Explain why radial velocity detections of extrasolar planets yield only lower limits on the mass

Explain why radial velocity detections of extrasolar planets...

Key Concepts

Radial Velocity Method

This method detects extrasolar planets by measuring the Doppler shifts in the spectrum of a star as it moves under the gravitational influence of an orbiting planet. The periodic change in the star's velocity indicates the presence of a companion and provides information about the star’s motion rather than directly revealing the planet’s mass.

Minimum Mass Determination (m sin i)

Due to the dependence of the measured velocity amplitude on the orientation of the planet's orbit relative to our line of sight, the mass inferred from the radial velocity method is expressed as m sin i, where m is the true mass and i is the orbital inclination. Since sin i is always less than or equal to one, the measurement gives only a lower limit on the planet's mass.

Orbital Inclination

The orbital inclination is the angle between the plane of the planet's orbit and the plane perpendicular to our line of sight. Its unknown value introduces ambiguity in the calculated mass because only a component of the motion is observed through the Doppler shift, resulting in the estimation of m sin i rather than the true mass.

Transcript

00:01 Hi, everybody.

00:01 So we're looking at number 11, problem 11 in chapter 7 of introduction of modern astrophysics.

00:07 So this once in all, it's just asking, explained why radial velocity detects of extra solar planet field only lower limits on the masses of the orbit of planets and what values actually measured and what unknown orbital parameter is involved.

00:24 Okay.

00:25 So extra solar planets are planets outside the solar system.

00:29 So we have.

00:30 Our little solar system here i guess me me galaxy galaxy and here is an extra solar planet okay it's out of our solar system our solar system out of our solar system okay that way you guys want to be confused and the extra solar planets are much cleaner compared to their stars and that's because usually, and if we do this, let's say we have this star.

01:25 It's this big.

01:26 And the planet is literally just a little speck, okay? that little thing is the planet.

01:36 So it's really hard to attack because we're over here.

01:39 Let's say where this, actually, let's make one some green.

01:43 I don't know why i'm not going to make us dream.

01:45 That makes sense.

01:46 Okay, we'll say here, we're, and we have this like many, whatever, light years away, it's going to be really hard to detect that because the star is in the way.

01:59 Okay.

02:00 So the detection of the actual plane is quite difficult.

02:05 And so the detection involves indirect methods, such as radial velocity measurements, astro -astromic wobbles, and eclipses.

02:12 This quite possible technique is radial velocity.

02:16 Measurement from so we have a radial velocity measurement okay here and from the radial velocity measurement technique and we'll put technique here is that where we can okay and that's one of the reason so from this technique the shapes and sizes of extra solar planets are discovered so we can put it down a green shapes and sizes are discovered okay...

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