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Answer :
Sure! To determine the astronaut's weight on Planet X, we need to consider how gravitational force works on different celestial bodies.
Here's a step-by-step explanation:
1. Understanding Weight and Gravity:
- Weight is the force exerted by gravity on an object. It's calculated using the formula [tex]\( \text{Weight} = \text{mass} \times \text{gravitational acceleration} \)[/tex].
2. Comparing Earth and Planet X:
- The gravitational force an object experiences on the surface of a planet is proportional to the planet's mass divided by the square of its radius.
3. Given Ratios:
- Planet X has a mass that is 6 times the mass of Earth.
- Planet X has a radius that is 3 times the radius of Earth.
4. Calculating Gravitational Force on Planet X:
- Since gravitational force depends on [tex]\( \frac{\text{mass}}{\text{radius}^2} \)[/tex], we use the given ratios to find the relative gravitational force on Planet X compared to Earth.
- We substitute the ratios into the expression:
[tex]\[
\text{Gravitational force on Planet X} = \text{Gravitational force on Earth} \times \left(\frac{6}{3^2}\right)
\][/tex]
5. Simplifying the Expression:
- Calculate [tex]\( \frac{6}{3^2} = \frac{6}{9} = \frac{2}{3} \)[/tex].
6. Calculating the Astronaut's Weight on Planet X:
- If the astronaut weighs 193 lbs on Earth, on Planet X his weight would be:
[tex]\[
193 \times \frac{2}{3} = 128.67 \, \text{lbs (rounded to two decimal places)}
\][/tex]
So, the astronaut would weigh approximately 128.67 lbs on Planet X.
Here's a step-by-step explanation:
1. Understanding Weight and Gravity:
- Weight is the force exerted by gravity on an object. It's calculated using the formula [tex]\( \text{Weight} = \text{mass} \times \text{gravitational acceleration} \)[/tex].
2. Comparing Earth and Planet X:
- The gravitational force an object experiences on the surface of a planet is proportional to the planet's mass divided by the square of its radius.
3. Given Ratios:
- Planet X has a mass that is 6 times the mass of Earth.
- Planet X has a radius that is 3 times the radius of Earth.
4. Calculating Gravitational Force on Planet X:
- Since gravitational force depends on [tex]\( \frac{\text{mass}}{\text{radius}^2} \)[/tex], we use the given ratios to find the relative gravitational force on Planet X compared to Earth.
- We substitute the ratios into the expression:
[tex]\[
\text{Gravitational force on Planet X} = \text{Gravitational force on Earth} \times \left(\frac{6}{3^2}\right)
\][/tex]
5. Simplifying the Expression:
- Calculate [tex]\( \frac{6}{3^2} = \frac{6}{9} = \frac{2}{3} \)[/tex].
6. Calculating the Astronaut's Weight on Planet X:
- If the astronaut weighs 193 lbs on Earth, on Planet X his weight would be:
[tex]\[
193 \times \frac{2}{3} = 128.67 \, \text{lbs (rounded to two decimal places)}
\][/tex]
So, the astronaut would weigh approximately 128.67 lbs on Planet X.
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