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Chapter 7: Problem 43

A satellite of Mars, called Phoebus, has an orbital radius of \(9.4 \times 10^{6} \mathrm{~m}\) and a period of \(2.8 \times 10^{4} \mathrm{~s}\). Assuming the orbit is circular, determine the mass of Mars.

Short Answer

Expert verified
By performing the calculations as indicated in step 3, we find that the mass of Mars is approximately 6.45 * 10^23 kg.

Step by step solution

01

Identification of Kepler's Third Law

We can use Kepler's Third Law, which states: T虏 = 4蟺虏/GM * r鲁, where: T = orbital period (which we know), G = gravitational constant = 6.67 * 10^-11 m鲁 kg鈦宦� s鈦宦� (a known scientific constant), M = mass of the large body (in our case, the mass of Mars, which we want to find), and r = orbital radius (which we know).
02

Transpose the equation to solve for M

We walk back the equation to M = 4蟺虏r鲁/GT虏. Using this equation, we will be able to isolate Mars' mass (M) on one side of the equation.
03

Substitute the values into the equation

Now it remains to substitute the given values into the equation: M = (4蟺虏 * (9.4*10^6 m)鲁) / ((6.67*10^-11 m鲁 kg鈦宦� s鈦宦�)*(2.8*10^4 s)虏). By performing these calculations, expressing 蟺 as 3.1415926, we will be able to achieve the answer.

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Most popular questions from this chapter

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A satellite of Mars, called Phoebus, has an orbital radius of \(9.4 \times 10^{6} \mathrm{~m}\) and a period of \(2.8 \times 10^{4} \mathrm{~s}\). Assuming the orbit is circular, determine the mass of Mars.
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