Question

Kepler 30b is an exoplanet orbiting a star of about 1 solar mass. Its orbital period is 290 days. The semimajor axis of its orbit is 0.180 au. Calculate the maximum Doppler shift that could be observed for this planet (in 10-4). (Round the final answer to two decimal places.)

Answer 1

The maximum Doppler shift that could be observed for Kepler 30b is approximately 0.0037.

Step-by-step explanation:

To calculate the maximum Doppler shift that could be observed for Kepler 30b, we can use the formula for Doppler shift:

Δλ/λ = vc/c

Where Δλ is the change in wavelength, λ is the original wavelength, v is the velocity of the planet, c is the speed of light, and a is the semimajor axis of the planet's orbit.

Since the maximum Doppler shift occurs when the velocity of the planet is at its maximum, we can calculate the maximum velocity using Kepler's third law:

v = 2πa/P

Where P is the orbital period of the planet. Substituting this value into the Doppler shift formula:

Δλ/λ = (2πa/P)(c/c)

Δλ/λ = 2πa/P

Finally, plugging in the values given in the question, we can calculate the maximum Doppler shift:

Δλ/λ = 2π(0.180)/(290)

Δλ/λ ≈ 0.0037