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

In summary, Keplers third law (and the asumption that M1+M2 ~ M1) gives that Mmars = 4*3.14^2*(9400*1000+3396.97*1000)^3/((6.67*10^-11*(7*60*60+39*60)^2)
  • #1
petha1
5
1
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)
 
Last edited by a moderator:
  • Like
Likes Delta2
Physics news on Phys.org
  • #2
:welcome:

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?
 
  • #3
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?
 
  • #4
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.
 
  • #5
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:
  • #6
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...
 
  • #7
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 .
 

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

1. What are Kepler's Laws of Planetary Motion?

Kepler's Laws of Planetary Motion are three laws that describe the motion of planets around the sun. The first law states that planets move in elliptical orbits with the sun at one focus. The second law states that a line connecting a planet to the sun sweeps out equal areas in equal times. The third law states that the square of a planet's orbital period is proportional to the cube of its semi-major axis.

2. How do Kepler's Laws relate to Newton's Laws of Motion?

Kepler's Laws of Planetary Motion were derived from observations made by Johannes Kepler, while Newton's Laws of Motion were developed by Isaac Newton to explain the underlying physical principles behind planetary motion. Kepler's Laws describe the motion of planets, while Newton's Laws provide a theoretical framework for understanding the forces that govern this motion.

3. What is the significance of Kepler's Laws in modern astrophysics?

Kepler's Laws are fundamental principles that have greatly contributed to our understanding of the universe. They have been used to accurately predict the positions and movements of planets, and have also been applied to other astronomical objects such as moons, comets, and asteroids. Additionally, Kepler's Laws have been instrumental in the development of the field of astrophysics, providing a foundation for studying the dynamics of celestial bodies.

4. How do Kepler's Laws apply to objects other than planets?

While Kepler's Laws were originally derived to describe the motion of planets, they can also be applied to other objects in the universe. For example, Kepler's Laws can be used to describe the motion of moons around planets, or the motion of comets and asteroids around the sun. However, they may not be applicable to objects that are subject to strong gravitational forces from multiple bodies, such as binary star systems.

5. Are Kepler's Laws still considered valid in modern astrophysics?

Yes, Kepler's Laws are still considered valid in modern astrophysics. While they have been refined and expanded upon with new discoveries and advancements in technology, the core principles of Kepler's Laws remain unchanged. They continue to be used in the study of planetary motion and other celestial phenomena, and have stood the test of time as fundamental principles in astrophysics.

Back
Top