Scientists have recently discovered an exoplanet oribiting a star at the same distance that Earth orbits our Sun. If this exoplanet is 2 the mass of Earth, but has a radius twice that of Earth's, compare the gravitational field (g)on the surface of this exoplanet to the gravitational field on Earth's surface. a. The gravitational field on the surface of the exoplanet will be the same as the gravitational field on Earth's surface. b. The gravitational field on the surface of the exoplanet will be 1/8 of the gravitational field on Earth's surface.

Scientists have recently discovered an exoplanet oribiting a star at the same distance that Earth orbits our Sun. If this exoplanet is 2 the mass of Earth, but has a radius twice that of Earth's, compare the gravitational field (g)on the surface of this exoplanet to the gravitational field on Earth's surface. a. The gravitational field on the surface of the exoplanet will be the same as the gravitational field on Earth's surface. b. The gravitational field on the surface of the exoplanet will be 1/8 of the gravitational field on Earth's surface.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter7: Gravity

Section: Chapter Questions

Problem 45PQ: Figure P7.45 shows a picture of American astronaut Clay Anderson experiencing weightlessness on...

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(a) Calculate Earth’s mass given the acceleratioln due to gravity at the North Pole is measured to be 9.832m/s2 and the radius of the Earth at the pole is 6356 km. (b) Compare this with the NASA’s Earth Fact Sheet value of 5.97261024kg .
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?
Figure P7.45 shows a picture of American astronaut Clay Anderson experiencing weightlessness on board the International Space Station. a. Most people have the misconception that a person in a spacecraft is weightless because he or she is no longer affected by gravity. Show that this premise cannot be true by computing the gravitational field of the Earth at an altitude of 200 km the typical altitude of a spacecraft in orbit. Compare this result with the gravitational field on the surface of the Earth. b. Why would astronauts in orbit experience weightlessness even if they are experiencing a gravitational field (and therefore a gravitational force)?
Astronomical 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.
For 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?
When a star dies, much of its mass may collapse into a single point known as a black hole. The gravitational force of a black hole on surrounding astronomical objects can be very great. Astronomers estimate the strength of this force by observing the orbits of such objects around a black hole. What is the gravitational force exerted by a black hole on a 1-solar-mass star whose orbit has a 1.4 1010 m radius and a period of 5.6 days?
Suppose astronomers find an earthlike planet that is twice the size of Earth (that is, its radius is twice that of Earth’s). What must be the mass of this planet such that the gravitational force (Fgravity) at the surface would be identical to Earth’s?
(a) What is the acceleration due to gravity on the surface of the Moon? (b) On the surface of Mars? The mass of Mars is 6.4181023 kg and its radius is 3.38106 m.
(a) What is the acceleration due to gravity on the surface of the Moon? (b) On the surface of Mars? The mass of Mars is SW 6.4181023kg and its radius is 3.38106m .
Check Your Understanding Earth exerts a tidal force on the Moon. Is it greater than, the same as, or less than that of the Moon on Earth? Be careful in your response, as tidal forces arise from the difference in gravitational forces between one side and the other. Look at the calculations we performed for the tidal force on Earth and consider the values that would change significantly for the Moon. The diameter of the Moon is one-fourth that of Earth. Tidal forces on the Moon are not easy to detect, since there is no liquid on the surface.
Three billiard balls, the two-ball, the four-ball, and the eight-ball, are arranged on a pool table as shown in Figure P7.26. Given the coordinate system shown and that the mass of each ball is 0.150 kg, determine the gravitational field at x=2m, y=0.
(a) Calculate Earth's mass given the acceleration due to gravity at the North Pole is 9.830 m/s2 and the radius of the Earth is 6371 km from center to pole. (b) Compare this with the accepted value of 5.9791024 kg.