21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Question
Chapter 20, Problem 39QP
(a)
To determine
The energy of cosmic ray photon.
(b)
To determine
The relativistic mass of cosmic ray photon.
(c)
To determine
The ratio of relativistic mass of cosmic ray photon and rest mass of proton.
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Problem 1. Mass-Energy conversion in the Sun (Palen, et. al. 3rd Edition, Chapter 11, problems 38, 39)
The Sun produces energy by converting mass m into energy E according to E = mc2 where c is the speed of light (c = 300,000 km/sec). Show that if the Sun produces 3.85 × 1026 joules (J) of energy per second, it must convert 4.3 billion kg of mass per second into energy. Note that 1 J/s is a watt (W), which may be more familiar to you.
How much mass has the Sun lost over its lifetime (4.5 billion years)?
The current mass of the Sun is 2 × 1030. What fraction of this mass has been converted into energy during the Sun’s lifetime?
The U.S.S. Enterprise is chased by a Borg Cube through a straight, 3000 meter-long, wormhole.- The Enterprise enters the wormhole with a speed of 100 m/s.- The Enterprise is out of fuel and is slowing at a constant rate of 1.66 m/s2.- The chasing Borg Cube travels with a constant speed of 60 m/s.- The Borg Cube enters the wormhole a full 8.00 seconds after the Enterprise.(A)How long does it take the Enterprise to move through the entire wormhole?(B) With what speed does the Enterprise exit the wormhole?(C)Does the Borg Cube catch the Enterprise before the end of the wormhole? If so, where andif not, how far behind is the Borg Cube when the Enterprise exits?(D)When the Borg Cube is in the middle of the 3000-meter passageway, what is theEnterprise’s speed?
a- A certain star is 18.618.6 light-years away. How long would it take a spacecraft traveling 0.950c to reach that star from Earth, as measured by observers on Earth?
19.6 years
b- How long would it take a spacecraft traveling 0.950c to reach that star from Earth, as measured by observers on the spacecraft?
6.11 years
c-What is the distance traveled according to observers on the spacecraft?
d-What will the spacecraft occupants compute their speed to be from the results of (b) and (c)?
Chapter 20 Solutions
21st Century Astronomy
Ch. 20.1 - Prob. 20.1CYUCh. 20.2 - Prob. 20.2CYUCh. 20.3 - Prob. 20.3CYUCh. 20.4 - Prob. 20.4CYUCh. 20 - Prob. 1QPCh. 20 - Prob. 2QPCh. 20 - Prob. 3QPCh. 20 - Prob. 4QPCh. 20 - Prob. 5QPCh. 20 - Prob. 6QP
Ch. 20 - Prob. 7QPCh. 20 - Prob. 8QPCh. 20 - Prob. 9QPCh. 20 - Prob. 10QPCh. 20 - Prob. 11QPCh. 20 - Prob. 12QPCh. 20 - Prob. 13QPCh. 20 - Prob. 14QPCh. 20 - Prob. 15QPCh. 20 - Prob. 16QPCh. 20 - Prob. 17QPCh. 20 - Prob. 18QPCh. 20 - Prob. 19QPCh. 20 - Prob. 20QPCh. 20 - Prob. 21QPCh. 20 - Prob. 22QPCh. 20 - Prob. 23QPCh. 20 - Prob. 24QPCh. 20 - Prob. 25QPCh. 20 - Prob. 26QPCh. 20 - Prob. 27QPCh. 20 - Prob. 28QPCh. 20 - Prob. 29QPCh. 20 - Prob. 30QPCh. 20 - Prob. 31QPCh. 20 - Prob. 32QPCh. 20 - Prob. 33QPCh. 20 - Prob. 34QPCh. 20 - Prob. 35QPCh. 20 - Prob. 36QPCh. 20 - Prob. 37QPCh. 20 - Prob. 38QPCh. 20 - Prob. 39QPCh. 20 - Prob. 40QPCh. 20 - Prob. 41QPCh. 20 - Prob. 42QPCh. 20 - Prob. 43QPCh. 20 - Prob. 44QPCh. 20 - Prob. 45QP
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- The sun energy at a rate of 3.85×10 26 W by the fusion of hydrogen. About 0.7% of each kilogram of hydrogen goes into the energy generated by the Sun. (a) How many kilograms of hydrogen undergo fusion each second? (b) If the sun is 90.0% hydrogen and half of this can undergo fusion before the sun changes character, how long could it produce energy at its current rate? (c) How many kilograms of mass is the sun losing per second? (d) What fraction of its mass will it have lost in the time found in part (b)?arrow_forwardA supernova explosion of a star produces of energy. (a) How many kilograms of mass are converted to energy in the explosion? (b) What is the ratio of mass destroyed to the original mass of the star?arrow_forwardA supernova explosion of a 2.001031 kg star produces 1.001044 J of energy. (a) How many kilograms of mass are converted to energy in the explosion? (b) What is the ratio m/m of mass destroyed to the original mass of the star?arrow_forward
- If astronauts could travel at v = 0.950c, we on Earth would say it takes (4.20/0.950) = 4.42 years to reach Alpha Centauri, 4.20 light-years away. The astronauts disagree. (a) How much time passes on the astronauts clocks? (b) What is the distance to Alpha Centauri as measured by the astronauts?arrow_forwardNear the center of our galaxy, hydrogen gas is moving directly away from us in its orbit about a black hole. We receive 19(N) nm electromagnetic radiation and know that it was 1875 nm when emitted by the hydrogen gas. What is the speed of the gas?arrow_forwardThe meter was redefined as a reference to Earth, then to krypton, and finally to the speed of light. Why do you think the reference point for a meter continued to change?arrow_forward
- The star Epsilon Eridani is 10.4 light-years from Earth. Imagine a spaceship that travels from Earth to Epsilon Eridani at a constant speed of 0.921c. On Earth, we would measure the time it takes for the ship to reach the star to be (10.4ly/0.921c)= 11.2 years. (a) How much time (in years) would it take the ship to travel from the Earth to the star as measured by a passenger aboard the ship? years (b) What is the distance to the star (in light years) as measured by a passenger aboard the ship?arrow_forwardIf astronauts could travel at v = 0.956c, we on Earth would say it takes (4.20/0.956) = 4.39 years to reach Alpha Centauri, 4.20 light-years away. The astronauts disagree. (a) How much time passes on the astronauts' clocks? years(b) What is the distance to Alpha Centauri as measured by the astronauts? light-yearsarrow_forwardThe sun produces energy by nuclear fusion reactions, in which matter is converted into energy. By measuring the amount of energy we receive from the sun, we know that it is producing energy at a rate of 3.8 * 1026 W. (a) How many kilograms of matter does the sun lose each second? Approximately how many tons of matter is this (1 ton = 2000 lb)? (b) At this rate, how long would it take the sun to use up all its mass?arrow_forward
- The highest-energy cosmic ray ever detected had an energy of about 3.0 x 1020 eV. Assume that this cosmic ray was a proton.a. What was the proton’s speed as a fraction of c?b. If this proton started at the same time and place as a photon traveling at the speed of light, how far behind the photon would it be after traveling for 1 ly?arrow_forwardA ship moves at a constant speed between Earth and Alpha Centauri, 4.2 light years away. According to the ship's passengers, the journey lasts 3 years. What is the speed of the ship?arrow_forwardA light-year is the distance light travels in one year at speed =2.998*10^8m/s a) How many inches are there in 1.00 light-year? (b) The parsec is an astronomical unit of length approximately equal to 3.08×1016 m. How many light-years are there in 1.00 parsec?arrow_forward
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