Astronomy Assignment #5: Newton’s Universal Law of Gravitation
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Submit this cover sheet with your assignment.
Complete the assigned problems from the text listed below and address the Instructor Assigned Topic. Mathematical
problems may be hand written. Write out the problem, show your work in solving the problem and state your answer in a
complete sentence. Failure to complete all three of these tasks will result in less than full credit awarded.
Answer the following Review Questions from Nick Strobel’s AstronomyNotes: Chapter 5: Newton’s Law of Gravity
Review Questions
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What basic fundamental assumption did Newton make about the laws of nature on the Earth and in space?
Why is gravity often the most important force in astronomical interactions?
What things does gravity depend on?
How does gravity vary with distance between objects and with respect to what do you measure the distances?
What would happen to the Earth’s orbit if the Sun suddenly turned into a black hole (of the same mass)? Why?
What important laws of planet motion can be derived from Newton’s law of gravity?
Why is gravity called an “inverse square force”? What is the difference between a simple inverse relation and an inverse
square relation?
If the Earth was 3 A.U. from the Sun (instead of 1 A.U.), would the gravity force between the Earth and the Sun be less or
more than it is now? By how many times?
If Mercury was 0.2 A.U. from the Sun (instead of 0.4 A.U.), would the gravity force between Mercury and the Sun be less or
more than it is now? By how many times?
Why do astronauts in orbit around the Earth feel “weightless” even though the Earth’s gravity is still very much present?
What keeps satellites orbiting the Earth moving along their curved paths?
What two things must be determined first in order to calculate the mass of a planet or a star?
Jupiter’s moon Io has about the same mass as the Moon and orbits Jupiter at about the same distance that the Moon orbits the
Earth (center to center). Then why does Io take only 1.8 days to orbit Jupiter but our Moon takes 27.3 days to orbit the Earth?
Astronomers were able to accurately measure the orbital periods of the moons of Jupiter since the time of Galileo, so why
was an accurate value for Jupiter’s mass not found for over 300 years until the astronomical unit was measured accurately?
Which would have a shorter orbital period, a planet orbiting a massive star at 3 A.U. or a planet orbiting a low-mass star at 3
A.U.? Explain your answer.
If a planet orbiting a massive star has the same orbital period as a planet orbiting a low-mass star, which of the planets orbits
at a greater distance from its star? Explain your answer.
The following four problems are numerical and require calculation or algebraic expressions.
17. If Io takes 1.8 days to orbit Jupiter at a distance of 422,000 kilometers from its center, find out how long it would take Europa
to orbit Jupiter at 671,000 kilometers from its center.
18. The Hubble Space Telescope orbits the Earth 220 kilometers above the surface and takes about 1.5 hours to complete one
orbit. How can you find out how far up to put a communication satellite, so that it takes 24 hours to circle the Earth? (Such an
orbit is called a “geosychronous orbit” because the satellite remains above a fixed point on the Earth.)
19. Find out how long it will take the Cassini spacecraft to travel to Saturn 9.5 A.U. from the Sun. (Hint: Use the Hohmann
Transfer Orbit and find the period of that orbit from its semi-major axis.)