Homework Problem Using the Universal Gravitation Equation

[jackplaysgames]

Homework Statement

You are on a deep space mission to search for Earth-like planets. Your crew locates a possible planet and with scanners find the radius to be 7.5 x 106m. they land and 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

F= Gm1m2/d2

For question A, I know that I am supposed to input the numbers given into the Universal Gravitation Equation, but I do not know how to solve for it beyond that.

For question B, I know that the astronauts weight depends on the mass and gravity of the new planet but I do not know how to prove it mathematically.

Thank you in advance!

 

[greg_rack]

For question A, I know that I am supposed to input the numbers given into the Universal Gravitation Equation, but I do not know how to solve for it beyond that.

What confuses you about using the Universal gravitation equation? It looks like you have all data required to find the mass of the planet. Don't you? Could you describe your precise problem/doubt about it?

For question B, I know that the astronaut's weight depends on the mass and gravity of the new planet but I do not know how to prove it mathematically.

The problem asks you to see whether the astronaut weighs more, less or the same on this planet as on earth. The weight $W$ of an object with mass $m$ depends on the gravitational acceleration $g$ to which its subject. Does $g$ changes depending on the planet you're in? If yes, how?

 

[jackplaysgames]

What confuses you about using the Universal gravitation equation? It looks like you have all data required to find the mass of the planet. Don't you? Could you describe your precise problem/doubt about it?The problem asks you to see whether the astronaut weighs more, less or the same on this planet as on earth. The weight $W$ of an object with mass $m$ depends on the gravitational acceleration $g$ to which its subject. Does $g$ changes depending on the planet you're in? If yes, how?

For the equation part:
The equation is f = Gm1m2/d^2

I know that G = (6.67×10−11Nm^2/kg^2)
f = 8.5N
d^2 = 7.5 x 10^6 m

The problem I am having is that I do not know how to rearrange the equation and solve for m1 or m2.And I understand part b now, thank you!

 

[greg_rack]

The problem I am having is that I do not know how to rearrange the equation and solve for m1 or m2.

You know the mass of the object to be 1.0kg, it's just a first-degree equation with one unknown now:
$$F=G\frac{m\cdot M}{d^2} \rightarrow 8.5N=G\frac{1.0kg\cdot M}{(7.5e6)^2}$$

And I understand part b now, thank you!

No worries!

 

[jackplaysgames]

You know the mass of the object to be 1.0kg, it's just a first-degree equation with one unknown now:
$$F=G\frac{m\cdot M}{d^2} \rightarrow 8.5N=G\frac{1.0kg\cdot M}{(7.5e6)^2}$$No worries!

I got it now, thank you for the help!

 

[greg_rack]

I got it now, thank you for the help!

You're welcome!