Question

13. A distant quasar is found to be moving away from the earth at 0.80 c . A galaxy closer to the earth and along the same line of sight is moving away from us at 0.60 c .

What is the recessional speed of the quasar, as a fraction of c, as measured by astronomers in the other galaxy?

Answer 1

The recessional speed of the quasar from the perspective of another galaxy moving away from Earth at 0.60c is calculated using the relativistic velocity addition formula, as both speeds are significant fractions of the speed of light.

Step-by-step explanation:

The question asks what the recessional speed of the quasar, as measured by astronomers in another galaxy that is moving away from Earth at 0.60c, would be if the quasar itself is moving away from Earth at 0.80c.

To find the recessional speed of the quasar from the perspective of astronomers in the other galaxy, we need to use the relativistic velocity addition formula, not the classical view, because the velocities involved are a significant fraction of the speed of light (c), and therefore relativistic effects cannot be ignored.

The relativistic velocity addition formula is:

V = (v1 + v2) / (1 + (v1*v2/c^2))

where V is the resultant velocity, v1 is the velocity of the quasar with respect to Earth (0.80c), and v2 is the velocity of the galaxy with respect to Earth (0.60c). After calculating, we would find that the quasar is receding from the galaxy at a speed less than 1c, which respects the cosmic speed limit set by the theory of relativity.

Answer 2

The recessional speed of the quasar, as measured by astronomers in the other galaxy, is approximately 0.9469c.

Step-by-step explanation:

The recessional speed of the quasar, as measured by astronomers in the other galaxy, can be calculated using the relativistic Doppler equation. The equation is given by:

v = (v1 + v2)/(1 + v1 * v2/c^2)

where v is the measured recession speed, v1 is the recession speed of the nearby galaxy, v2 is the recession speed of the quasar, and c is the speed of light. Plugging in the given values, we get:

v = (0.60c + 0.80c)/(1 + 0.60c * 0.80c/c^2)

Simplifying this equation, we find that the recessional speed of the quasar, as a fraction of c, is approximately 0.9469c.