21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 4, Problem 41QP
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Compare the tidal force of Jupiter with that of the doctor in attendance at your birth.
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The ratio of the radius of a planet A to that of a planet B is “r”. The ratio of acceleration due to gravity on the planets is “p”. The ratio of escape velocities of the two planets is _____
a) (pr)1/2
b) (p/r)1/2
c) (pr)
d) (p/r)
Somewhere far, far away on the other side of our galaxy, there is a new protoplanetary disk where
two baby planetesimals are growing. Planetesimal A is currently 5x10° kg, and Planetesimal B is
2x105 kg. If these two planetesimals are 100 meters apart, what is the gravitational force between
them? (Hint: the Universal Gravitational Constant (G) is 6.67x10-11 Nm²/kg²)
Gm,m2
FG
r2
Planetesimal A
Planetesimal B
5 x 10°kg
2 x 105kg
100 meters
The semimajor axis of Mars orbit is about 1.52 astronomical units (au), where an au is the Earth's average distance from the Sun, meaning the semimajor axis of Earth's orbit is 1 au. To go from Earth to Mars and use the least energy from rocket fuel, the orbit has a semimajor axis of 1.26 au and an eccentricity of about 0.21. Starting at Earth's orbit, to follow this path we give the spacecraft an orbital velocity of 40 km/s. Which of the following describes this best?
a. It arrives at Mars orbit at the same moment that Mars is there, and must speed up to go into an orbit next to Mars or else drop back into perihelion (closest to the Sun) at Earth's orbit.
b. It arrives at Mars orbit at the same moment that Mars is there, and must slow down to go into an orbit next to Mars or else drop back into perihelion (closest to the Sun) at Earth's orbit.
c. It flys past Mars on its trajectory unless it is braked by accelerating toward the Sun. It which leaves Earth when Mars is nearly…
Chapter 4 Solutions
21st Century Astronomy
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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- Io, a satellite of Jupiter, has an orbital period of 1.77 days and an orbital radius of 4.22 105 km. From these data, determine the mass of Jupiter.arrow_forwardThe semimajor axis of Mars orbit is about 1.52 astronomical units (au), where an au is the Earth's average distance from the Sun, meaning the semimajor axis of Earth's orbit is 1 au. To go from Earth to Mars and use the least energy from rocket fuel, the orbit has a semimajor axis of 1.26 au and an eccentricity of about 0.21. Starting at Earth's orbit, to follow this path we give the spacecraft an orbital velocity of 40 km/s. Which of the following describes this best? It arrives at Mars orbit at the same moment that Mars is there, and must speed up to go into an orbit next to Mars or else drop back into perihelion (closest to the Sun) at Earth's orbit. It arrives at Mars orbit at the same moment that Mars is there, and must slow down to go into an orbit next to Mars or else drop back into perihelion (closest to the Sun) at Earth's orbit. It flys past Mars on its trajectory unless it is braked by accelerating toward the Sun. It which leaves Earth when…arrow_forwardAn unknown planet (mass is equal to 4.26 x 10^24 kg) is orbiting around the sun (mass of the sun is equal to 6.623703×1035kg). Knowing that the gravitational force between the unknown planet and the sun is (5.18 x 10^9)N, is the unknown planet nearer or farther to the sun compared to earth? (earth's distance to sun is 1 AU) Express your answer in terms of astronomical units or AU (1AU = 1.496 x 108 km). Assuming that the sun is fixated at a center point, calculate the area (in of the unknown planet's orbit (assume that the orbit is circle).arrow_forward
- For a planet of uniform density, how would the magnitude of the gravitational field halfway to the center compare with the field at the surface?arrow_forwardThe Earth’s radius is about 6400 km. The International Space Station (ISS) orbits about 400 km above Earth’s surface. So the center-to-center distance between Earth’s center and the space station is about 6800 km. Estimate Earth’s gravitational acceleration at the space station orbital height, giss. Use the ratio approach: giss / g = giss /980 = (6400 /6800)^2 = giss = cm/s^2.arrow_forwardMars has two moons orbiting it. One moon is named Deimos ( terror/dread from Greek mythology). Deimos has a mass of 2(10)^15 kg and is 23,460 km from Mars. The mass of Mars is 6.42 (10) ^23 kg a) What is the gravitational force between Mars and Deimos? (give this answer in Scientific Notation with 2 decimal places) b) What is the velocity of Deimos as it orbits Mars? ( give this answer in decimal form to 2 decimal places) a) = FG __________________ N b) V = ________________ m/sarrow_forward
- The International Space Station is in a 270-mile-high orbit. What is the station's orbital speed? The radius of Earth is 6.37×106m6.37×106m, its mass is 5.98×1024kg5.98×1024kg. What is the station's orbital period?arrow_forwardWhat is the total gravitational potential energy of the three masses in (Figure 1)? Assume m1=20kg, m2=15kg and m3=10kg.arrow_forwardA married couple is standing on a bus stop waiting for a ride. The wife and the husband have a mass of 65kg and 80 kg, respectively. Calculate the gravitational force that exist between them if they are 50cm apart from each other. Planet A and Planet B have a mass of 4 x 1024 kg and 4.5 x 1025 kg. The gravitational force between the two planets is 4.8 x 1020. How apart is Planet A from Planet B?arrow_forward
- The gravitational force between two giant lead spheres is 0.010 N when the centers of the spheres are 20 m apart. What is the distance between their centers when the gravitational force between them is 0.160 N?arrow_forwardAn unknown planet (mass is equal to 1.29 x 10^12 kg) is orbiting around the sun (mass of the sun is equal to 6.623703×10^35kg). Knowing that the gravitational force between the unknown planet and the sun is (5.61 x 10^20 )N, is the unknown planet nearer or farther to the sun compared to earth? (earth's distance to sun is 1 AU) Express your answer in terms of astronomical units or AU (1AU = 1.496 x 10^8 km). Assuming that the sun is fixated at a center point, calculate the area of the unknown planet's orbit (assume that the orbit is circle). Express your answer using proper scientific notation conventionarrow_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
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