Question

The existence of the dwarf planet Pluto was proposed based on irregularities in Neptune's orbit. Pluto was subsequently discovered near its predicted position. But it now appears the discovery was fortuitous, because Pluto is small and the irregularities in Neptune's orbit were not well known. To illustrate that Pluto has a minor effect on the orbit of Neptune, calculate the acceleration due to gravity at Neptune, in m/s2, due to Pluto when they are 4.50x1012 m apart, as they are at present. The mass of Pluto is 1.4x1022 kg.

Group of answer choices
4.6x10-14
5.7x10-15
6.8x10-16
7.9x10-17

Answer 1

Acceleration due to gravity,
`a=4.61* 10^(-14)\ m/s^2`

Step-by-step explanation:

It is given that,

Mass of Pluto,
`m=1.4* 10^(22)\ kg`

Distance between Neptune and Pluto,
`r=4.5* 10^(12)\ m`

The force of gravity is balanced by the gravitational force between Neptune and Pluto. It is given by :

`a=(Gm)/(r^2)`

`a=(6.67* 10^(-11)* 1.4* 10^(22))/((4.5* 10^(12))^2)`

`a=4.61* 10^(-14)\ m/s^2`

So, the acceleration due to gravity at Neptune due to Pluto is
`4.61* 10^(-14)\ m/s^2`. Hence, this is the required solution.