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An introduction to exoplanets
An introduction to exoplanets

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5  Simplifying the numbers

You’ve seen in the last few sections that studying planets involves dealing with some very big numbers. To simplify calculations, astronomers have introduced their own units, and you’ve already seen most of the important units for this course.

  • The sizes of planetary systems are measured in terms of astronomical units, written AU.
  • Giant planets are measured in terms of the mass and radius of Jupiter, written MJ and RJ.
  • Terrestrial planets are measured in terms of the mass and radius of the Earth, written ME and RE. Sometimes the alternative forms M and R are used, but you will use ME and RE in this course.
  • Stars are measured in terms of the mass and radius of the Sun: the solar mass and solar radius, written MSun and RSun. Sometimes the alternative forms M and R are used, but you will use MSun and RSun in this course.
Table _unit3.5.1 Table 2  Units used in exoplanet science
Quantity Symbol Value
Earth mass ME 5.97 × 1024  kg
Earth radius RE 6.38 × 106 m
Jupiter mass MJ 1.90 × 1027 kg
Jupiter radius RJ 7.15 × 107 m
Solar mass MSun 1.99 × 1030 kg
Solar radius RSun 6.96 × 108 m
Distance between Earth and Sun AU 1.50 × 1011 m

Now, instead of saying, for example, that the mass of Saturn is 5.68 × 1026 kg, you can express the mass of Saturn in terms of the mass of Jupiter, MJ. To do this you need to work out how many Jupiter masses there are in Saturn. Mathematically, divide the mass of Saturn by the mass of Jupiter and the answer is the number of Jupiter masses in Saturn.

So:

multiline equation row 1 mass of Saturn equation left hand side equals right hand side 5.68 multiplication 10 super 26 normal k times normal g divided by 1.90 multiplication 10 super 27 normal k times normal g normal cap m sub normal cap j row 2 equals 0.3 normal cap m sub normal cap j

Or instead you could express Saturn’s mass in terms of the mass of the Earth.

In this case:

multiline equation row 1 mass of Saturn equation left hand side equals right hand side 5.68 multiplication 10 super 26 normal k times normal g divided by 5.97 multiplication 10 super 24 normal k times normal g normal cap m sub normal cap e row 2 equals 95 normal cap m sub normal cap e

So, you can say that Saturn’s mass is 0.3 MJ, or 95 ME. Both of these alternatives give you an immediate feeling for where Saturn fits compared with other planets.

Activity _unit3.5.1 Activity 5  Sizes and masses of planets in terms of Earth and Jupiter

Timing: Allow about 10 minutes

You are given the masses and radii for some of the Solar System planets. You need to calculate the masses in terms of MJ and ME, and the radii in terms of RJ and RE. For each planet, which is the most sensible comparison to use?

Useful values are provided in Table 3. Note that all radii are given in km here.

Table _unit3.5.2 Table 3  Units used in exoplanet science
Quantity Symbol Value
Earth mass ME 5.97 × 1024 kg
Earth radius RE 6.38 × 103 km
Jupiter mass MJ 1.90 × 1027 kg
Jupiter radius RJ 7.15 × 104 km
  1. Calculate the mass of Uranus in terms of Earth and Jupiter. Which comparison is more useful?

    Uranus mass: 8.68 × 1025 kg

Answer

0.046 MJ or 14.5 ME; either comparison is useful.

  1. Calculate the radius of Neptune in terms of Earth and Jupiter. Which comparison is more useful?

    Neptune radius: 2.48 × 104 km

Answer

0.35 RJ or 3.9 RE; either comparison is useful.

  1. Calculate the radius of Mercury in terms of Earth and Jupiter. Which comparison is more useful?

    Mercury radius: 2.44 × 103 km

Answer

0.034 RJ or 0.38 RE; comparison with Earth is more useful.