Calculating mass of a planet (Law of Universal Gravitation)

In summary, the new planet has a gravitational field that is 8.5m/s2 weaker than on Earth, resulting in the astronaut weighing 425 N less on the planet than he does on Earth.
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Homework Statement


You are on a deep space mission to search for Earth-like planets. Your crew locates a possible planet and with scanners finds the radius to be 7.5 x 106 m. A team lands on the surface. There, they hang a 1.0 kg mass from a spring scale. It reads 8.5 N. Determine the mass of the planet and whether an astronaut standing on this new planet weighs more, less, or the same as on Earth. Show your work.

Homework Equations


F = G M1M2/r2
M2 = F (r2) / Gm1
F = ma
F = mg

The Attempt at a Solution


First using the equation to find the mass of this new Earth-like planet:
M2 = 8.5 N (7.5 x 106)2 / (6.67 x 10-11) (1.0 kg)
M2 = 8.5 N (56.25 x 1012) / (6.67 x 10-11) (1.0 kg)
M2 = 7.168 x 1024

Then the gravitational field strength on this new planet:
a = G x M2 / r2
a = (6.67 x 10-11) (7.168 x 1024) / (56.25 x 1012)
a = 47.81 x 1013 / 56.25 x 1012 = 8.5m/s2

Now let's suppose that the astronaut's mass is 50 kg. To calculate how much he weighs on this new planet:
F = ma = (50 kg) x (8.5m/s2) = 425 N

Now calculating his weight on Earth:
F = mg = (50 kg) x (9.8m/s2) = 490 N

Therefore the astronaut weighs more on planet Earth, than he does on this newly-found planet.

Did I do everything correctly? I really appreciate confirmations and guidance on pointing me in the right direction if I made mistakes anywhere. Thank you in advance to anyone who helps and/or confirms.
 
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You did fine, but be sure to always include units when you present a result. When you calculated the mass of the planet, M2, you didn't show the units.

After you calculated the acceleration due to gravity on the planet's surface, it would have sufficed to compare that value to the acceleration due to gravity on Earth and noting that it is smaller on the planet, hence the astronaut would weigh less there. :smile:
 
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gneill said:
You did fine, but be sure to always include units when you present a result. When you calculated the mass of the planet, M2, you didn't show the units.

After you calculated the acceleration due to gravity on the planet's surface, it would have sufficed to compare that value to the acceleration due to gravity on Earth and noting that it is smaller on the planet, hence the astronaut would weigh less there. :smile:
Understood. Thank you so much for the confirmation, and yes I agree, I could've simply made it easier for myself at the acceleration point, I have not thought about it though :)
 

Related to Calculating mass of a planet (Law of Universal Gravitation)

1. How do you calculate the mass of a planet using the Law of Universal Gravitation?

To calculate the mass of a planet, you need to know the planet's radius, the gravitational constant, and the acceleration due to gravity on the planet's surface. Then, you can use the formula M = (r^2 * g) / G, where M is the mass of the planet, r is the radius, g is the acceleration due to gravity, and G is the gravitational constant.

2. What is the Law of Universal Gravitation?

The Law of Universal Gravitation states that any two objects in the universe are attracted to each other with a force that is directly proportional to their masses and inversely proportional to the square of the distance between them. This law was formulated by Sir Isaac Newton in 1687.

3. Why is it important to calculate the mass of a planet?

Calculating the mass of a planet allows us to understand its composition, density, and gravitational pull. This information is crucial for studying the planet's formation, evolution, and potential habitability.

4. What are the units used to measure mass and distance in the Law of Universal Gravitation formula?

The units used for mass are kilograms (kg), while the units for distance are meters (m). It is important to use consistent units in the formula to get an accurate result.

5. Can the mass of a planet change over time?

Yes, the mass of a planet can change over time due to factors such as meteorite impacts, volcanic activity, and gas escaping from the planet's atmosphere. However, these changes are usually very small and do not significantly affect the overall mass of the planet.

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