The Solar System
9th Edition
ISBN: 9781305804562
Author: Seeds
Publisher: Cengage
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Chapter 5, Problem 4RQ
To determine
The reason for which Aristotle’s explanation of gravity becomes invalid if Earth isn’t the centre of the universe.
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Newton’s law of gravitation and the formula for centripetal acceleration can be used to show that:
T^2=(4π^2/Gms)R^3 where G is the universal constant of gravitation and MS is the mass of the Sun. Take logarithms to base 10 of both sides of the equation to complete the expression for 2 lg T.2 lg T = ……………… × lg R + ……………………
A satellite is geostationary if it appears fixed in the sky as seen by an observer
on Earth. Geostationary satellites are very useful for communication and a lot of them
are in use. Access to geostationary orbit is regulated by international treaty and a
spot in geostationary orbit is probably the most desirable "unreal estate" I can think of.
What goes into making an orbit geostationary? Kepler's and Newton's laws,
and location, location, location. We will determine how this works in these exercises.
Kepler's first law in this context states that the orbit of a satellite is an ellipse
with the center of the Earth at one focus. Kepler's second law states that the line
joining the satellite and the center of the Earth sweeps out equal areas in equal intervals
of time. Kepler's third law (in Newtonian form) relates the orbital period of the satellite
to the semi-major axis of the orbit and the mass of the Earth.
In order to appear geostationary, a satellite must have a circular orbit,…
Many people mistakenly believe that the astronauts who orbit earth are "above gravity." earth's mass is 6*10^24 kg, and its radius is 6.38*10^6 m (6380 km). use the inverse-square law to find a height above earth's surface at that the force gravity on a shuffle is about 99% that at earth's surface.
Chapter 5 Solutions
The Solar System
Ch. 5 - Prob. 1RQCh. 5 - Today, what do we call the Aristotelean violent...Ch. 5 - Which of Keplers or Newtons laws best describes...Ch. 5 - Prob. 4RQCh. 5 - Prob. 5RQCh. 5 - If you drop a feather and a steel hammer at the...Ch. 5 - What is the difference between mass and weight?
Ch. 5 - Prob. 8RQCh. 5 - An astronaut working in space near the...Ch. 5 - Prob. 10RQ
Ch. 5 - A car is on a circular off ramp of an interstate...Ch. 5 - Prob. 12RQCh. 5 - Prob. 13RQCh. 5 - An astronaut is in space with a baseball and a...Ch. 5 - Prob. 16RQCh. 5 - Why did Newton conclude that some force had to...Ch. 5 - Why did Newton conclude that gravity has to be...Ch. 5 - Prob. 19RQCh. 5 - Prob. 20RQCh. 5 - Prob. 21RQCh. 5 - You are sitting next to a person who has twice as...Ch. 5 - Prob. 23RQCh. 5 - Why cant a spacecraft go beyond Earths gravity?Ch. 5 - Prob. 25RQCh. 5 - Balance a pencil lengthwise on the side of your...Ch. 5 - Prob. 27RQCh. 5 - Why can’t you leave Earth’s gravitational field...Ch. 5 - Prob. 29RQCh. 5 -
How do planets orbiting the Sun and skaters doing...Ch. 5 - Prob. 31RQCh. 5 - If you hold this textbook out at shoulder height...Ch. 5 - Today at the beach you see the highest of all high...Ch. 5 - Why is the period of an open orbit undefined?
Ch. 5 - In what conditions do Newtons laws of motion and...Ch. 5 - Prob. 36RQCh. 5 - Prob. 37RQCh. 5 - Prob. 38RQCh. 5 - How is gravity related to acceleration? Are all...Ch. 5 - Prob. 40RQCh. 5 - Prob. 41RQCh. 5 - Prob. 42RQCh. 5 - An astronomy textbook is to be dropped from a tall...Ch. 5 - Compared to the strength of Earth’s gravity at its...Ch. 5 - Compare the force of gravity on a 1 kg mass on the...Ch. 5 - Prob. 4PCh. 5 - Prob. 5PCh. 5 - If a small lead ball falls from a high tower on...Ch. 5 - What is the circular velocity of an Earth...Ch. 5 - What is the circular velocity of an Earth...Ch. 5 - Prob. 9PCh. 5 - Describe the shape of the orbit followed by the...Ch. 5 - Prob. 13PCh. 5 - What is the orbital period of a satellite orbiting...Ch. 5 - What would be the escape velocity at the surface...Ch. 5 - A moon of Jupiter takes 1.8 days to orbit at a...Ch. 5 - Prob. 1LTLCh. 5 - Prob. 2LTLCh. 5 - Why is it a little bit misleading to say that this...
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- You are planning a dream vacation to Mars. For the orbital dynamics part of the vacation planning assume that Earth is in a circular orbit 1.00 AU from the Sun and Mars is in a circular orbit 1.52 AU from the Sun. Assume the the orbits of Earth and Mars are coplanar and that they go around the Sun the same way. The orbit you plan to use for your trip is an ellipse with the Sun at one focus (Kepler's 1st Law). The perihelion of the ellipse is at Earth's orbit at 1.00 AU and the aphelion is at Mars' orbit at 1.52 AU. Your spacecraft will go around the Sun in the same sense as Earth and Mars. The orbit you have chosen is called a Hohmann Transfer Orbit. A. What is the semi-major axis a of the spacecraft's orbit? What is the eccentricity of the spacecraft's orbit? B. What is the orbital period of the spacecraft? How long does it take to get to Mars? How long does it take to get back? C. When (at what Earth - Mars configuration) do you launch to go? In other words, where does Mars need to…arrow_forwardAre Kepler’s laws purely descriptive, or do they contain causal information? Why?arrow_forwardAn astronaut exploring a distant solar system lands on a planet with with a radius of 2,360 km and a gravitational acceleration of 7.46 m/s2. The astronaut launches a space probe straight up starting with an initial speed of 1.10 km/s. What is the height the space probe could reach? (consider G=6.67×10–11 m3kg–1s–2)arrow_forward
- Which of the following is true about the Universal Gravitational Law? Group of answer choices Force of gravity is directly proportional to the product of masses and also directly proportional to the square of the distance between them Force of gravity is inversely proportional to the product of masses and also inversely proportional to the square of the distance between them Force of gravity is inversely proportional to the product of masses and directly proportional to the square of the distance between them Force of gravity is directly proportional to the product of masses and inversely proportional to the square of the distance between themarrow_forwardMany people mistakenly believe that the astronauts who orbit Earth are "above gravity." Earth's mass is 6×1024kg , and its radius is 6.38×106m (6380 km ). Use the inverse-square law to find a height above Earth's surface at that the force of gravity on a shuttle is about 94% that at Earth's surface. Express your answer to two significant figures and include the appropriate units.arrow_forwardTwo astroids one with a mass of 4x10^6KG and the other with the mass of 5x10^7 KG are 2x10^5 m apart. What is the gravitational force on the larger astroid?arrow_forward
- Use a distance of R = 1.48x10^11 meters for the distance between the earth and the sun. Use a mass of 1.99x10^30 kg to be 1 solar mass. For each of the different sun masses (as values of solar mass, aka 0.5 solar masses = 1x10^30 kg), as outlined in the lecture, calculate the period of the earth's orbit in days using Kepler's law for circular orbits (I double-checked it with these values and it works) and also calculate the corresponding orbital velocity of the earth. Questions: 1.) Using these values, and 6x10^24 kg for the mass of the earth, what is the strength of the gravitational force between the earth and the sun? 2.) If the earth were twice as far from the sun, what would be its period of orbit? 3.) Mars orbits the sun at a distance of 2.18x10^11 meters. How long is a Martian year, using Kepler's law for circular orbits?arrow_forwardUsing the PappusGuldinus theorem, calculate the volume of the object that will be formed by rotating the following geometric figure 360 degrees along the X - X-axis.arrow_forwardI am trying to calculate the gravitational mass (in solar masses) I have the formula M= V^2 R / G (4.31 x 10^-6) The paperwork says our numbers should be big but I am coming up with .002 etc. What am I doing wrong?arrow_forward
- Describe the gravitational forces.arrow_forwardName the absolute unit and gravitational unit of force.arrow_forwardKepler's 1st law says that our Solar System's planets orbit in ellipses around the Sun where the closest distance to the Sun is called perihelion. Suppose I tell you that there is a planet with a perihelion distance of 2 AU and a semi-major axis of 1.5 AU. Does this make physical sense? Explain why or why not.arrow_forward
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