Question

Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line. The masses are Mv=0.815ME, MJ=318ME, Msat=95.1ME, Msun=1.99x10^30kg, ME=5.98x10^24kg and the mean distances of the four planets from the Sun are 108, 150, 778, and 1430 million km. Apparently the answer is 9.56x10^17 N but I'm not sure how to get to that .-.,

Answer 1

Answer: Total Force = $9.56*10^{17}$

Explanation:

Line points are:  Sun - Venus - Earth - Jupiter - Saturn

Newton's law of universal gravitation states that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This means:

$F=G\frac{m_{1} m_{2}}{r^{2} }$

Where,

G is the gravitational constant,

m1 and m2 are the masses of the objects,

and r is the distance between the centers of their masses.

So, if G value is $6.674*10^{-11} [\frac{m^{3}}{kg*s^{2}}]$, then we replace the equation with the corresponding values:

$F=6.674*10^{-11} (-\frac{0.815ME^{2}}{(4.2*10^{10})^{2}} + \frac{318ME^{2}}{(6.28*10^{11})^{2}} + \frac{95.1ME^{2}}{(1.28*10^{12})^{2}})$

To get the distances we subtract the distances between the sun and earth and the distances between the other planets and the sun.

Answer 2

You need to consider the following:
Me (mass of Earth) = 5.98 x 10^24 kg 
Ms (mass of Sun) = 1.99 x 10^30 kg 
G = 6.67 x 10^-11 N 

Formula:
 F = G * M1M2/r^2 
The ratio FT/F = 4.02x10^-4 / 14.8
 = 2.72x10^-5 

Since,
1/2.72x10^-5 = 36800
The fraction ratio is  1/36800
= 9.56x10^17 N