Chapter 44: Q36P (page 1364)

What would the mass of the Sun have to be if Pluto (The outermost “planet: most of the time) were to have the same orbital speed that Mercury (the innermost planet) has now? Use data from Appendix C, express your answer in terms of the Sun’s current mass, $M_{s}$ and assume circular orbits.

Short Answer

Expert verified

The mass of the Sun under the given circumstances is $102 M_{S}$

Step by step solution

Given Information

Consider that the Pluto has the same orbital speed that Mercury have now.

Write the formula for the gravitational mass as:

From the formula of the gravity force $F_{g r a v}$ is as follows:

$F_{g r a v} = \frac{G M m}{r^{2}}$ …… (1)

Determine the mass of the Sun under the given condition.

Consider the equation $M \infty v^{2}$ then equation (1) becomes,

$\begin{matrix} F_{g r a v} = \frac{G M m}{r^{2}} \\ = \frac{m v^{2}}{r} \end{matrix}$

Determine the mass of the sun as:

${M_{s}}^{'} = {(\frac{v_{m e r c u r y}}{v_{p l u t o}})}^{2} M_{s}$

${M_{s}}^{'} = {(\frac{47.9 \frac{km}{s}}{4.74 \frac{km}{s}})}^{2} M_{s}$

Therefore, the mass of the Sun under the given circumstances is $102 M_{S}$

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What would the mass of the Sun have to be if Pluto (The outermost “planet: most of the time) were to have the same orbital speed that Mercury (the innermost planet) has now? Use data from Appendix C, express your answer in terms of the Sun’s current mass, $M_{s}$ and assume circular orbits.

Short Answer

Step by step solution

Given Information

Write the formula for the gravitational mass as:

Determine the mass of the Sun under the given condition.

One App. One Place for Learning.

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What would the mass of the Sun have to be if Pluto (The outermost “planet: most of the time) were to have the same orbital speed that Mercury (the innermost planet) has now? Use data from Appendix C, express your answer in terms of the Sun’s current mass,Msand assume circular orbits.

Short Answer

Step by step solution

Given Information

Write the formula for the gravitational mass as:

Determine the mass of the Sun under the given condition.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Radiation

Electricity and Magnetism

Work Energy and Power

Nuclear Physics

Translational Dynamics

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

What would the mass of the Sun have to be if Pluto (The outermost “planet: most of the time) were to have the same orbital speed that Mercury (the innermost planet) has now? Use data from Appendix C, express your answer in terms of the Sun’s current mass, $M_{s}$ and assume circular orbits.