Question

We are going to look at how the radial velocity method can be used to determine the mass of a planet. The observations that get made look at two things: the wobble of the star (it is measured as a change in the speed the star appears to be traveling towards or away from us) and the amount of time it takes for the pattern to repeat itself. Let's consider the planet beta Gemini b. The change in the speed of the star due to the planet's tug is approximately v star = 40 m/sec. Knowing that the mass of the star is M star = 2 M ? and that the period of the orbit is approximately P = 2 years, we can estimate the orbital separation a . Recall that Kepler's Third Law is M star M ? ( P year ) 2 = ( a AU ) 3 where M is the mass of the star, P is the period of the orbit, and a is the separation. Notice the scaling. If M , P , and a are expressed in the right units then the calculation becomes much easier. What is the orbital separation between the star and the planet in astronomical units? Given your answer above, let's estimate the speed of the planet in kilometers per second. This can be determined using the equation v planet = 2 ? a P ? 6 a P for a circular orbit (and this planet is nearly on a circular orbit). What is the velocity of the planet in km/sec? Now we can calculate the planet's mass by using the equation M star v star = m planet v planet What is the mass of the planet in Jupiter masses? A convenient conversion factor is that 1 M ? = 10 3 M Jupiter

Answer 1

The mass and the size of any planet is given by the experimental analysis of the different calatorial methods for the observations of the stars. in the above question it is mentioned that we can use the kepler's third method for the determinations of the same. according to this law it is stated that when the planet orbit any other heavenly body like sun then it will try to orbit in the elliptical path. in this orbiting the sun will be at the focii point and acts as a center for the centrifugal force which apply on the rotation of the planet as well as the revolution.

now this path of the orbit have the two section as one section is near to the focii while the other section is far from the focal point which is sun in this case. now when the palnet will orbit the sun in the near most postion then it will have the maximum orbital speed while in the case of the orbiting of the planet with the far distance it will have the minimum orbital speed.