 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 2  Units used in exoplanet science
QuantitySymbolValue
Earth massME5.97 × 1024  kg
Jupiter massMJ1.90 × 1027 kg
Solar massMSun1.99 × 1030 kg
Distance between Earth and SunAU1.50 × 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:

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

In this case:

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 5  Sizes and masses of planets in terms of Earth and Jupiter

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 3  Units used in exoplanet science
QuantitySymbolValue
Earth massME5.97 × 1024 kg
Jupiter massMJ1.90 × 1027 kg
1. Calculate the mass of Uranus in terms of Earth and Jupiter. Which comparison is more useful?

Uranus mass: 8.68 × 1025 kg

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

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

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