Astronomy
posted by qwerty .
What is the size, i.e. the radius, of a black hole with a mass equal to that of Earth (MEarth=6×1024kg)? Give your answer to one significant figure.

R = 2 M in natural units. To convert to SI units, you have to insert c and G in here, that's most easily done as follows.
In Si units M^2 G/R has the dimensions of an energy and Mc^2 also has the dimensions of an energy, the ratio of the two is thus dimensionless:
M G/(R c^2) = dimensionless
So, we need to multiply M by G/c^2 to convert it to a lentgth in SI units. The equation in natural units must this be changed into:
R = 2 M G/c^2
You can also argue that since c = G = 1 in natural units, yo are free to write the natural units equations in this form first as it is strictly the same as R = 2 M but you then have an equation that in SI units is dimensionally correct and you can then insert the mass in kilograms in there with for c and G the SI units values to obtain R in meters.
Respond to this Question
Similar Questions

physics (check my answers)
When the nuclear fuel in the sun is gone, the sun will collapse to a a. black hole b. white dwarf c. supernova d. neutron star My answer: I think its a black hole. If the mass of the Earth were suddenly doubled while the radius was … 
Astronomy
Need some help with Astronomy. I need to figure out the acceleration of gravity on the surface of certain planets. For example, I need to find the acceleration of gravity on Mars when the mass is .11 times the mass of Earth and the … 
space/astronomy
Rank the objects based on the strength of the gravitational force that would be felt by a spacecraft traveling at a distance of 10 AU from the center of each of the objects, from weakest to strongest. 1)red giant mass: 1Msun radius: … 
Physics
The Hubble Space Telescope (HST) has recorded evidence of a black hole at the center of the M87 galaxy. Using Doppler data, it's been measured that matter is orbiting the center of this galaxy at an orbital speed of 7.5x10 5 m/s, out … 
physic
Consider the earth following its nearly circular orbit (dashed curve) about the sun.(Figure 2) The earth has mass mearth=5.98×1024kg and the sun has mass msun=1.99×1030kg. They are separated, center to center, by r=93millionmiles=150millionkm. 
physics
Consider the earth following its nearly circular orbit (dashed curve) about the sun.(Figure 2) The earth has mass mearth=5.98×1024kg and the sun has mass msun=1.99×1030kg. They are separated, center to center, by r=93millionmiles=150millionkm. 
Physics
Consider the earth following its nearly circular orbit (dashed curve) about the sun.(Figure 2) The earth has mass mearth=5.98×1024kg and the sun has mass msun=1.99×1030kg. They are separated, center to center, by r=93millionmiles=150millionkm. … 
AStronomy/ Math
I do not understand how to do one of my online homework questions: What is the Schwarzschild radius of a 100 millionsolarmass black hole? 
physics
radius R of the orbit of a geosynchronous satellite that circles the earth. (Note that R is measured from the center of the earth, not the surface.) You may use the following constants: The universal gravitational constant G is 6.67×10−11N⋅m2/kg2. … 
ap physics
Suppose that Superman wants to stop Earth so it does not rotate. He exerts a force on Earth F⃗ SonE at Earth's equator tangent to its surface for a time interval of 1 year. The mass of Earth is 5.98×1024kg, the radius is 6.37×106m. …