During a solar eclipse , the moon , earth , and and sun all lie on the same line,with the moon between earth and sun. what force is exerted by the sun on the moon? what force is exerted by earth on the moon? what force is exerted by the sun on earth

1 Answer
Jul 5, 2015

During a solar eclipse, the forces between the sun, earth and moon are:

sun-earth: 3.56*10^22N
earth-moon: 1.97*10^20N
sun-moon: 4.33*10^20N

Explanation:

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)