Question

Two stars with different masses are in a circular binary system. The heavier star is 3 times more massive than the low mass star. The high mass star is 3 Astronomical Units (AU) away from the centre of mass. The average speed of an object is the distance travelled divided by the time taken to travel the distance. Which star travels at the faster speed?

a) The low mass star
b) The high mass star
c) Both stars travel at the same speed.
d) The speed depends on their individual masses.

Answer 1

In a circular binary star system with two stars of different masses, the low-mass star travels at a faster speed because it is further from the center of mass and has a larger orbit to complete in the same period.

Step-by-step explanation:

The star in a circular binary system travels at a faster speed given that the heavier star is three times more massive than the lighter star and is 3 Astronomical Units (AU) away from the center of mass. In such a binary system, the star with the higher mass will be found closer to the center of mass, while the star with the lower mass will be farther from it. As the relative orbital speeds of two stars can inform us about their respective masses, in this case, the heavier star, being closer to the center of mass, will have a smaller orbit and therefore move more slowly compared to the lower-mass star which, being further from the center of mass, will travel a longer distance over the same period and consequently at a faster speed. Therefore, the answer is (a) the low-mass star travels at a faster speed.