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.
| 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:
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 _unit3.5.1 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.
| 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 |
- 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.
- 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.
- 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.