uppose a mass approximately the size of the Earth’s mass 6 . 72 × 10 24...
uppose a
mass approximately the size of the Earth’s
mass 6
.
72
×
10
24
kg is packed into a small
uniform sphere of radius
r
.
Use:
The speed of light
c
= 2
.
99792
×
10
8
m
/
s
.
The universal gravitational constant
G
=
6
.
67259
×
10
−
11
N m
2
/
kg
2
.
Hint:
The escape speed must be the speed
of light.
Based on Newtonian mechanics, determine
the limiting radius
r
0
when this mass (approx-
imately the size of the Earth’s mass) becomes
a black hole.
Answer in units of m.
Homework Answers
Add Answer to:
uppose a
mass approximately the size of the Earth’s
mass 6
.
72
×
10
24...
The Schwarzschild radius RBH for an object of mass M is defined as RBH = 2GM...
The Schwarzschild radius RBH for an object of mass M is defined as RBH = 2GM where c is the speed of light and G is the universal gravitational constant. RBH gives the radius of the event horizon of a black hole with mass M. In other words, it gives the radius to which some amount of mass M would need to be compressed in order to form a black hole. The mass of the Sun is about 1.99 x...
The Schwarzschild radius RBH for an object of mass M is defined as 2GM RBH =...
The Schwarzschild radius RBH for an object of mass M is defined as 2GM RBH = - where c is the speed of light and G is the universal gravitational constant. RBH gives the radius of the event horizon of a black hole with mass M. In other words, it gives the radius to which some amount of mass M would need to be compressed in order to form a black hole. The mass of the Sun is about 1.99...
The Schwarzschild radius is the distance from an object at which the escape velocity is equal...
The Schwarzschild radius is the distance from an object at which the escape velocity is equal to the speed of light. A black hole is an object that is smaller than its Schwarzschild radius, so not even light itself can escape a black hole. The Schwarzschild radius r depends on the mass m of the black hole according to the equation 2Gm r = where G = 6.673 x 10-11 N.m²/ kg? is the gravitational constant and c = 2.998...
Now we consider a black hole of the same mass as the Sun: Mbh 2x 1030 kg. (a) (2 marks) Show that if you are launching...
Now we consider a black hole of the same mass as the Sun: Mbh 2x 1030 kg. (a) (2 marks) Show that if you are launching a rocket with velocity v upwards from a pl M, you can only escape the planet's gravity if you start from a radius r > 2GM/ t of mass Hint: Use Newtonian mechanics. What if your rocket is acutally a beam of light? If we forget about relativity for a minute, we can put...
Now we consider a black hole of the same mass as the Sun: Mbh 2 x 1050 k (a) (2 marks) Show that if you are launching a...
Now we consider a black hole of the same mass as the Sun: Mbh 2 x 1050 k (a) (2 marks) Show that if you are launching a rocket with velocity v upwards from a planet of mass M, you can only escape the planet's gravity if you start from a radius r > 2GM/v2 Hint: Use Newtonian mechanics What if your rocket is acutally a beam of light? If we forget about relativity for a minute, we can put...
3. The radius of a black hole is the distance from the black hole's center at...
3. The radius of a black hole is the distance from the black hole's center at which the escape speed is the speed of light (c = 3.0 x 10 m/s). What is the radius of a 24 solar mass black hole? Sun has a mass of M -2.0-10 kg and a radius of R = 7.10 m
3. The radius of a black hole is the distance from the black hole's center at...
3. The radius of a black hole is the distance from the black hole's center at which the escape speed is the speed of light (c = 3.0 x 10 m/s). What is the radius of a 24 solar mass black hole? Sun has a mass of M = 2.0-10 kg and a radius of R - 7.10 m
3. The radius of a black hole is the distance from the black hole's center at which the escape speed is the speed o...
3. The radius of a black hole is the distance from the black hole's center at which the escape speed is the speed of light (c-3.0 x 10° m/s). What is the radius of a 24 solar mass black hole? Sun has a mass of M = 2.0.10 kg and a radius of R - 7.10 m
If the mass of the Earth increased without any change in its radius your weight would...
If the mass of the Earth increased without any change in its radius your weight would increase decrease stay the same The value of acceleration due to gravity. O depends on the radius of Earth O depends on the mass of the Earth B. O depends on the universal gravitational constant, G o is different on different planets all of the above Which is true: the gravitational potential energy of an object in Earth's orbit depends on the radius of...
4. An astronaut whose height h is 1.70 m floats feet "down" in an orbiting space...
4. An astronaut whose height h is 1.70 m floats feet "down" in an orbiting space shuttle at a distance center of Earth. 6.77 x 10° m from the (a) What is the dif her feet and at her head? ference in the gravitational acceleration at (b) If the astronaut is now feet "down" at the same orbital radius r of 6.77 x 10° m about a black hole of mass M1.99 x 10" kg (which is 10 times our...
The Schwarzschild radius RBH for an object of mass M is defined as RBH = 2GM where c is the speed of light and G is the universal gravitational constant. RBH gives the radius of the event horizon of a black hole with mass M. In other words, it gives the radius to which some amount of mass M would need to be compressed in order to form a black hole. The mass of the Sun is about 1.99 x...
The Schwarzschild radius RBH for an object of mass M is defined as 2GM RBH = - where c is the speed of light and G is the universal gravitational constant. RBH gives the radius of the event horizon of a black hole with mass M. In other words, it gives the radius to which some amount of mass M would need to be compressed in order to form a black hole. The mass of the Sun is about 1.99...
The Schwarzschild radius is the distance from an object at which the escape velocity is equal to the speed of light. A black hole is an object that is smaller than its Schwarzschild radius, so not even light itself can escape a black hole. The Schwarzschild radius r depends on the mass m of the black hole according to the equation 2Gm r = where G = 6.673 x 10-11 N.m²/ kg? is the gravitational constant and c = 2.998...
Now we consider a black hole of the same mass as the Sun: Mbh 2x 1030 kg. (a) (2 marks) Show that if you are launching a rocket with velocity v upwards from a pl M, you can only escape the planet's gravity if you start from a radius r > 2GM/ t of mass Hint: Use Newtonian mechanics. What if your rocket is acutally a beam of light? If we forget about relativity for a minute, we can put...
Now we consider a black hole of the same mass as the Sun: Mbh 2 x 1050 k (a) (2 marks) Show that if you are launching a rocket with velocity v upwards from a planet of mass M, you can only escape the planet's gravity if you start from a radius r > 2GM/v2 Hint: Use Newtonian mechanics What if your rocket is acutally a beam of light? If we forget about relativity for a minute, we can put...
3. The radius of a black hole is the distance from the black hole's center at which the escape speed is the speed of light (c = 3.0 x 10 m/s). What is the radius of a 24 solar mass black hole? Sun has a mass of M -2.0-10 kg and a radius of R = 7.10 m
3. The radius of a black hole is the distance from the black hole's center at which the escape speed is the speed of light (c = 3.0 x 10 m/s). What is the radius of a 24 solar mass black hole? Sun has a mass of M = 2.0-10 kg and a radius of R - 7.10 m
3. The radius of a black hole is the distance from the black hole's center at which the escape speed is the speed of light (c-3.0 x 10° m/s). What is the radius of a 24 solar mass black hole? Sun has a mass of M = 2.0.10 kg and a radius of R - 7.10 m
If the mass of the Earth increased without any change in its radius your weight would increase decrease stay the same The value of acceleration due to gravity. O depends on the radius of Earth O depends on the mass of the Earth B. O depends on the universal gravitational constant, G o is different on different planets all of the above Which is true: the gravitational potential energy of an object in Earth's orbit depends on the radius of...
4. An astronaut whose height h is 1.70 m floats feet "down" in an orbiting space shuttle at a distance center of Earth. 6.77 x 10° m from the (a) What is the dif her feet and at her head? ference in the gravitational acceleration at (b) If the astronaut is now feet "down" at the same orbital radius r of 6.77 x 10° m about a black hole of mass M1.99 x 10" kg (which is 10 times our...
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