Gravitation and Newton's Synthesis

In summary, by using Kepler's Law and choosing Earth as a reference point, the mean distance of the asteroid Icarus from the Sun is calculated to be approximately 1.87 E 11 m, while the book lists it as 1.62 E 11 m. The discrepancy may be due to the conversion of the Earth's period into seconds.
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Homework Statement


The asteroid Icarus, though only a few hundred meters across, orbits the Sun like the other planents. Its period is about 410 d. What is its mean distance from the Sun?


Homework Equations



Keplers Law
T_1 ^2 / T_2 ^2 = S_1 ^3 / S_2 ^3

The Attempt at a Solution



I chose my second reference point to be the earth
the distance from the Earth to the sun is about 1.5 E 11 m
the period of the Earht is one day or 8.64E4 s
410 d is equal to 3.542E7 s

from keplers law

S_1 = CUBEROOT( (T_1^2 S_2^3)/T_2^2

CUBEROOT( ((3.542 E 7 s)^2 (1.5 E 11 m)^3)/(8.64 E 4 s)^2
I'm getting about 1.87 E 11 m
the book says 1.62 E 11 m

what am I doing wrong
 
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  • #2
What for the period of the Earth is one day ?
 
  • #3
Also, it is not necessary to convert the periods into seconds in this problem.
 

1. What is the concept of gravitation?

Gravitation is the natural phenomenon by which all objects with mass are attracted to one another. It is responsible for the motion of planets, stars, and galaxies in the universe.

2. Who is Isaac Newton and what is his contribution to the study of gravitation?

Sir Isaac Newton was an English physicist and mathematician who is widely recognized as one of the most influential scientists in history. He proposed the theory of gravitation in his famous book "Principia Mathematica", which explains the laws of motion and the concept of universal gravitation.

3. What is Newton's law of gravitation?

Newton's law of gravitation states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This law is mathematically represented as F = G * (m1 * m2)/d^2, where F is the force of attraction, G is the gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them.

4. How did Newton's synthesis revolutionize our understanding of the universe?

Newton's synthesis of the laws of motion and gravitation helped to explain and predict the motion of objects in the universe, from the smallest particles to the largest celestial bodies. It also laid the foundation for further advancements in physics and astronomy, leading to a better understanding of the laws that govern the universe.

5. What are the limitations of Newton's law of gravitation?

Although Newton's law of gravitation is highly accurate for most everyday situations, it fails to accurately predict the motion of objects at very high speeds or near extremely massive objects. It was later replaced by Albert Einstein's theory of general relativity, which provides a more comprehensive and accurate explanation of the effects of gravitation on objects in the universe.

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