If Earth were 10 times farther from the sun than now, which planet would it be closest to? (Assume all the planets are aligned with the sun and are on the same side of the sun.) Compare Earth's new distance to that planet. About how far apart would they be in standard notation and in km? How far apart in scientific notation in km? Show your work.
If Earth were 10 times farther from the sun than it is currently, it would be closest to Uranus.
To calculate the new distance between Earth and Uranus, we first need to determine Earth's current average distance from the sun. The average distance between Earth and the sun is approximately 149.6 million kilometers (km) or 1.496 x 10^8 km.
If Earth was 10 times farther away, its new distance from the sun would be 10 x 149.6 million km = 1.496 billion km or 1.496 x 10^9 km.
The average distance between Uranus and the sun is approximately 2.88 billion km or 2.88 x 10^9 km.
Therefore, Earth and Uranus would be approximately 2.88 billion km - 1.496 billion km = 1.384 billion km apart.
In scientific notation, this would be 1.384 x 10^9 km apart.
The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shuttle to reach Saturn (1,443,500,000 km) from Earth (149,600,000 km). (Assume both planets are aligned with the sun and are on the same side of the sun.) Show your work. Convert your answer into scientific notation if necessary.
To determine the time it would take for the space shuttle to reach Saturn from Earth, we can use the formula distance = speed × time.
The distance between Earth and Saturn is 1,443,500,000 km, and the speed of the space shuttle is 28,000 km per hour.
To find the time it takes to travel this distance, we can rearrange the formula: time = distance / speed.
Plugging in the values, we have:
time = 1,443,500,000 km / 28,000 km per hour = 51,482.1429 hours.
Rounding to the nearest hour, it would take approximately 51,482 hours for the space shuttle to reach Saturn.
Converting this to scientific notation: 5.1482 x 10^4 hours.
If Earth were 10 times farther from the sun than it is now, it would be closest to Saturn.
Currently, the average distance from Earth to the sun is about 149.6 million kilometers (km). If we multiply this distance by 10, we get 1.496 billion km.
The average distance from Saturn to the sun is roughly 1.429 billion km.
To find the difference between Earth's new distance and the distance to Saturn, we subtract Earth's new distance from the distance to Saturn:
1.496 billion km - 1.429 billion km = 67 million km
In standard notation, Earth and Saturn would be about 67 million kilometers apart.
In scientific notation, 67 million is written as 6.7 x 10^7 km.
To determine which planet Earth would be closest to if it were 10 times farther from the Sun, we need to compare Earth's new distance to the distances of the other planets. Let's break down the steps to find the answer:
Step 1: Determine Earth's current average distance from the Sun.
Earth's current average distance from the Sun is approximately 150 million kilometers, which is referred to as 1 astronomical unit (AU).
Step 2: Calculate Earth's new distance from the Sun if it were 10 times farther.
To find Earth's new distance, we multiply its current distance by 10.
New distance = 150 million km x 10 = 1.5 billion kilometers.
Step 3: Compare Earth's new distance to the distances of the other planets to determine the closest planet.
We will compare Earth's new distance of 1.5 billion kilometers to the distances of the other planets.
- Mercury: Average distance from the Sun is approximately 58 million km.
- Venus: Average distance from the Sun is approximately 108 million km.
- Mars: Average distance from the Sun is approximately 228 million km.
- Jupiter: Average distance from the Sun is approximately 778 million km.
- Saturn: Average distance from the Sun is approximately 1.4 billion km.
- Uranus: Average distance from the Sun is approximately 2.9 billion km.
- Neptune: Average distance from the Sun is approximately 4.5 billion km.
- Pluto (considered a dwarf planet): Average distance from the Sun is approximately 5.9 billion km.
Comparing Earth's new distance to these values, we find that the closest planet would be Saturn, with an average distance of 1.4 billion kilometers.
Step 4: Calculate the distance between Earth and Saturn in standard notation.
The distance between Earth and Saturn would be the difference between their distances.
Distance = 1.4 billion km - 1.5 billion km = -0.1 billion kilometers.
So, Earth and Saturn would be 0.1 billion kilometers apart in standard notation.
Step 5: Convert the distance between Earth and Saturn into scientific notation.
Scientific notation represents a number as a coefficient multiplied by a power of 10, where the coefficient is between 1 and 10.
To convert our distance into scientific notation, we divide the value by 10^9.
-0.1 billion km / 10^9 = -1e-7 billion km.
Therefore, the distance between Earth and Saturn in scientific notation is approximately -1e-7 billion kilometers.
In kilometers, it would be -100,000 km (in standard notation) or -0.1 million km (in scientific notation).