Newton's law of gravitation states that the force exerted by a body on another body is calculated as below:
F=(G*m_1*m_2)/d^2
with
G=6.67*10^(-11) m^3s^(-2)kg^(-1) the universal gravitation constant
m_1 the first body's mass (expressed in kg)
m_2 the second body's mass (expressed in kg)
d the distance between the two bodies' mass centers (expressed in m)
Knowing that:
m_S=2.0*10^30kg is the sun's mass
m_E=6.0*10^24kg is the earth's mass
m_M=7.3*10^22kg is the moon's mass
d_(SE)=1.5*10^11m is the distance between the sun and the earth
d_(EM)=3.85*10^8m is the distance between the earth and the moon
We can calculate:
color(red)(F_(SE))=(G*m_S*m_E)/(d_(SE))^2
=(6.67*10^(-11)*2.0*10^30*6.0*10^24)/(1.5*10^11)^2
=(6.67*2.0*6.0*10^(30+24-11))/(1.5^2*10^22)
=(6.67*12*10^(43-22))/2.25=80.04/2.25*10^21~~color(red)(3.56*10^22N)
color(blue)(F_(EM))=(G*m_E*m_M)/(d_(EM))^2
=(6.67*10^(-11)*6.0*10^24*7.3*10^22)/(3.85*10^8)^2
=(6.67*6.0*7.3*10^(24+22-11))/(3.85^2*10^16)
=(6.67*43.8*10^(35-16))/14.8225=292.146/14.8225*10^19~~color(blue)(1.97*10^20N)
color(purple)(F_(SM))=(G*m_S*m_M)/(d_(SE)-d_(EM))^2
=(6.67*10^(-11)*2.0*10^30*7.3*10^22)/(1.5*10^11-3.85*10^8)^2
=(6.67*2.0*7.3*10^(30+22-11))/((1.5-0.00385)^2*10^22)
~~(6.67*14.6*10^41)/(1.5^2*10^22)
=(6.67*14.6*10^(41-22))/2.25=97.382/2.25*10^19~~color(purple)(4.33*10^20N)