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
Olivier B.
Jul 5, 2015

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

sun-earth: 3.56⋅1022N
earth-moon: 1.97⋅1020N
sun-moon: 4.33⋅1020N

Explanation:

Newton's law of gravitation states that the force exerted by a body on another body is calculated as below:

F=G⋅m1⋅m2d2

with

G=6.67⋅10−11m3s−2kg−1 the universal gravitation constant
m1 the first body's mass (expressed in kg)
m2 the second body's mass (expressed in kg)
d the distance between the two bodies' mass centers (expressed in m)

Knowing that:

mS=2.0⋅1030kg is the sun's mass
mE=6.0⋅1024kg is the earth's mass
mM=7.3⋅1022kg is the moon's mass

dSE=1.5⋅1011m is the distance between the sun and the earth
dEM=3.85⋅108m is the distance between the earth and the moon

We can calculate:

FSE=G⋅mS⋅mE(dSE)2

=6.67⋅10−11⋅2.0⋅1030⋅6.0⋅1024(1.5⋅1011)2

=6.67⋅2.0⋅6.0⋅1030+24−111.52⋅1022

=6.67⋅12⋅1043−222.25=80.042.25⋅1021≈3.56⋅1022N

FEM=G⋅mE⋅mM(dEM)2

=6.67⋅10−11⋅6.0⋅1024⋅7.3⋅1022(3.85⋅108)2

=6.67⋅6.0⋅7.3⋅1024+22−113.852⋅1016

=6.67⋅43.8⋅1035−1614.8225=292.14614.8225⋅1019≈1.97⋅1020N

FSM=G⋅mS⋅mM(dSE−dEM)2

=6.67⋅10−11⋅2.0⋅1030⋅7.3⋅1022(1.5⋅1011−3.85⋅108)2

=6.67⋅2.0⋅7.3⋅1030+22−11(1.5−0.00385)2⋅1022

≈6.67⋅14.6⋅10411.52⋅1022

=6.67⋅14.6⋅1041−222.25=97.3822.25⋅1019≈4.33⋅1020N

Related questions
Impact of this question
40681 views around the world
You can reuse this answer
Creative Commons License