Asteroids X, Y, and Z have equal mass of 4.0 kg each. They orbit around a planet

Question

Asteroids X, Y, and Z have equal mass of 4.0 kg each. They orbit around a planet with M = 7.20×1024 kg. The orbits are in the plane of the paper and are drawn to scale.

The three asteroids orbit in the same clockwise direction.

*Options: greater than, less than, equal to

a.) The period of Y is .... that of Z.

b.) The angular velocity of X at v is .... that at c.

c.) The angular velocity of Y at c is .... that at n.

d.) The angular velocity of X at c is .... that of Y at c.

e.) The angular momentum of Y is .... that of X.

f.) The period of Y is .... that of X.

g.) The angular momentum of Z at n is .... that at e.

Explanation / Answer

Consider the given data and now if we assume that all the orbits have equal eccentricity or the equal major axis then this allows us to compare the periods of the asteroids as we will get radius of orbit common for all the astroids, let us assume that as x.

a) The period of Y is equal to that of Z

because according to Kepler's 3rd law of planetary motion T2 = 4(pi)2x2/ GM that is period only depends on the mass of the object around which asteroid is moving and the distance of the asteroid in the orbit x. here mass M of object about which asteroids are orbiting is same for both the asteroids.

b) The angular velocity of X at v is greater than that at c.

Because according to Kepler's second law planets swips out an equal area in equal time interval. So all the time when asteroid X moves in each interval it will sweep out equal area. Therefore, when it will be closer to the object around which it is revolving it will be moving faster than that when it is farther to keep area swept out (areal velocity) constant. Here v is closer than c to the central object.

c) The angular velocity of Y at c is less than that at n.

Because of the same reason as mentioned in part b. For details one can refer the following figure.

d) The angular velocity of X at c is equal to that of Y at c

If we observe the figure distance of the asteroids from the central object are same.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.