The planet Venus is on average 2.5×10^7 kilometers from Earth. The planet Mars is on average 2.25×10^8 kilometers from Earth. When Venus, Earth, and Mars are aligned, what is the a... The planet Venus is on average 2.5×10^7 kilometers from Earth. The planet Mars is on average 2.25×10^8 kilometers from Earth. When Venus, Earth, and Mars are aligned, what is the average distance from Venus to Mars? Part A: 2.25×(blank)×(blank) Part B: (blank)=×10^7 Part C: 2.5×10^7 + (blank)×10^7 =(2.5 + (blank))×10^7 Part D: = (blank) ×10^7 Part E: = (blank) × (blank) fill in the blanks.
Understand the Problem
The question is asking to find the average distance from Venus to Mars when all three planets are aligned. It involves calculations with scientific notation and requires filling in specific blanks for parts A through E based on the given values.
Answer
The average distance from Venus to Mars when aligned is $1.20 \times 10^{11}$ meters.
Answer for screen readers
The average distance from Venus to Mars when aligned is $1.20 \times 10^{11}$ meters.
Steps to Solve
- Identify the distances in scientific notation
First, we need to gather the distances from Venus to the Sun and Mars to the Sun. For example:
- Distance from Venus to the Sun: $D_V = 1.08 \times 10^{11}$ meters
- Distance from Mars to the Sun: $D_M = 2.28 \times 10^{11}$ meters
- Calculate the distance from Venus to Mars
To find the distance between Venus and Mars when they are aligned, we simply subtract the two distances from the Sun:
$$ D_{VM} = |D_V - D_M| $$
Plugging the values in:
$$ D_{VM} = |1.08 \times 10^{11} - 2.28 \times 10^{11}| $$
This results in:
$$ D_{VM} = | -1.20 \times 10^{11} | = 1.20 \times 10^{11} $$ meters
- Express the average distance if needed
If averaging over a specified number, determine how many distances you're averaging. In this problem, if you are focusing just on them aligned, the average will actually be equal to the distance found. However, if you require the average based on multiple alignments, you divide the total distance calculated by the number of instances.
In this specific question, the average distance is thus:
$$ \text{Average distance} = D_{VM} = 1.20 \times 10^{11} $$ meters
The average distance from Venus to Mars when aligned is $1.20 \times 10^{11}$ meters.
More Information
Venus and Mars have orbits that are distinctly different, causing their distance to vary significantly. Understanding these distances in scientific notation is essential when dealing with astronomical measurements, as they can be very large values.
Tips
- Misunderstanding the problem and calculating the average incorrectly by adding distances rather than subtracting.
- Neglecting the absolute value when determining distance, leading to incorrect negative results.
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