Kepler's laws and orbits question?

In summary, the strength of the gravitational field at the surface of an imaginary planet with a diameter twice that of Earth and one moon with an orbital radius of 5.0x10^7 km and orbital period of 10 Earth days is 40,597,576.67 N/kg. This is calculated using the equation GM = (4pi^2(5x10^10)^3)/(8.64x10^5)^2, where G is the gravitational constant, M is the mass of the planet, and r is the radius of the moon's orbit.
  • #1
Kratos321
20
0

Homework Statement



An imaginary planet has a diameter twice that of our earth. The planet has one moon with an orbital radius of 5.0x10^7 km and orbital period of 10 Earth days.
Determine the strength of the gravitational field at the surface of the planet.

Radius of Earth = 6.38 x 10^6m
Orbital radius of moon = 5x10^10m
orbital period = 8.64 x 10^5 s

Homework Equations



r^3/T^2 = GM/4pi^2
g = GM/r^2

i think that's all..?...

The Attempt at a Solution



GM = (4pi^2(5x10^10)^3)/(8.64x10^5)^2
= 6.61 x 10^21

g = 6.61x10^21/(12.76x10^6)^2
= 40597576.67N/kg

this number is massive! I must be doing something wrong. any help?
 
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  • #2
Your calculation looks fine. I wouldn't want to live there!
 

Related to Kepler's laws and orbits question?

1. What are Kepler's laws of planetary motion?

Kepler's laws of planetary motion are three principles that describe the motion of planets around the sun. The first law, also known as the law of ellipses, states that planets orbit the sun in elliptical paths with the sun at one focus. The second law, known as the law of equal areas, states that a line connecting a planet to the sun will sweep out equal areas in equal intervals of time. The third law, also known as the law of harmonies, states that the square of the orbital period of a planet is directly proportional to the cube of its semi-major axis.

2. How did Kepler come up with his laws?

Johannes Kepler developed his laws of planetary motion by analyzing the extensive astronomical observations made by his mentor Tycho Brahe. Kepler used mathematical calculations and observations of the planets' motions to formulate his laws, which were published in his book Astronomia nova in 1609.

3. Are Kepler's laws still relevant today?

Yes, Kepler's laws are still relevant today and are considered fundamental principles in the field of astronomy. They have been used to accurately predict the positions of planets and other celestial bodies in our solar system and beyond. They also serve as the basis for understanding the motion of objects in space.

4. What is the significance of Kepler's laws?

Kepler's laws are significant because they provided a new understanding of how planets move in our solar system. They also laid the foundation for Isaac Newton's theory of gravity and the development of modern physics. Kepler's laws also helped scientists to better understand the nature of the universe and our place in it.

5. How do Kepler's laws apply to other objects in space?

While Kepler's laws were originally developed to describe the motion of planets around the sun, they can also be applied to other objects in space, such as moons orbiting planets or comets orbiting the sun. As long as there is a central body with a significant mass, and an orbiting object with a much smaller mass, Kepler's laws can be used to describe their motion.

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