Why is there a greater gravitational force between the sun and earth than between the sun and moon?

Answer 1

It is the force of gravity between the earth and the moon that is greater than the force of gravity between the sun and earth. Let's look at the variables and see what's what.

Gravity is the force of attraction between two masses. Each pulls on the other, but there is just one net force (the force of gravity) acting between them. There is a mathematical formula which describes this force. The formula contains these variables:

Mass of object A (in kilograms)

Mass of object B (in kilograms)

Distance between objects A and B (in meters)

Gravitational constant (6.674 x 10-11 m3 kg-1 sec-2)

The actual formula is that the force (F) equals the gravitational constant (G) times the product of the masses (m1, m2) divided by the square of the distance (r) between them:

F = G (m1 x m2 / r2)

As mass increases, the force of gravity increases.

As distance increases, the force of gravity decreases.

If we put in the numbers and turn the crank to find an answer, we'll discover that the sun exerts a lot less force to keep the earth in orbit than the earth does to keep the moon in orbit. The earth-moon distance is short, so the r2 factor in the force between us and our satellite is an overwhelming "advantage" to the gravitational force in the earth-moon system. The sun is a monster, and its mass dwarfs that of the earth and moon, but it is so far away that the r2 factor in the sun-earth system offsets the sun's overpowering mass and leaves the gravitational force between us and our neighborhood star smaller than that between the us and luna.

Actually the sun's gravity at the earth is about 179 times the moon's. People think the moon's is larger because it has a bigger effect on tides. But that is because the difference between the moon gravity on the near side of the earth from the far side is greater than the sun's gravity difference. This is spelled out (with a lot of math) on the Wikipedia "tide" topic.

It is amazing how many web references get this wrong.

Also, it is intuitive as follows: the apparent size of the sun and moon is nearly the same. If you know that the sun is around 360 times as far away, then, since volume is proportional to the cube of radius, it is 360 cubed times as big. If you assume they have the same density, then it is also 360 cubed times as heavy. Gravity is proportional to weight and inversely proportional to distance squared, so you get the gravity being 360cubed/360squared=360 times as much. Now actually the density of the moon is about twice that of the sun so the answer is closer to 180 times. (these numbers are rough approximations, but it works out pretty close).

Answer 2

Force of gravity between any two objects is F = G (M1M2/R2).

'F' is the force. 'G' is the gravitational constant. 'M1','M2' are the masses of the objects. 'R' is the distance between their centers of mass.

Force between the sun and earth: Fse = G (MsMe/Rse2)

Force between the moon and earth: Fme = G (MmMe/Rme2)

Their ratio: Fse/Fme = ( G Ms Me Rme2 ) / ( G Mm Me Rse2 )

Fse/Fme = ( Ms Rme2 ) / ( Mm Rse2 ). This is interesting ... the answer doesn't depend on the mass of the earth !

Now we can just look up the 4 numbers in the TIME Almanac, and fill 'em in:

Fse/Fme = ( 1.98 x 1030kg x 3.844 x 108m ) / ( 7.3 x 1022kg x 1.496 x 1011m )

= (1.98 x 3.844)x 105 / (7.3 x 1.496) = 6.969 x 104. (rounded)

This says that the gravitational attraction between the sun and earth is almost 70,000 times as strong as the attraction between the earth and moon.

**** actually, he said all the right things, but forgot to square the distances. If he had done that, he'd get that the sun-earth attraction is 179 times the earth-moon one. By the way, the Wikipedia page on tides confirms this and also explains why tides are more influenced by the moon in spite of the sun's greater attraction: basically because the difference in moon attraction on the near and far side of the earth is greater than the difference in sun attractions.

Answer 3

The gravitational pull from the moon, on the earth is the same as the earth's pull on the moon. There is no difference between the two.

This is because the equation for gravity is F=kMm/R2 M is the mass of one object, m the other, you need both to find the total force of attraction. In this case we have M for earth, and m for the moon...you cannot separate the two.

Answer 4

Newton's Law of gravitation states that

F = G M1 M2/R2

Where F is the force in newtons, G is the universal gravitational constant and is 6.674 x 10-11 N m2 kg-2, M1 and M2 are the masses of the two objects, and R is the distance between them.

MSun = 1.989 x 1030 kg

MEarth = 5.9736 x 1024 kg

MMoon = 7.3477 x 1022 kg

REarth-Sun = 1.496 x 1011 m

REarth-Moon = 3.843 x 108 m

Plugging in these numbers into Newton's equation, we get...

FEarth-Sun = 3.54 x 1022 N

FEarth-Moon = 1.98 x 1020 N

... so the force of gravity between the sun and the earth is bigger than the force of gravity between the earth and the moon by about a factor of 200, in round numbers.

Answer 5

The Sun's gravity is 28 times greater than Earth's gravity.

Answer 6

Because there is no gravitational effect between the Moon and the Sun. The Moon relies entirely on the Earth for its attraction.

Answer 7

Because the gravitational forces depend on mass and distance. The Earth is more massive than the moon. and closer to the sun than the moon

Answer 8

earth is more massive than the moon