Gravitational Forces between planets/objects

[mavid]

Homework Statement

The gravitational acceleration at the surface of planet X is 12.0 m/s2, and the radius of the planet is 67,400 km. The altitude above the surface of planet X, at which the weight of a body is equal to that on the surface of the Earth, in km, is closest to what value ?

Homework Equations

W(weight of object at the Earth surface)=(G*m_1*m_2)/r^2
m_1--- the mass of the object
m_2----- the mass of the Earth

W(weight of the object above the planet X)=(G*m_1*m_3)/(r+h)^2
m_3 ----the mass of the planet X
m_1----the mass of the object

Looking for h----the altitude at which the object weights the same as at the surface of the Earth;

The Attempt at a Solution

Not sure which equations to use or how to relate the correct equations to each other;but:

W(of the object at the Earth's surface)= 9.8*m_1
W(of the object at the X planet's surface)= 12*m_1

Possibly substitute 12*m_1 into W=(G*m_1*m_3)/(r+h)^2
Then m_1 will cancel out; but have two unknowns left: m_3 and h...not sure how to go from here. Please help.

 

[Asphyxion]

Hint: $$G\dfrac{m_1 m_2}{r^{2}} = m_2 g$$ is what is used to caluclate the approximation $$F=mg$$ at earth.

 

[mavid]

I understand the formula, but what do I need it for?
m_1 wil cancel out if I set both equations equal to each other. But I still need m_3 inorder to find h. Please help.

I went to the tutoring center in my college, and even they were not able to help me solve this problem( after being there for 2 hours :( )

How do I ( if I can at all) figure out the mass of the planet X? Or maybe there is another way to go around it, and I just do not see it. Not sure. Really need help.

 

[mavid]

here is what I came up with:

1. a=g=12=(G*m_3)/r^2

m_3(mass of the planet X)= 8.17e26 kg

2. Then:
W(weight of the object above the planet X)=(G*m_1*m_3)/(r+h)^2

9.8*m_1=W=(G*m_1*m_3)/(r+h)^2...where m_1 cancels out, and we are left with following:

9.8=(G*m_3)/(r+h)^2
9.8=[(6.67*10^(-11))*8.17e26 kg]/[67400000m+ h]^2 ... solvinf gor h:
7.46e7=67400000+h
h= 7.2e6 m or 7200 km...is it correct? Please let me know, and if it...then thank you very much for your help :)

 

[Asphyxion]

This was exactly what i was hinting for :) Good work!