# How to determine the mass of a planet using redshift?

• avito009

#### avito009

The size of the shift (Redshift or Blue shift) combined with measurement of the period of orbit tells us how massive an object is. How? How can we know the mass of a planet using redshift or blue shift?

It depends on first of all being able to estimate the mass of the STAR that the planet is orbiting
The mass of a normal star can be estimated by it spectrum (its colors of light). More massive stars burn HOTTER and bluer (shorter wavelengths).

Logically you might first ask how people discovered and calibrated this relation between color and mass. they used binary pairs of stars, that orbit their common center of mass. if you know the mass of one star (say it is the same color as the sun, which we know the mass of) and you can watch them go around each other, then you can tell the mass of the other. then you measure the color of the other and that gives another data point. Information about how color and mass are related builds up.

Once you know the mass of the star you can figure out the mass of the planet by how much it causes the star to wobble too and fro. the more massive star takes a more massive planet to make it wobble a certain amount.
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The wobble method is just one of several methods to detect planets. Let's focus on that. In that case you don't even have to SEE the planet. You just see the star approaching, say at 10 meters per second (max), and after a while you see it slow down and start receding, at 10 meters per second (max). And then approach, and then recede, and so on. Let's assume for simplicity that we are looking at the orbit plane edge on, so we see all the to and fro speed.

Maybe someone else will take over and explain this in more detail, with Kepler's law etc. It's after midnight here and I'm too sleepy to continue.

anyway, good question! The PERIOD of the wobble gives away the distance between the two bodies (Kepler). If you know the distance, you can relate the speeds to the masses. Gotta sleep.

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What if we use the formula F=ma or m=F/a to figure out the mass of this planet? If we observe the wobble can we estimate the gravitational force F? Also if me observe the orbit speed we could get to know the acceleration?

What if we use the formula F=ma or m=F/a to figure out the mass of this planet? If we observe the wobble can we estimate the gravitational force F? Also if me observe the orbit speed we could get to know the acceleration?
Calculating the force is an unnecessary detour if you are interested in the mass, but it is possible.

If you are just using redshift then you could rearrange the following equation relative to m-

$$1+z=\left(1-\frac{2M}{r}\right)^{-1/2}$$

where $M=Gm/c^2$ and z is the fractional shift in a spectral wavelength $z=(\lambda_o-\lambda_e)/\lambda_e)$ ($\lambda_o$ is wavelength observed and $\lambda_e$ is wavelength emitted).

There will be other redshifts to contend with, redshift related to velocity as the planet orbits the star (the planet moving away and towards you), the additional gravitational redshift of the star (the stars own gravity well that the planet sits in) and any cosmological redshift that might apply to the system based on how far away it was from us.