Some homework questions in astrophysics (Kepler's Laws, Newton's Laws)

AI Thread Summary
The discussion revolves around homework questions related to Kepler's and Newton's laws in astrophysics, specifically focusing on calculations involving Mars and its moon Phobos. The original poster struggles with deriving the mass of Mars and the orbital speed of Phobos, expressing confusion over their calculations and the interpretation of radius. Participants note that while the application of Kepler's and Newton's laws appears correct, numerical errors seem to be the main issue, particularly in how the radius from Mars to Phobos is calculated. Clarifications are made regarding the correct use of Mars' radius in the calculations. Overall, the thread emphasizes the importance of accurate numerical computation in astrophysical problems.
petha1
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Homework Statement
1. Mars has a moon, Phobos. orbiting mars in circular orbit with T= 7h39min and r=9400 km.
Use Keplers laws to determine the mass of mars.

2. Calculate the mass of Mars from the orbital velocity, Newtons laws and gravitation

3. Given a star with M = 3*Mass of sun and R = 2.5*R_sun and T=11000K determine the thermal time scale of the planet if the total energy radiated during this time is 3/10 *GM^2/R

4. For the same star determine the nuclear time scale, given that the available nuclear energy is 0.1*0.007*M*c**2
Relevant Equations
T^2 = 4*pi^2*a^3/(G*M1+M2)
d=2*pi*r
v=d/t
v_r=sqrt(G(M1+M2)*(2/r-1/a))
L=4*pi*r^2*T^4*σ
T_th = E_g/L
T_n = E_n/L
1. Keplers third law (and the asumption that M1+M2 ~ M1) gives that
M_Mars = 4*Pi^2*a^3/(G*T^2)
With numerical values inserted

Mmars = 4*3.14^2*(9400*1000+3396.97*1000)^3/((6.67*10^-11*(7*60*60+39*60)^2)

2. Phobos needs 7h39 minutes to complete a circle, this gives a speed of 2*pi*(9400*1000+3396.97*1000)/(7*60*60+39*60) = 2912 m/s
The orbit is circular so the semi-major axis has the same value as radius. This gives the equation
2912 = sqrt(G*M_mars*(1/r))

3) T_th = (3/10*((3*1.981*10^30)^2*6.671*10^-11)/(2.5*6.95508*10^8))/(4*3.14*(2.5*6.95508*10^8)^2*11000^4*5.67*10^-8)

4) T_n = 0.1*0.007*3*1.981*10^3*(3*10^8)^2/(4*3.14*(2.5*6.95508*10^8)^2*11000^4*5.67*10^-8)
 
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I'm struggling to see what your answers are. All I can see is indecipherable number salad.

Is that really what you'd hand in as homework?
 
I have shown my calculations as far as I have done them, but they are nowhere near the correct answers. E.g.
Mars has a mass of 6,39×10^23 Kg, my answer is nowhere near that answer. Am I thinking wrong? Are my calculations wrong?
 
petha1 said:
I have shown my calculations as far as I have done them, but they are nowhere near the correct answers. E.g.
Mars has a mass of 6,39×10^23 Kg, my answer is nowhere near that answer. Am I thinking wrong? Are my calculations wrong?
I've never taught physics, but if you handed that to me as your homework, I would hand it straight back to you. Sorry.
 
I honestly don't understand what you are asking of me. I have banged my head for 6 hours straight on these 3 questions, and I am nowhere near an answer. Are my equations wrong? Are my calculations wrong? I solved two of the questions now.
Turns out that R=9400km was the radius from the middle of Mars to Phobos. Not as I thought, from the middle of Phobos to the surface of Mars.
 
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petha1 said:
Turns out that R=9400km was the radius from the middle of Mars to Phobos. Not as I thought, from the middle of Phobos to the surface of Mars.
Yes i was wondering why you add 3396.97*1000 to the radius. This 3396*1000 is the radius of Mars?

It seems to me that you correctly apply the laws (Kepler's law and Newton's Gravity Law) for 1 and 2 so the mistake must be in numerical calculations and that you added the radius of mars...
 
PeroK said:
I'm struggling to see what your answers are. All I can see is indecipherable number salad
You have got a point to some extent but I have seen much more worst posts here in PF. I think the OP has shown some considerable effort and deserves to be helped .
 
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