21st Century Astronomy 6E
6th Edition
ISBN: 9780393690675
Author: Laura Kay, Stacy Palen, George Blumenthal
Publisher: W. W. Norton
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Chapter 4, Problem 36QP
(a)
To determine
The shape of that orbit.
(b)
To determine
The minimum velocity required for the spacecraft to move its way to Mars.
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a. Calculate the escape velocity of our solar system, from the surface of the sun.
b. What velocity would an object leaving Earth need, to escape from our solar system?
(ignore the gravitational effect from Earth and other planets for a & b)
5. For a satellite to be in a circular orbit 780 km above the surface of the earth.
A. What orbital speed must it be given?
B. What is the period of the orbit (in hours)?
A number of gas giant planets orbiting other stars at distances less than 1 A.U. have been discovered. Because of their proximity to their parent stars, and their compositional similarity to Jupiter, they have been labeled “Hot Jupiters”.
The orbital radius of one of these planets is 0.06 A.U. with average orbital speed 600 km/sec. What is the length of this planet’s year in Earth (solar) days?
Estimate the mass, M, of its parent star in terms of the mass of the sun (M) using Newton’s first form of Kepler’s 3rd Law.
Calculate the star’s luminosity, L, in terms of the luminosity of the sun (L☉), Note: (LL=MM4where L ~ 4 × 1026 W ).
The radius of this planet is 1.5 times the radius of Jupiter. Assuming its equilibrium temperature is the temperature at which the planet radiates as much energy as it receives from its star, estimate the temperature of the planet. The value of the planet’s albedo is 0.8. (NOTE: The intensity of the star’s radiant power at a distance d from the star is…
Chapter 4 Solutions
21st Century Astronomy 6E
Ch. 4.1 - Prob. 4.1ACYUCh. 4.1 - Prob. 4.1BCYUCh. 4.2 - Prob. 4.2CYUCh. 4.3 - Prob. 4.3CYUCh. 4.4 - Prob. 4.4CYUCh. 4 - Prob. 1QPCh. 4 - Prob. 2QPCh. 4 - Prob. 3QPCh. 4 - Prob. 4QPCh. 4 - Prob. 5QP
Ch. 4 - Prob. 6QPCh. 4 - Prob. 7QPCh. 4 - Prob. 8QPCh. 4 - Prob. 9QPCh. 4 - Prob. 10QPCh. 4 - Prob. 11QPCh. 4 - Prob. 12QPCh. 4 - Prob. 13QPCh. 4 - Prob. 14QPCh. 4 - Prob. 15QPCh. 4 - Prob. 16QPCh. 4 - Prob. 17QPCh. 4 - Prob. 18QPCh. 4 - Prob. 19QPCh. 4 - Prob. 20QPCh. 4 - Prob. 21QPCh. 4 - Prob. 22QPCh. 4 - Prob. 23QPCh. 4 - Prob. 24QPCh. 4 - Prob. 25QPCh. 4 - Prob. 26QPCh. 4 - Prob. 27QPCh. 4 - Prob. 28QPCh. 4 - Prob. 29QPCh. 4 - Prob. 30QPCh. 4 - Prob. 31QPCh. 4 - Prob. 32QPCh. 4 - Prob. 33QPCh. 4 - Prob. 34QPCh. 4 - Prob. 35QPCh. 4 - Prob. 36QPCh. 4 - Prob. 37QPCh. 4 - Prob. 38QPCh. 4 - Prob. 39QPCh. 4 - Prob. 40QPCh. 4 - Prob. 41QPCh. 4 - Prob. 42QPCh. 4 - Prob. 43QPCh. 4 - Prob. 44QPCh. 4 - Prob. 45QP
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- An object of mass m is located on the surface of a spherical planet of mass M and radius R. The escape speed from the planet does not depend on which of the following? (a) M (b) m (c) the density of the planet (d) R (e) the acceleration due to gravity on that planetarrow_forwardWhat is the orbital radius of an Earth satellite having a period of 1.00 h? (b) What is unreasonable about this result?arrow_forwardSuppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon B has twice the mass and twice the radius of moon A. What is the gravitational acceleration at its surface? Neglect the gravitational acceleration due to Jupiter. (a) 8 m/s2 (b) 4 m/s2 (c) 2 m/s2 (d) 1 m/s2 (e) 0.5 m/s2arrow_forward
- Planetary orbits are often approximated as uniform circular motion. Figure P7.9 is a scaled representation of a planets orbit with a semimajor axis of 1.524 AU. a. Use Figure P7.9 to find the ratio of the Suns maximum gravitational field to its minimum gravitational field on the planets orbit. b. What is the ratio of the planets maximum speed to its minimum speed? c. Comment on the validity of approximating this orbit as uniform circular motion.arrow_forwardAstronomical observatrions of our Milky Way galaxy indicate that it has a mass of about 8.01011 solar masses. A star orbiting on the galaxy’s periphery is about 6.0104 light-years from its center. (a) What should the orbital period of that star be? (b) If its period is 6.0107 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of other matter, such as a very massive black hole at the center of the Milky Way.arrow_forwardA massive black hole is believed to exist at the center of our galaxy (and most other spiral galaxies). Since the 1990s, astronomers have been tracking the motions of several dozen stars in rapid motion around the center. Their motions give a clue to the size of this black hole. a. One of these stars is believed to be in an approximately circular orbit with a radius of about 1.50 103 AU and a period of approximately 30 yr. Use these numbers to determine the mass of the black hole around which this star is orbiting, b. What is the speed of this star, and how does it compare with the speed of the Earth in its orbit? How does it compare with the speed of light?arrow_forward
- Model the Moons orbit around the Earth as an ellipse with the Earth at one focus. The Moons farthest distance (apogee) from the center of the Earth is rA = 4.05 108 m, and its closest distance (perigee) is rP = 3.63 108 m. a. Calculate the semimajor axis of the Moons orbit. b. How far is the Earth from the center of the Moons elliptical orbit? c. Use a scale such as 1 cm 108 m to sketch the EarthMoon system at apogee and at perigee and the Moons orbit. (The semiminor axis of the Moons orbit is roughly b = 3.84 108 m.)arrow_forwardConsider the previous problem and include the fact that Earth has an orbital speed about the Sun of 29.8km/s . (a) What speed relative to Earth would be needed and in what direction should you leave Earth? (b) What will be the shape of the trajectory?arrow_forwardFor many years, astronomer Percival Lowell searched for a Planet X that might explain some of the perturbations observed in the orbit of Uranus. These perturbations were later explained when the masses of the outer planets and planetoids, particularly Neptune, became better measured (Voyager 2). At the time, however, Lowell had proposed the existence of a Planet X that orbited the Sun with a mean distance of 43 AU. With what period would this Planet X orbit the Sun?arrow_forward
- Unreasonable Results (a) Based on Kepler's laws and information on the orbital characteristics of the Moon, calculate the orbital radius for an Earth satellite having a period of 1.00 h. (b) What is unreasonable about this result? (c) What is unreasonable or inconsistent about the premise of a 1.00 h orbit?arrow_forward(a) One of the moons of Jupiter, named Io, has an orbital radius of 4.22 108 m and a period of 1.77 days. Assuming the orbit is circular, calculate the mass of Jupiter, (b) The largest moon of Jupiter, named Ganymede, has an orbital radius of 1.07 109 m and a period of 7.16 days. Calculate the mass of Jupiter from this data, (c) Are your results to parts (a) and (b) consistent? Explain.arrow_forwardYou are a scientist exploring a mysterious planet. You have performed measurements and know the following things: The planet has radius d. It is orbiting his star in a circular orbit of radius b. it takes time T to complete one orbit around the star. the free-fall acceleration on the surface of the planet is a. Derive an expression for the mass and of the star in terms of b,T, and G the universal gravitational constant.arrow_forward
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