Question

What is the magnitude of the gravitational force acting on the earth due to the sun?

Answer 1

Answer: $3.524(10)^{22}N$

Explanation:

According to Newton's law of Gravitation, the force $F$ exerted between two bodies of masses $m1$ and $m2$  and separated by a distance $r$  is equal to the product of their masses and inversely proportional to the square of the distance:

$F=G\frac{(m1)(m2)}{r^2}$   (1)

Where:

$G$ is the Gravitational Constant and its value is $6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}$  

$m1=1.99(10)^{30}kg$ is the mass of the Sun

$m2=5.972(10)^{24}kg$ is the mass of the Earth

$r=1.50(10)^{11}m$  is the distance between the Sun and the Earth

Substituting the values in (1):

$F=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}\frac{(1.99(10)^{30}kg)(5.972(10)^{24}kg)}{(1.50(10)^{11}m)^2}$   (2)

Finally:

$F=3.524(10)^{22}N$   This is the gravitational force acting on the earth due to the sun

Answer 2

The magnitude of the gravitational force : 3.48.10²² N

Further explanation

Gravity is a force that arises because of the attraction between objects with mass.

The magnitude of this attraction is proportional to the mass of the object.

The greater the mass of the object, the greater the gravitational force

Relationships can both be stated in

Newton's Gravity Law:

$\rm F=G.\dfrac{m_1.m_2}{r^2}$

with F = gravitational force,

G = gravitational constant,

m1, m2 = mass of object,

r = distance between two objects.

From the available data:

m earth = 5.98.10²⁴ kg

m sun = 1.99.10³⁰ kg

r = 150 million km = 15.10⁷ km  = 15.10¹⁰ m

G = 6.67.10⁻¹¹N.m² / kg²

We put in the formula:

$\rm F=6.67.10^{-11}.\dfrac{5.98.10^{24}.1.99.10^{30}}{(15.10^{10})^2}\\\\F=3.48.10^{22}\:N$

So The earth exerts 3.48.10²² N  of force on the sun, exactly the same amount of force the sun exerts on the earth

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Keywords: gravitational force, Newton's Gravity Law, mass, sun,earth