Question

A comet passes near the Sun. When the comet is closest to the Sun, it is $\mathbf{9}\mathbf{\times }{\mathbf{10}}^{\mathbf{10}}$m from the Sun. You need to choose a time step to use in predicting the comet’s motion. Which of the following would be a reasonable distance for the comet to move in one time step, doing an iterative calculation by hand?$\mathbf{\left(}\mathbf{a}\mathbf{\right)}\mathbf{}\mathbf{1}\mathbf{\times }{\mathbf{10}}^{\mathbf{2}}\mathbf{m}\mathbf{}\mathbf{\left(}\mathbf{b}\mathbf{\right)}\mathbf{}\mathbf{1}\mathbf{\times }{\mathbf{10}}^{\mathbf{10}}\mathbf{m}\mathbf{}\mathbf{}\mathbf{\left(}\mathbf{c}\mathbf{\right)}\mathbf{}\mathbf{1}\mathbf{\times }{\mathbf{10}}^{\mathbf{11}}\mathbf{m}\mathbf{}\mathbf{\left(}\mathbf{d}\mathbf{\right)}\mathbf{}\mathbf{1}\mathbf{\times }{\mathbf{10}}^{\mathbf{9}}\mathbf{}\mathbf{m}$

Short answer

$1\times {10}^{11}\mathrm{m}$

Step-by-step solution

Identification of the given data

The given data can be listed below as,

The distance between the sun and the coment is, $9\times {10}^{10}\mathrm{m}$.

Significance of the Newton’s second law in predicting the comet’s motion

This law illustrates that the change in the momentum of a body is mainly equal to the imposed force’s direction and magnitude.

The equation of the Newton’s first law gives the distance for the comet to move in one-time step.

Determination of the reasonable distance of the comet to move in one time step

From Newton’s second law, the equation of the distance moved by the comet can be expressed as follows,

$\mathrm{s}=\mathrm{ut}+\frac{1}{2}{\mathrm{at}}^2$

Here, s is the distance moved, u is the initial velocity is the time taken, and is the acceleration.

As the closest distance of the comet from the sun is $9\times {10}^{10}\mathrm{m}$, then a same distance or more than this distance will be beneficial for understanding the velocity of the comet, otherwise the comet will vaporise if it gets more closer to the sun. Here, the distances such as $1\times {10}^2\mathrm{m},1\times {10}^{10}\mathrm{m}$, and $1\times {10}^9\mathrm{m}$goes beyond the closest distance between the comet and the sun, hence the comet will vaporise and its motion cannot be predicted. Only the distance $1\times {10}^{11}\mathrm{m}$is greater than the closest distance between the comet and the sun, hence, this distance is useful for predicting the motion of the comet if it’s initial velocity, time and the acceleration of the comet are known.

Thus, the reasonable distance for the comet to move in one time step is $1\times {10}^{11}\mathrm{m}$.