Question

The Mass of planet Jupiter is 1.9*1.10²7 kg and that of the sun is 1.99*³0 kg. The mean distance of the Jupiter from the sun is 7.8*10¹¹m. Calculate the gravitational force which the sun exerts on Jupiter.

Answer 1

Gravitation

Given,
The mass of jupiter = 1.91×10^27 kgs
and the mass of sun = 1.99×10^30 kgs (there is a mistake in the question)
mean distance between them = 7.8×10^11 m

Have to find the gravitational force.

Now we know that gravitational force = {(GMm)/r²} [where M and m are the masses of the two bodies, r is the distance between them and G is the gravitational constant (G=6.67×10^(-11)Nm^2/kg^2 ]

So plotting the values we get
$f = \frac{6.67 \times {10}^{ - 11} \times 1.91 \times {10}^{27} \times 1.99 \times {10}^{30} } {(7.8)^{2} \times 10^{11 \times 2}}$
where f is the force excerted by Sun or say Jupiter.
$or \: f = \frac{6.67 \times {10}^{ - 11-(11 \times 2)} 1.91 \times {10}^{27} \times 1.99 \times {10}^{30} }{(7.8)^2 }$
$or \: f = \frac{6.67 \times 1.91 \times 1.99 \times {10}^{30 + 27-33} }{(7.8)^2 }$
$or \: f = 0.00416699 \times {10}^{26} newtons$$or \: f = 4.16699 \times {10}^{23} newtons$

So the force exerted by sun on Jupiter is 4.16699×10^23 N or kg.m/s²

That's it
Hope it helped (●´ϖ`●)

Answer 2

Explanation:

We have,

• $\sf M_J=1.9×10^{27}\: kg$
• $\sf M_S = 1.99×10^{30}\: kg$
• $\sf r=7.8×10^{11}\: m$
• $\sf G =6.67×10^{-11}\: Nm^2 \: kg^{-2}$

$\sf F = \dfrac{GM_JM_S}{r^2}$

$\sf = \dfrac{6.67×10^{-11}×1.9×10^{27}×1.99×10^{30}}{(7.8×10^{11})^2}$

$\sf = 4.15×10^{23} \: N$