Solar System
Introduction
The term "solar" indicates the sun; the solar system includes the sun and the other eight planets. The eight planets are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Pluto is considered a dwarf planet. Some primary data on the solar system includes: Age: 4.57 Billion years, Mass of the sun: 1.98 x 1030 kg, Mass of the earth: 5.97 x 1024 kg, Mass of the moon: 7.35 x 1022 kg, Distance between the sun and Earth: 150 million kilometers; Distance between Earth and moon: 384400 kilometers. The planets of our solar system are classified into two types: Terrestrial Planets and Gas Giants. Terrestrial Planets include the first four planets: Mercury, Venus, Earth, and Mars. The Gas Giants include the last four planets: Jupiter, Saturn, Uranus, and Neptune. The first four planets are classified as Terrestrial Planets since they were mostly composed of rocks, stones, and metals. The last four planets, as their names suggest, were mainly composed of gases like hydrogen and helium.
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Source: NASA's Goddard Space Flight Center |
Objective of the Post
This post's objective is mainly to make you familiarize yourself with the Solar system, use the Fundamental Concepts of Gravitations to find some data regarding the solar system, and provide some well-established data and some interesting features about the solar system. After reading and understanding this post, you will be able to critically apply the concept of gravitation force, Kepler's Law of Planetary Motion, and gain some information about some special features of our solar system. More on fields, potentials, and energy systems will be dealt with in upcoming posts.
Fundamentals of Gravitation
Any two objects in the universe attract each other with an attractive force of magnitude proportional to the product of their masses and inversely proportional to the square of the distance between them. So, the Force F = GMm/(R2), M and m are the masses of two particles, and R is the distance between them. This is popularly known as the Universal Law of Gravitation. The value of G is 6.67x10e-11. Its unit is Nm2kg2. This law is valid everywhere in our universe.
Calculate the force of attraction between the Sun and the earth, assuming the earth orbits around the sun in a perfectly circular orbit. (Use the provided data in the introduction section.)
Use Newton's Universal law of gravitation to find the force of attraction between the Sun and the Earth. M (Mass of the sun) = 2x10e30kg, m (Mass of the earth) = 6x10e24 kg, R = 150x109 m, and G = 6.67x10e-11. Finding F by substitution, we get the value of F = 3.557e22 N.
Calculate the approximate radius of the moon around the earth if the force of interaction between the earth and the moon is 1.95 e20 N. Check if the calculated radius of the moon's orbit around Earth matches the given data in the post. (TASK 1) (DIFFICULTY: 1/5)
Calculate the distance at which a satellite should be placed between the Sun and the Earth along the line joining them so that it does not receive any gravitational force of attraction. Use the given data. (TASK 2) (DIFFICULTY: 3/5)
An asteroid of mass M explodes equally and spreads uniformly in a radial direction. If the scientist measures the radius of a homogenous cloud to be R when the particles on the surface recede with velocity V, what is the final radius of the sphere? (TASK 3) (DIFFICULTY: 5/5)
Kepler's Law of Gravitation
First Law: All planets revolve around the sun in an elliptical orbit with the sun as one of their foci.
Second Law: All radius vectors from the sun pointing towards the planet sweep an equal area in an equal interval of time. Mathematically, Change in Area / Change in time = constant = L/2M, where L is the angular momentum of the planet and M is its mass.
Thirds Law: The square of the time period of the revolution of the planet around the sun is proportional to the cube of the radius of its orbit. The constant of proportionality changes with the mass of the object around which it revolves.
If the earth takes time T to swap the area ABC, what is the time of the revolution of the earth around the sun? Find the value of T as well.
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| fig.1: Not to the scale |
If the shaded region is A/4 units in area, then the area of the curve ABCS is A/4 + A/2 = 3A/4. So, the remaining area is A/4. If it takes T time to revolve the 3A/4 area, then how much time will it take to cover the remaining A/4 units of the area? Use Kepler's Law,
3A/4T = A/4 (t)
So t = T/3, So the total time of revolution is 4T/3. So 4T/3 = 365.25 days, so T = 273.9375 days.
Scientists have found out that the distance between Mars and the Sun is 228 million kilometers. Now, how will they calculate the time period of the Mars Revolution?
Using Kepler's third law between the earth and Mars for a common central object, i.e., the sun,
We use
T2 / R3 for earth = T2 / R3 for mars
365*365 / 150*150*150 = T2 / 228*228*228
T = 684.00 days, very close to the experimental value (687 days).
A satellite of mass M revolves around the earth such that it remains static with respect to an observer on the earth. Find the distance of the satellite from the earth's surface if the moon revolves around the earth every 27.3 days. (TASK 4) (DIFFICULTY: 2/5)
In the above question, if the satellite revolves around the earth in a time period of 11.2 hours with respect to an observer on the earth, find the distance. (TASK 5) (DIFFICULTY: 4/5)
Interesting Fact:
Why is Pluto a dwarf planet? Why was it recently excluded from the system of planets in the solar system?
The International Astronomical Union (IAU) decided to give Pluto the status of a dwarf planet because they have redefined the definition of the planets. The new definition of the planet is that
The planet is the celestial body:
1. is in orbit around the Sun
2. has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (a nearly round shape).
3. has cleared its neighborhood
----- (IAU)
Pluto does not follow the third definition since it shares its neighborhood with the other icy objects.