 10^11 m
F_SM = (6.67 x 10^-11 Nm^2/kg^2) * ((1.99 x 10^30 kg) * (7.35 x 10^22 kg)) / (1.50 x 10^11 m)^2
Now, calculate the gravitational force exerted by the earth on the moon:
F_EM = G * (m_earth * m_moon) / r_EM^2
Substituting the given values:
m_earth = 5.98 x 10^24 kg
r_EM = 3.85 x 10^8 m
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
Finally, find the vector sum of these forces to determine the net gravitational force on the moon:
F_net = sqrt(F_SM^2 + F_EM^2)
Calculate the square of each force, add the squared values, and then take the square root of the sum.
F_net = sqrt(F_SM^2 + F_EM^2)
Now you can substitute the calculated values into the equation to find the magnitude of the net gravitational force on the moon.