Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

At its closest approach to the sun (perihelion), Mars is approximately 2.07 E 8 km away from our closest star. At aphelion, the point furthest away in its orbit, Mars is approximately 2.49 E 8 km away. Which of the following is a true statement? (1 point)

At aphelion, Mars is traveling at its highest speed.

At perihelion, Mars is traveling at its highest speed.

The speed at aphelion and perihelion are equal.

At perihelion, Mars is traveling at its lowest speed.

Sagot :

jacob193

Answer:

The first choice: Mars travels at the highest speed at the closest approach to the sun.

Explanation:

Assume that the sun is stationary and that the gravitational pull from the sun is the only force on Mars.

The mechanical energy of Mars is the sum of two components:

  • The gravitational potential energy [tex]\rm GPE[/tex] of Mars in relation to the sun,  and
  • The kinetic energy of planet Mars, [tex]\rm KE[/tex].

Let [tex]r[/tex] denote the distance between the sun and Mars. The [tex]\rm GPE[/tex] between the two would be proportional to [tex](-1/r)[/tex]. Thus, increasing the distance between the sun and Mars would increase the [tex]\rm GPE\![/tex] of Mars in relation to the sun.

The kinetic energy [tex]\rm KE[/tex] of Mars is proportional to the square of the speed of Mars. Increasing the speed of Mars would thus add to the [tex]\rm KE\![/tex] of this planet.

Since the gravitational pull from the sun is the only force on Mars, the mechanical energy of Mars would be conserved. In other words, the sum of the [tex]\rm KE[/tex] of Mars and the [tex]\rm GPE[/tex] of Mars in relation to the sun would be constant.

Thus, as the [tex]\rm GPE[/tex] of Mars decrease (as the planet moves closer to the sun,) the [tex]\rm KE[/tex] of Mars (and thus the speed of this planet) would necessarily increase.

The speed of Mars is maximized when the [tex]\rm KE[/tex] of this planet is maximized. Because of the conservation of [tex]({\rm KE} + {\rm GPE})[/tex], the [tex]\rm GPE[/tex] of Mars in relation to the sun would need to be minimized. Thus, the distance between Mars and the sun at that moment would also need to be minimized. Hence, Mars would be travelling at the highest speed at its closest approach to the sun.

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.