Question: Information about five planets is shown in the table below.
Planet Diameter (km) Mass (kg)
Mercury 4.88 \times 10^3 3.3 \times 10^{23}
Jupiter 1.43 \times 10^5 1.898 \times 10^{27}
Earth 1.28 \times 10^4 5.97 \times 10^{24}
Mars 6.78 \times 10^3 6.42 \times 10^{23}
Saturn 1.21 \times 10^5 5.68 \times 10^{26}
a) Write down the name of the planet with the greatest mass.
b) Work out the radius of Mercury giving your answer as an ordinary number.
c) Work out the difference between the masses of Jupiter and Saturn.
Give your answer in standard form.
1. **State the problem:** We have data for five planets including their diameters and masses. We need to answer three questions: (a) identify the planet with the greatest mass, (b) calculate the radius of Mercury, and (c) find the difference between the masses of Jupiter and Saturn in standard form.
2. **Part (a): Find the planet with the greatest mass.**
- The masses given are:
- Mercury: $3.3 \times 10^{23}$ kg
- Jupiter: $1.898 \times 10^{27}$ kg
- Earth: $5.97 \times 10^{24}$ kg
- Mars: $6.42 \times 10^{23}$ kg
- Saturn: $5.68 \times 10^{26}$ kg
- Clearly, $1.898 \times 10^{27}$ (Jupiter) is the greatest mass.
3. **Part (b): Calculate the radius of Mercury.**
- Diameter of Mercury is $4.88 \times 10^3$ km.
- Radius $r$ is half the diameter:
$$r = \frac{\text{diameter}}{2} = \frac{4.88 \times 10^3}{2}$$
- Show cancellation:
$$r = \frac{\cancel{4.88 \times 10^3}}{\cancel{2}} = 2.44 \times 10^3$$
- Convert to ordinary number:
$$2.44 \times 10^3 = 2440$$
- So, radius of Mercury is $2440$ km.
4. **Part (c): Find the difference between the masses of Jupiter and Saturn in standard form.**
- Mass of Jupiter: $1.898 \times 10^{27}$ kg
- Mass of Saturn: $5.68 \times 10^{26}$ kg
- Write Saturn's mass with the same power of ten as Jupiter:
$$5.68 \times 10^{26} = 0.568 \times 10^{27}$$
- Difference:
$$1.898 \times 10^{27} - 0.568 \times 10^{27} = (1.898 - 0.568) \times 10^{27} = 1.33 \times 10^{27}$$
**Final answers:**
- (a) Jupiter
- (b) Radius of Mercury = $2440$ km
- (c) Difference in mass = $1.33 \times 10^{27}$ kg