Answer :
Alright, let's break down the provided planet data and statements to understand the relationships.
### Planetary Data:
The data includes planets of our Solar System with their semi-major axis [tex]\( A \)[/tex] (in astronomical units, au) and their orbital periods [tex]\( T \)[/tex] (in years). Here is the table of given data:
| Planet | [tex]\( A \)[/tex] (au) | [tex]\( T \)[/tex] (years) |
|----------|---------------|-----------------|
| Mercury | 0.39 | 0.242 |
| Venus | 0.72 | 0.616 |
| Earth | 1.00 | 1.00 |
| Mars | 1.52 | 1.88 |
| Jupiter | -- | -- |
| Saturn | 19.18 | 84.0 |
| Uranus | -- | 165.0 |
| Neptune | 30.06 | 165.0 |
### Statements to Fill:
1. Mercury and Venus are ____ the sun than Earth is.
2. So, their orbital periods ____ than Earth's orbit.
3. The further a planet is from the Sun, the ____ its orbit is.
### Step-by-Step Analysis and Conclusion:
1. Proximity to the Sun:
- We observe from the table that Mercury (0.39 au) and Venus (0.72 au) have semi-major axes smaller than Earth's 1.00 au. This indicates they are indeed closer to the Sun than Earth is.
Therefore, the first statement will be:
- Mercury and Venus are closer to the sun than Earth is.
2. Orbital Periods:
- We see that Mercury and Venus have shorter orbital periods compared to Earth. Specifically, Mercury's orbital period is 0.242 years and Venus’s is 0.616 years, both of which are less than Earth's 1 year.
Therefore, the second statement will be:
- So, their orbital periods are shorter than Earth's orbit.
3. Distance vs. Orbital Period Relationship:
- The data shows that as a planet's distance from the Sun increases, its orbital period also increases. For example, Mars, which is further from the Sun than Earth, has a longer orbital period of 1.88 years. Saturn and Neptune, which are significantly further away, have much longer orbital periods (84.0 and 165 years, respectively).
Therefore, the third statement will be:
- The further a planet is from the Sun, the longer its orbit is.
### Final Graph and Interpretation:
If we were to graph this data, plotting the semi-major axis [tex]\( A \)[/tex] on the x-axis and the orbital period [tex]\( T \)[/tex] on the y-axis, we'd see an increasing trend indicating that planets further from the Sun have longer orbital periods.
Thus, completing our statements:
1. Mercury and Venus are closer to the sun than Earth is.
2. So, their orbital periods are shorter than Earth's orbit.
3. The further a planet is from the Sun, the longer its orbit is.
### Planetary Data:
The data includes planets of our Solar System with their semi-major axis [tex]\( A \)[/tex] (in astronomical units, au) and their orbital periods [tex]\( T \)[/tex] (in years). Here is the table of given data:
| Planet | [tex]\( A \)[/tex] (au) | [tex]\( T \)[/tex] (years) |
|----------|---------------|-----------------|
| Mercury | 0.39 | 0.242 |
| Venus | 0.72 | 0.616 |
| Earth | 1.00 | 1.00 |
| Mars | 1.52 | 1.88 |
| Jupiter | -- | -- |
| Saturn | 19.18 | 84.0 |
| Uranus | -- | 165.0 |
| Neptune | 30.06 | 165.0 |
### Statements to Fill:
1. Mercury and Venus are ____ the sun than Earth is.
2. So, their orbital periods ____ than Earth's orbit.
3. The further a planet is from the Sun, the ____ its orbit is.
### Step-by-Step Analysis and Conclusion:
1. Proximity to the Sun:
- We observe from the table that Mercury (0.39 au) and Venus (0.72 au) have semi-major axes smaller than Earth's 1.00 au. This indicates they are indeed closer to the Sun than Earth is.
Therefore, the first statement will be:
- Mercury and Venus are closer to the sun than Earth is.
2. Orbital Periods:
- We see that Mercury and Venus have shorter orbital periods compared to Earth. Specifically, Mercury's orbital period is 0.242 years and Venus’s is 0.616 years, both of which are less than Earth's 1 year.
Therefore, the second statement will be:
- So, their orbital periods are shorter than Earth's orbit.
3. Distance vs. Orbital Period Relationship:
- The data shows that as a planet's distance from the Sun increases, its orbital period also increases. For example, Mars, which is further from the Sun than Earth, has a longer orbital period of 1.88 years. Saturn and Neptune, which are significantly further away, have much longer orbital periods (84.0 and 165 years, respectively).
Therefore, the third statement will be:
- The further a planet is from the Sun, the longer its orbit is.
### Final Graph and Interpretation:
If we were to graph this data, plotting the semi-major axis [tex]\( A \)[/tex] on the x-axis and the orbital period [tex]\( T \)[/tex] on the y-axis, we'd see an increasing trend indicating that planets further from the Sun have longer orbital periods.
Thus, completing our statements:
1. Mercury and Venus are closer to the sun than Earth is.
2. So, their orbital periods are shorter than Earth's orbit.
3. The further a planet is from the Sun, the longer its orbit is.
