Determine the mass of the planet using Newton’s Law of Universal Gravitation

[Petronius]

Homework Statement

You are on a deep space mission to search for Earth-like planets. Your crew locates a possible they hang a 1.0 kg mass from a spring scale. It reads 8.5 N.

a. Determine the mass of the planet using Newton’s Law of Universal Gravitation.

b. Describe whether an astronaut standing on this new planet weighs more, less, or the same as on Earth. Show your work.

Relevant Equations

From course: F= (Gm_1 m_2)/r^2

m_1= Fr^2/(Gm_2 )
(Could not find in my course but discovered this rearranged version on the internet. Appeared essential in solving the second part of the problem . https://www.ajdesigner.com/phpgravity/newtons_law_gravity_equation_force.php)

Fg=mg

Hello, and thank you again to anyone who can confirm if I have the right answer or who can give me some suggestions. This question felt like a bit of a surprise because we have not yet covered one where the mass of a planet was missing. Thus, my confidence in my work is low. Part b felt like a bit of an extension as well.

Part a) Determine the mass of the planet using Newton’s Law of Universal Gravitation.

I first determined given and missing data:

Given:
F= 8.5 N
G: 6.67 x 10^-11 nm^2/kg^2
m2= 1.0kg
r = 7.5x 10^6

Unknown: m1: = ?

I then attempted to solve knowing I would have to rearrange the standard equation from my course.

F= (Gm_1 m_2)/r^2
rearranged..

m_1= Fr^2/(Gm_2 )

m1 = (8.5N) x (7.5 x 10^6) / (6.67 x 10^-11) x (1.0kg)

m1 = 478125000000000/(6.67 x 10^-11) x (1.0kg)

m1 = 7.16829085 x 10^24 kg

m1 = 7.17 x 10^24 kg ( I think I should round to this ?)

Therefore the mass of the planet is 7.17 x 10^24 kg.Part b) Describe whether an astronaut standing on this new planet weighs more, less, or the same as on Earth. Show your work.Given:
9.8 N/kg
M= 1.0kg

Unknown: Fg

Fg = (1.0)(9.8 N/kg)
Fg = 9.8 N

I than concluded that since the force of gravity on the 1.0kg mass was greater on Earth than on the new planet, an astronaut would weigh less on this new planet than on earth.

Any help would be greatly appreciated!
Thank you,

 

[PeroK]

Looks okay to me.

 

[Petronius]

Thank you for looking it over.