Question

name mauricio
what is the weight of a 75 pound person
moon sun
mercury venus
earth mars
jupiter saturn
uranus neptune
show your work!

Explanation:

To solve the problem of finding the weight of a 75 - pound person on different celestial bodies, we need to know the gravitational acceleration (or the weight - multiplier) for each celestial body relative to Earth. The formula to calculate the weight \(W\) on a celestial body is \(W = m\times g_{body}\), where \(m\) is the mass of the person (and since weight on Earth \(W_{Earth}=m\times g_{Earth}\), we can also use the ratio of the gravitational accelerations. If we let \(k\) be the ratio of the gravitational acceleration of the celestial body (\(g_{body}\)) to the gravitational acceleration of Earth (\(g_{Earth}\)), then the weight on the celestial body \(W_{body}=W_{Earth}\times k\), and \(W_{Earth} = 75\) pounds.

1. Moon

The gravitational acceleration on the Moon is about \(\frac{1}{6}\) of that on Earth. So the weight - multiplier \(k=\frac{1}{6}\)
\(W_{Moon}=75\times\frac{1}{6}=\frac{75}{6} = 12.5\) pounds

2. Sun

The gravitational acceleration on the Sun is about 27.9 times that on Earth. So the weight - multiplier \(k = 27.9\)
\(W_{Sun}=75\times27.9 = 2092.5\) pounds

3. Mercury

The gravitational acceleration on Mercury is about 0.38 times that on Earth. So the weight - multiplier \(k = 0.38\)
\(W_{Mercury}=75\times0.38=28.5\) pounds

4. Venus

The gravitational acceleration on Venus is about 0.91 times that on Earth. So the weight - multiplier \(k = 0.91\)
\(W_{Venus}=75\times0.91 = 68.25\) pounds

5. Earth

The weight on Earth is given as 75 pounds (since \(W_{Earth}=m\times g_{Earth}\), and we are using this as the reference)
\(W_{Earth}=75\) pounds

6. Mars

The gravitational acceleration on Mars is about 0.38 times that on Earth. So the weight - multiplier \(k = 0.38\)
\(W_{Mars}=75\times0.38 = 28.5\) pounds

7. Jupiter

The gravitational acceleration on Jupiter is about 2.36 times that on Earth. So the weight - multiplier \(k = 2.36\)
\(W_{Jupiter}=75\times2.36=177\) pounds

8. Saturn

The gravitational acceleration on Saturn is about 1.06 times that on Earth. So the weight - multiplier \(k = 1.06\)
\(W_{Saturn}=75\times1.06 = 79.5\) pounds

9. Uranus

The gravitational acceleration on Uranus is about 0.89 times that on Earth. So the weight - multiplier \(k = 0.89\)
\(W_{Uranus}=75\times0.89=66.75\) pounds

10. Neptune

The gravitational acceleration on Neptune is about 1.14 times that on Earth. So the weight - multiplier \(k = 1.14\)
\(W_{Neptune}=75\times1.14 = 85.5\) pounds

Answer:

s:

• Moon: \(\boldsymbol{12.5}\) pounds
• Sun: \(\boldsymbol{2092.5}\) pounds
• Mercury: \(\boldsymbol{28.5}\) pounds
• Venus: \(\boldsymbol{68.25}\) pounds
• Earth: \(\boldsymbol{75}\) pounds
• Mars: \(\boldsymbol{28.5}\) pounds
• Jupiter: \(\boldsymbol{177}\) pounds
• Saturn: \(\boldsymbol{79.5}\) pounds
• Uranus: \(\boldsymbol{66.75}\) pounds
• Neptune: \(\boldsymbol{85.5}\) pounds