Question

1) Two planets, A and B, with unknown masses are uniformly rotating around a star maintaining a fixed distance of 4 million kilometers and 5 million kilometers respectively from the star. In the following answer boxes, enter the work done by that star on the two planets, A and B, respectively:

Answer 1 of 2:

Answer 2 of 2:

Answer 1

1) Two planets, A and B, with unknown masses are uniformly rotating around a star maintaining a fixed distance of 4 million kilometers and 5 million kilometers respectively from the star. In the following answer boxes, enter the work done by that star on the two planets, A and B, respectively:

Answer 1 of 2:

Answer 2 of 2:

Solution:

Let the mass of the star is M

The mass of planet A is m_A and the distance from the star is R_A = 4*10⁶ km

The mass of planet B is m_B and the distance from the star is R_B = 5*10⁶ km

Both the stars are uniformly rotating around the star maintaining the fixed distance of R_A and R_B.

Gravitaional potential energy (U), kinetic energy (K) and total mechanical energy (T) of planet A-star system is given as,

U = -GMm_A/R_A ; K = GMm_A/(2R_A) and T = K + U = -GMm_A/(2R_A)

Similarly for planet B, we have

U = -GMm_B/R_B ; K = GMm_B/(2R_B) and T = K + U = -GMm_B/(2R_B)

We observe that potential energy, kinetic energy and total energy depend the distance between the planets and the star.

The star can do work on the planet by increasing or decreasing planets kinetic energy or potential energy and for that the distance between the planet and the star should change. But since the planet strictly maintain the distance of R_A and R_B, there is no change in the kinetic energy or potential energy. The total energy remains the same for both the planet.

Thus the star does not do any work. In other words, star does 0 joules of work on the planet.

Thus work done by the star on planet A and B respectively is

0 J           and

0 J