Question

One planet is 3.00 x 1012 kg and another is 2.00 x 1010 kg and they are separated by a distance of 10 x 1015 m. Calculate the gravitational force between the two planets.

Answer 1

The gravitational force between the two planets is
`4\cdot 10^(-20) \ N`

Step-by-step explanation:

Newton’s Law of Universal Gravitation

Objects attract each other with a force that is proportional to their masses and inversely proportional to the square of the distance between them.

`\displaystyle F=G{\frac {m_(1)m_(2)}{r^(2)}}`

Where:

m1 = mass of object 1

m2 = mass of object 2

r = distance between the objects' center of masses

G = gravitational constant:
`6.67\cdot 10^(-11)~Nw*m^2/Kg^2`

The mass of the planets are:

`m1 = 3\cdot 10^(12)\ Kg`

`m2 = 2\cdot 10^(10)\ Kg`

And the distance is:

`r = 10\cdot 10^(15)\ m`

Applying the formula:

`\displaystyle F=6.67\cdot 10^(-11){\frac {3\cdot 10^(12)*2\cdot 10^(10)}{(10\cdot 10^(15))^(2)}}`

Calculating:

`\displaystyle F=6.67\cdot 10^(-11){\frac {6\cdot 10^(22)}{1\cdot 10^(32)}`

`F = 4\cdot 10^(-20) \ N`

The gravitational force between the two planets is
`4\cdot 10^(-20) \ N`