You are participating in a NASA traineeship, working with a group planning a new landing on Mars. Your supervisor has come up with an idea for putting a synchronous satellite over the landing spot near the Martian equator, so that radio communication between Earth and the lander is improved. She asks you to report to her on the required height above the Martian surface of a synchronous satellite. Note: The rotation period of Mars is 1.026 d. (

You are participating in a NASA traineeship, working with a group planning a new landing on Mars. Your supervisor has come up with an idea for putting a synchronous satellite over the landing spot near the Martian equator, so that radio communication between Earth and the lander is improved. She asks you to report to her on the required height above the Martian surface of a synchronous satellite. Note: The rotation period of Mars is 1.026 d. (

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter11: Gravity, Planetary Orbits, And The Hydrogen Atom

Section: Chapter Questions

Problem 6OQ: Suppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon...

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Calculate the effective gravitational field vector g at Earths surface at the poles and the equator. Take account of the difference in the equatorial (6378 km) and polar (6357 km) radius as well as the centrifugal force. How well does the result agree with the difference calculated with the result g = 9.780356[1 + 0.0052885 sin 2 0.0000059 sin2(2)]m/s2 where is the latitude?
Let gM represent the difference in the gravitational fields produced by the Moon at the points on the Earths surface nearest to and farthest from the Moon. Find the fraction gM/g, where g is the Earths gravitational field. (This difference is responsible for the occurrence of the lunar tides on the Earth.)
In this problem you will measure the gravitational constant in a series of “observational experiments,” making use of Newton’s law of gravitation and second law of motion as well as Kepler’s third law of planetary motion Suppose a rocket is launched as described in part (d) with an initial speed of vi = 494 m/s and attains a peak altitude of H = 12.7 km above the surface of Earth. Taking ME = 5.95×1024 kg and Ri = 6.41×106 m, what is the measured value of the gravitational constant, in units of N⋅m2/kg2?
The International Space Station (ISS) completes one orbit of Earth in 92 minutes. What is the radius of the orbit in kilometers (km)? You may assume the orbit is circular. The mass of the ISS is 420 kg, and the mass of the Earth is 6.0×10246.0×1024kg. Newton’s gravitational constant is 6.7×10−11N⋅m2kg26.7×10−11kg2N⋅m2.
The planet Mercury has a mass of 3.30×1023 kilograms (kg) and a radius of 2440 kilometers (km). The universal gravitational constant is G = 6.67 × 10−11 Nm2/kg2. A) If a is ball is launched upwards from the surface of Mercury with an initial speed of 2.15 kilometers per second (km/s), what height maximum height above the surface will it reach before falling back down? Give your answer in units of kilometers (km). Assume that the total mechanical energy of the ball is conserved. B) What is the escape speed of Mercury? Give your answer in units km/s.
Suppose that a planet were discovered between the Sun and Mercury, with a circular orbit of radius equal to 2/3 of the average orbit radius of Mercury. What would be the orbital period of such a planet? (Such a planet was once postulated, in part to explain the precession of Mercury's orbit. It was even given the name Vulcan, although we now have no evidence that it actually exists. Mercury's precession has been explained by general relativity.)
Find the speed (in m/s) needed to escape from the solar system starting from the surface of Venus. Assume there are no other bodies involved, and do not account for the fact that Venus is moving in its orbit. [Hint: vesc = 2GM R does not apply. Use conservation of energy, and include the potential energy of both Venus and the Sun.]
Scientists determine the masses of planets by observing the effect of the gravitational field of those planets on nearby objects - mainly upon their moons. By measuring the orbital period and orbital radius of a moon about a planet, Newton's laws of motion can be used to determine the mass of the planet. Phobos, a moon of the planet Mars, was discovered in 1877. It's orbital radius is 9380 km and its orbital period is 0.319 days (2.77 x 104 seconds). Determine the mass of Mars based on this data.
The Earth is 149.6 billion meters from the sun, and the moon is 384.4 million meters from the Earth, on average. The mass of Earth is 5.97 x 10^24 kg, the mass of the sun is 1.99×1030 kg, and the mass of the moon is 7.35x10^22 kg. Newton's gravitational constantis 6.67 x 10^-11. There are certain points near the Earth where the gravitational forces on an object caused by the Earth, moon, and Sun all add up to zero. A satellite placed at such a position would be stationary with respect to the Earth, and would require very little fuel to remain in that position. Find one of these positions with an explanation.
Newton’s version of Kepler’s third law is: P2 = 4 π2 / [G (M1 + M2)] × a3. The space shuttle orbits 271 km above the Earth's surface. How often do the astronauts see a sunrise (in minutes)? Use the gravitational constant G = 6.67 × 10-11 m3 kg-1 s-2, the mass of the Earth M = 5.97 × 1024 kg, and the radius of the Earth to be 7000 km.
(a) Calculate the magnitude of the gravitational force exerted by Mars on a 65 kg human standing on the surface of Mars. (The mass of Mars is 6.4x1023 kg and its radius is 3.4x106 m.) 240.0277 ✓ N (b) Calculate the magnitude of the gravitational force exerted by the human on Mars. 240.0277 N (c) For comparison, calculate the approximate magnitude of the gravitational force of this human on a similar human who is standing 2.5 meters away. 1.76e8 XN (d) What approximations or simplifying assumptions must you make in these calculations? (Note: Some of these choices are false because they are wrong physics!) ✔Treat Mars as though it were spherically symmetric. Ignore the effects of the Sun, which alters the gravitational force that one object exerts on another. ✔Treat the humans as though they were points or uniform-density spheres. O Use the same gravitational constant in (a) and (b) despite its dependence on the size of the masses. Additional Materials eBook
So let's consider a person with a mass of 51.0 kg standing on the Earth. To find the gravitational force on the person, we'll again use Newton's law of universal gravitation with the Earth as m2 and the radius of the Earth for the distance F = GmME RE2 . Now all we need to do is substitute values and calculate. We already said m = 51.0 kg, and we know G = 6.67 ✕ 10−11 N · m2/kg2. The Earth is not a perfect sphere, but, its average radius is RE = 6.37 ✕ 106 m. The mass of the Earth is ME = 5.97 ✕ 10−24 kg. We can then substitute these values in the following formula. (Enter your answer in N.) F = (6.67 ✕ 10−11 N · m2/kg2)(51.0 kg)(5.97 ✕ 1024 kg) (6.37 ✕ 106 m)2 (A) = _______ N Now let's compare this result to the person's weight (in N) found by multiplying the person's mass by g (or, that is, w = mg) where g = 9.80 m/s2. w = (51.0 kg)(9.80 m/s2) =(b) __________________ N You should have found that these two methods give about the same result!…