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

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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Delta2

## Answers and Replies

PeroK
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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?

PeroK
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2020 Award
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.

Last edited:
Delta2
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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...

Delta2
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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 .