Exam 13: Universal Gravitation

Two satellites are placed in geosynchronous orbits,orbits with a period of 24 hours,where each satellite hovers over a spot on the Earth's equator.Satellite B has three times the mass of satellite A.What is the relationship between the magnitudes of the gravitational forces of the Earth on the two satellites?

What is the kinetic energy of a 200-kg satellite as it follows a circular orbit of radius 8.0 × 10⁶ m around the Earth? (Mass of Earth = 6.0 × 10²⁴ kg. )

Planet Zero has a mass of 4.0 × 10²³ kg and a radius of 2.0 × 10⁶ m.A 10-kg space probe is launched vertically from the surface of Zero with an initial kinetic energy of 8.0 × 10⁷ J.What maximum distance from the center of Zero is achieved by the probe?

A 50-kg satellite circles planet Cruton every 5.6 h in an orbit with a radius of 12 × 10⁶ m.What is the magnitude of the gravitational force on the satellite by planet Cruton?

A projectile is launched from the surface of a planet (mass = M,radius = R).What minimum launch speed is required if the projectile is to rise to a height of 2R above the surface of the planet? Disregard any dissipative effects of the atmosphere.

The period of oscillation of a near-Earth satellite (neglecting atmospheric effects)is 84.3 min.What is the period of a near-Moon satellite? (R_E = 6.37 × 10⁶ m;R_M = 1.74 × 10⁶ m;M_E = 5.98 × 10²⁴ kg;M_M = 7.36 × 10²² kg. )

A satellite circles planet Roton every 2.8 h in an orbit having a radius of 1.2 × 10⁷ m.If the radius of Roton is 5.0 × 10⁶ m,what is the magnitude of the free-fall acceleration on the surface of Roton?

Carla and Jenny are arguing about whether or not it is possible to escape the gravitational field of the Earth.Carla shows Jenny a system where mass m is r_E (not the Earth's radius)distant from Earth and r_P (not planet P's radius)distant from planet P,the mass being on the line connecting the Earth and planet P.Carla states that the mass m has escaped if F_{P on m} = −F_{E on m}.Jenny disagrees.Which one,if either,is correct,and why?

Planet Roton has a mass of 4.0 × 10²³ kg and a radius of 2.0 × 10⁶ m.With what speed should a space probe be launched from the surface of Roton so as to achieve a maximum distance of 3.0 × 10⁶ m from the center of Roton?

What is the magnitude of the free-fall acceleration at a point that is a distance 2R above the surface of the Earth,where R is the radius of the Earth?

At the moment of a total eclipse,the moon lies along a line from the Earth to the sun.If your normal weight is 600 N,how much is your weight decreased by the combined pull of the sun and moon? M_SUN = 2.0 × 10³⁰ kg, r_S-E = 1.5 × 10⁸ km M_MOON = 7.4 × 10²² kg, r_M-E = 3.8 × 10⁵ km

An object is released from rest at a distance h above the surface of a planet (mass = M,radius = R < h).With what speed will the object strike the surface of the planet? Disregard any dissipative effects of the atmosphere of the planet.

The period of a satellite circling planet Nutron is observed to be 84 s when it is in a circular orbit with a radius of 8.0 × 10⁶ m.What is the mass of planet Nutron?

The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse.When the planet is at point A,

A satellite is placed in a geosynchronous orbit.In this equatorial orbit with a period of 24 hours,the satellite hovers over one point on the equator.Which statement is true for a satellite in such an orbit?

A spacecraft (mass = m)orbits a planet (mass = M)in a circular orbit (radius = R).What is the minimum energy required to send this spacecraft to a distant point in space where the gravitational force on the spacecraft by the planet is negligible?

Isaac Newton was able to estimate a value for G,the universal gravitational constant,from the following data: the radius of the Earth is about 6 400 km,the average density of rocks is about 5.50 g/cm³,and g = 9.80 m/s² near the surface of the Earth.What value did Newton obtain for G?

What is the gravitational force on a 20-kg satellite circling the Earth (radius = 6.4 × 10⁶ m,mass = 6.0 × 10²⁴ kg)with a period of 5.0 h?

Planet Zero has a mass of 5.0 × 10²³ kg and a radius of 2.0 × 10⁶ m.A space probe is launched vertically from the surface of Zero with an initial speed of 4.0 km/s.What is the speed of the probe when it is 3.0 × 10⁶ m from Zero's center?

A satellite is in a circular orbit about the Earth at an altitude at which air resistance is negligible.Which of the following statements is true?