mass of extra-solar planet from M, r and R

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Equation / Last modified by KurtHeckman on 2017/10/16 19:38
mass of extra-solar planet from M, r and R
Variable Instructions Datatype
`(M)"Mass of star"` Enter the mass of the star Decimal (Solar_Mass)
`(R)"Distance to planet"` Enter the distance to the planet. Decimal (ua)
`(r)"Distance to star"` Enter the distance to the star. Decimal (km)
Type
Equation
Category
vCommons
Contents
3 variables
Rating
Copied from
ID
sspickle.mass of extra-solar planet from M, r and R
UUID
95813a92-81c6-11e5-9770-bc764e2038f2

The  Mass of an Extra-solar Planet calculator computes the mass of a planet based on the mass of the star (M), the distance to the star (R) and the distance to the planet (r).

INSTRUCTIONS: Choose the preferred units and enter the following:

  • (M) This is the mass of the star.
  • (R) This is the orbital radius of the planet.
  • (r)  This is the orbital radius of the star about the center of mass.

Planet Mass (m): The calculator returns the mass of the planet in Jupiter_Mass units (multiples of the mass of Jupiter).  However, this can be automatically converted to other mass units (e.g. Earth_Mass or kilograms) via the pull-down menu.

The Math / Science

If you know the mass of a star, and the orbital radius of the star and the planet, you can compute the mass of the planet using the fact that the center of mass obeys the relation: m•R = M•r.

Example:

Consider Jupiter in our own solar system:

  • (M) The mass of our star (the Sun) is 1.0 Solar_Mass
  • (R) This orbital radius of Jupiter is 5.2 ua
  • (r) The orbital radius of our Sun around the solar system's center of mass is 0.005 ua

If you enter the above, the calculator returns an exoplanet mass of approximately 1 Jupiter Mass which fits the model and describes our solar system.