Synchronous orbit* Find the radius of the orbit of a synchronous satellite that circles the Earth. (A synchronous satellite goes around the Earth once ev- ery 24 h, so that its position appears stationary with respect to a ground station.) The simplest way to find the answer and give your results is by expressing all distances in terms of the Earth's radius Re.

Synchronous orbit* Find the radius of the orbit of a synchronous satellite that circles the Earth. (A synchronous satellite goes around the Earth once ev- ery 24 h, so that its position appears stationary with respect to a ground station.) The simplest way to find the answer and give your results is by expressing all distances in terms of the Earth's radius Re.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter39: Relativity

Section: Chapter Questions

Problem 55PQ

See similar textbooks

Similar questions

(a) At what relative velocity is (b) At what relative velocity is
Nuclear-powered rockets were researched for some years before safety concerns paramount. (a) What fraction of a rocket's mass would have to be destroyed to get it into a low Earth orbit, neglecting the decrease in gravity? (Assume an orbital altitude of 250 km, and calculate both the kinetic energy (classical) and the gravitational potential energy needed.) (b) If the ship has a mass of 1.00×105kg (100 tons), what total yield nuclear explosion in tons of TNT is needed?
If a GUT is proven, and the four forces are unified, it will still be correct to say that the orbit of the moon is determined by the gravitational force. Explain why.
A neutral -meson is a particle that can be created by accelerator beams. If one such particle lives 1.401016 s as measured in the laboratory, and 0.8401016 s when at rest relative to an observer, what is its velocity relative to the laboratory?
Two astronomical events are observed to occur at a time of 0.30 s apart and a distance separation of 2.0109m from each other. How fast must a spacecraft travel from the site of one event toward the other to make the events occur at the same time when measured in the frame of reference of the spacecraft?
The formula for length contraction gives the length of an interval on a ruler_moving with velocity v relative to an observer as times the length of the same interval on a ruler at rest with respect to the observer. By what fraction is the length of a meter stick reduced if its velocity relative to you is measured to be 95 percent the speed of light?
Collapse of a dust ball under Newtonian gravity. Suppose that a spherical ball of dust with no internal pressure and with an initial radius R0 and total mass M gravitationally collapses from rest. Show that the outer shell of the collapsing dust ball obeys the equation of motion Solve this equation of motion and show that the time to collapse is given by Hint: Write Newton’s law as . Let f(R) = dF(R)/dR and multiply both sides of by by . The resulting equation may be immediately integrated with respect to time by recognizing that . Integrating again with respect to time, this general technique yields t as a function of R where and C and C1 are constants determined by the initial conditions. Find the time of collapse of a dust ball with a mass and radius equal to that of the Sun. (RS = 6.96 × 1010 cm, MS = 1.99 × 1033 g, G = 6.67 × 10−8 cgs units) What prevents the Sun from collapsing in this way?
An Earth satellite used in the Global Positioning System moves in a circular orbit with period 11 h 58 min. (a) Determine the radius of its orbit. (b) Determine its speed. (c) The satellite contains an oscillator producing the principal nonmilitary GPS signal. Its frequency is 1 575.42 MHz in the reference frame of the satellite. When it is received on the Earths surface, what is the fractional change in this frequency due to time dilation, as described by special relativity? (d) The gravitational blueshift of the frequency according to general relativity is a separate effect. The magnitude of that fractional change is given by ff=Ugmc2 where Ug/m is the change in gravitational potential energy per unit mass between the two points at which the signal is observed. Calculate this fractional change in frequency. (e) What is the overall fractional change in frequency? Superposed on both of these relativistic effects is a Doppler shift that is generally much larger. It can be a redshift or a blueshift, depending on the motion of a particular satellite relative to a GPS receiver (Fig. P1.39).
. How many years would you have to wait to observe a 1° angular shift in the perihelion of Mercury due to general relativistic effects?
What is the relationship between weight and mass? Which is an intrinsic, unchanging Property of a body?
Show that the velocity of a star orbiting its galaxy in a circular orbit is inversely proportional to the square root of its orbital radius, assuming the mass of the stars inside its orbit acts like a single mass at the center of the galaxy. You may use an equation from a previous chapter to support your conclusion, but you must justify its use and define all terms used.
3.4 Synchronous orbit* Find the radius of the orbit of a synchronous satellite that circles the Earth. (A synchronous satellite goes around the Earth once ev-ery 24 h, so that its position appears stationary with respect to a ground station.) The simplest way to find the answer and give your results is by expressing all distances in terms of the Earth's radius R,.