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Humbleness

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- 1

## 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 10

^{6}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 M

_{1}M

_{2}/r

^{2}

M

_{2}= F (r

^{2}) / Gm

_{1}

F = ma

F = mg

## The Attempt at a Solution

First using the equation to find the mass of this new Earth-like planet:

M

_{2}= 8.5 N (7.5 x 10

^{6})

^{2}/ (6.67 x 10

^{-11}) (1.0 kg)

M

_{2}= 8.5 N (56.25 x 10

^{12}) / (6.67 x 10

^{-11}) (1.0 kg)

M

_{2}= 7.168 x 10

^{24}

Then the gravitational field strength on this new planet:

a = G x M

_{2}/ r

^{2}

a = (6.67 x 10

^{-11}) (7.168 x 10

^{24}) / (56.25 x 10

^{12})

a = 47.81 x 10

^{13}/ 56.25 x 10

^{12}= 8.5m/s

^{2}

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/s

^{2}) = 425 N

Now calculating his weight on Earth:

F = mg = (50 kg) x (9.8m/s

^{2}) = 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.