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Chapter 13: Q45P (page 381)

The Martian satellite Phobos travels in an approximately circular orbit of radius 9.4×106mwith a period of7h39min .Calculate the mass of Mars from this information.

Short Answer

Expert verified

The mass of the Mars is 6.5×1023kg.

Step by step solution

01

Step 1: Given

Radius,R=9.4×106m

Period,7hours39minutes=2.754×104s

02

Determining the concept

Using the formula for Kepler’s third law, we can find themass of Mars from the given radius and period. According to Kepler’s third law, the squares of the orbital periods of the planets are directly proportional to the cubes of the semi major axes of their orbits.

Formula is as follow:

T2=4π2GMR3

where, T is time, G is gravitational constant, M is mass and R is radius.

03

Determining themass of Mars

Now,

T2=4π2GMR3M=4π2R3GT24π29.4×106m3G2.754×104s2

Hence, the mass of the Mars is 6.5×1023kg.

Therefore, using the formula for Kepler’s third law, the mass of Mars from the given radius and period can be found.

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Most popular questions from this chapter

MooneffectSome people believe that the Moon controls their activities. If the Moon moves from being directly on the opposite side of Earth from you to being directly overhead, by what percent does (a) the Moon’s gravitational pull on you increase and (b) your weight (as measured on a scale) decrease? Assume that the Earth–Moon (center-to-center) distance is3.82×108mand Earth’s radius is6.37×106m.

A satellite is in a circular Earth orbit of radius r. The area A enclosed by the orbit depends on r2 because A=πr2. Determine how the following properties of the satellite depend on r:

(a) period,

(b) kinetic energy,

(c) angular momentum, and

(d) speed.

Question: A satellite is in elliptical orbit with a period of 8.00×104s about a planet of massM=7.00×1024kg . At aphelion, at radius4.5×107m , the satellite’s angular speed is7.158×10-5rads .What is its angular speed at perihelion?

A solid uniform sphere has amass of1.0×104kgand a radius of1.0  m. What is the magnitude of the gravitational force due to the sphere on a particle of massmlocated at a distance of(a) 1.5 m and (b) 0.50 m from the center of the sphere? (c) Write a general expression for the magnitude ofthe gravitational force on the particle at a distancer≤1.0mfrom the center of the sphere.

A satellite, moving in an elliptical orbit, is 360kmabove Earth’s surface at its farthest point and 180kmabove at its closest point.

Calculate (a) the semimajor axis and

(b) the eccentricity of the orbit.
See all solutions

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