Question

Scientists are observing and recording data for two different planets, planet X and planet Y. Each planet orbits a different star. The planets have the same mass. The scientists record the following data.

Star X – Planet X Star Y – Planet Y
Distance (millions of kilometers) 100 100
Orbital period of the planet
(Earth days) 390 260

Which of the following statements is most likely true?
A.
The star close to planet Y is hotter.
B.
The star close to planet Y has more mass.
C.
The star close to planet Y has less mass.
D.
The star close to planet Y is cooler.

Answer 1

B.

Because the planet at the same orbital distance has a shorter period, the central star must exert a stronger gravitational pull. From orbital dynamics (Kepler's 3rd law or v = sqrt(GM/r)), T = 2π sqrt(r^3/(GM)), so a smaller T at the same r implies a larger stellar mass.