Answer:
Car velocity when crossing checkpoint = 60 m/s
Explanation:
For an object traveling at an acceleration of a m/s², with an initial velocity of u m/s the displacement at time = t secs is given in meters by the equation
[tex]\displaystyle d=ut+\frac{1}{2}at^{2}[/tex]
Here we are given displacement, and time but not acceleration and initial velocity : d = 225 meters, t = 5 seconds
Let's find an equation relating u and a in terms of d and using data given
Switching sides we get
[tex]ut+\frac{1}{2}at^{2}=d[/tex]
Substituting values for t = 5, d = 225 we get
[tex]5u+\frac{1}{2}a.25=225[/tex]
Multiplying both sides by 2 yields
[tex]10u+25a=450\;\;\; ...... (1)[/tex]
We also have the formula:
[tex]\displaystyle a=\frac{{v-u}}{t}[/tex]
where v is the current velocity and u the initial velocity
So
[tex]\displaystyle a=\frac{30-u}{5}[/tex]
[tex]u+5a=30\;\;...... (2)[/tex]
Multiply equation (2) by 5 and subtract from (1) to eliminate the a terms and solve for u
[tex]\displaystyle 10u+25a-5u-25a=450-150\\\\5u=300\\\\u=60m/s\\\\\textsf{which is the speed at which the car passes the checkpoint}\\[/tex]
paraffin wax–cs0.33wo3 composite windows with excellent near- infrared shielding and thermal energy storage abilities
paraffin wax–cs0.33wo3 [cesium tungsten bronze]
Its coating effectively reduce the solar heat gain and air conditioning energy utilization of building because of high selective NIR
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the solar energy that absorbed by the window glass will overheat the glass due to photothermal conversion of paraffin wax.
to reduce this problem.
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This composite window is expected to better the energy efficiency of buildings located in the high temp fluctuations.
The given question is incomplete The complete question is.
paraffin wax–cs0.33wo3 composite windows with excellent near- infrared shielding and thermal energy storage abilities
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An object of mass 0. 85 kg is initially at rest. When a force acts on it for 2. 9 ms it acquires a speed of 10. 6 m/s. Find the magnitude (in n) of the average force acting on the object during the 2. 9 ms time interval. (enter a number. )
By using uniform motion, the average force is 3106.89 N.
We need to know about the uniform motion to solve this problem. The uniform motion is an object's motion under acceleration. It should follow the rule
vt = vo + a . t
vt² = vo² + 2a . s
s = vo . t + 1/2 . a . t²
where vt is final velocity, vo is initial velocity, a is acceleration, t is time and s is displacement.
From the question above, we know that
vo = 0 m/s
vt = 10.6 m/s
m = 0.85 kg
t = 2.9 ms = 2.9 x 10¯³ second
Find the acceleration by using the first equation
vt = vo + a . t
10.6 = 0 + a. 2.9 x 10¯³
a = 3655.17 m/s²
Find the average force
F = m . a
F = 0.85 . 3655.17
F = 3106.89 N
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Two waves on one string are described by the wave functions
y₁ = 3.0 cos (4.0x - 1.6t) y₂ = 4.0 sin (5.0x - 2.0t) where x and y are in centimeters and t is in seconds. Find the superposition of the waves y₁ + y₂ at the points (b) x = 1.00, t = 0.500 ; and
The resultant superposition of waves is -1.647cm
We are given that
y₁ = 3.0 cos (4.0x - 1.6t)
y₂ = 4.0 sin (5.0x -2.0t)
where x and y are in centimeters and seconds respectively
It is given that resultant wave is y1+y2
at x=1, t=1
y= y1+y2
= 3.0 cos (4.0x - 1.6t) + 4.0 sin (5.0x - 2.0t)
= 3.0 cos ( 4 x 1 -1.6 x1) + 4.0 sin(5 x 1 - 2.0 x 1)
= 3 cos (2.4rad) + 4 sin(3rad)
= -2.212 + 0.5645
= -1.647cm
Hence the superposition of waves is -1.647cm
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GP Submarine A travels horizontally at 11.0 m/s through ocean water. It emits a sonar signal of frequency f = 5.27× 10³Hz in the forward direction. Submarine B is in front of submarine A and traveling at 3.00 m/s relative to the water in the same direction as submarine A. A crewman in submarine B uses his equipment to detect the sound waves ("pings") from submarine A. We wish to determine what is heard by the crewman in submarine B. (d) In Equation 17.19 , what speed of sound should be used?
The speed of sound used in water is 5408 Hz.
(d) The frequency that submarine B is able to detect is [tex]fo = fs (V -V_O/ v +V_s).[/tex]
[tex]=53.273[/tex] × [tex]10 3hz) (1533 m/s + 11 m/s / (45 m/s - 1533 m/s))[/tex]
Frequency [tex]= 5408 HZ[/tex]
Hence, the speed of sound used in water is [tex]5408Hz[/tex].
What is principle of Submarine?Submarine, any naval vessel capable of propulsion both below and above the surface of the ocean. Submarines are very distinct from surface ships in terms of appearance and design, making this a unique capacity among warships.
When Germany used them to attack surface merchant ships during World War I (1914–18), submarines initially played a significant role in naval warfare. Torpedo's, a type of self-propelled underwater missile used by submarines, were used as their main armament in such attacks. In World War II (1939–1955), submarines participated in similar operations on a bigger scale, in both the Atlantic (by Germany) and Pacific (by the United States).
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A cubical gaussian surface surrounds a long, straight, charged filament that passes perpendicularly through two opposite faces. No other charges are nearby. (ii) Through how many of the cube's faces is the electric flux zero? Choose from the same possibilities as in part (i).
The electric flux is zero through four cube surfaces.
Assuming the charged filament is quite long, and you are not near the edges, the two opposing sides that the filament travels through have no flux. If the charge filament is long, which you may assume is indefinitely long, then there is the equal amount of charge on the left and right of where you are, therefore the electric field has no preference for left or right.
This implies that the electric field can only travel in or out of the filament. No field lines run through the two faces of the cube that the filament goes through if the electric field is not moving left or right. There are electric field lines on the four sides of the filament.
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Answer asappppp
A book is at rest on a table. Identify the correct free body diagram for this situation
Answer:
Third answer choice
Explanation:
Dot in the middle and Fn and Fg
Hope this helps! :)
A step-up transformer is designed to have an output voltage of 2200V (rms) when the primary is connected across a 110-V (rms) source. (a) If the primary winding has exactly 80 turns, how many turns are required on the secondary?
The number of turns required on the secondary winding is 1,600 turns.
Number of turns needed in the secondary winding
The number of turns needed in the secondary winding is calculated as follows;
Ns/Np = Es/Ep
where;
Np is number of turns in primary windingNs is number of turns in secondary windingEs is secondary voltageEp is primary or input voltageNs/80 = 2200/110
Ns = 80( 2200/110)
Ns = 1,600 turns
Thus, the number of turns required on the secondary winding is 1,600 turns.
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two point charges -5 uc and 4 uc charge are 21 cm apart. what is the magnitude of the electric field at a point half-way between the two charges?
The electric field at a point halfway is 18.37 x 10⁵ N/C.
We need to know about the electric fields to solve this problem. The electric field produced by a single-point positive charge is a radial field, whose strength is given by the equation
E = k.Q/r²
where E is the electric field, Q is the charge and r is the radius.
From the question above, we know that
k = 9 x 10⁹ Nm²/C²
Q1 = -5μC = -5 x 10¯⁶ C
Q2 = 4μC = 4 x 10¯⁶ C
x = 21 cm = 0.21 m
from midpoint (r = 0.105 m)
The electric field directly outward from Q2 to Q1 so that the total electric field between the charges will be added up.
Etotal = E1 + E2
Etotal = k.Q1/r² + k.Q2/r²
Etotal = k/r² x (Q1 + Q2)
Etotal = 9 x 10⁹/(0.21)² x (5 x 10¯⁶ + 4 x 10¯⁶)
Etotal = 18.37 x 10⁵ N/C
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Most data security breaches can be prevented.
A.
True
B.
False
Answer:
A?
Explanation:
i don't know correct me if i'm wrong
a student stays at her initial position for a bit of time, then walks slowly in a straight line for a while, then stops to rest awhile and finally runs quickly back to her initial position along a straight line.
The displacement versus time plots that best represent the student’s trip will be graph C. Then the correct option is C.
What is kinematics?The examination of motion without taking the mass or the motion's source into account.
The first student spends some hours in the nest position. so that time and location are represented on a graph from t₀ to t₁.
When a pupil moves slowly in a straight line, their position changes, and their speed increases. Thus, location is represented in the graph by "ab" in the time range from t₁ to t₂.
The condition is shown in the time interval from t₂ to t₃ when the person stops and the velocity is nil.
The constant decrease in velocity and displacement occurs as a student sprint back to her starting position.
Then the correct option is C.
The remaining question is attached below.
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Which of these is a data type that is made up of whole numbers represented as
binary values? (1 point)
object
integer
string
stack
Integers is referred to as the data type that is made up of whole numbers represented as binary values and is therefore denoted as option B.
What is a Data?
This is referred to as discrete values which are used to describe information which could be in different forms such as quantity, quality etc.
Integers is referred to the data type which comprises of whole numbers represented as binary values and it could be zero , a positive or negative number and examples include 0, 1, -2 etc. This is therefore the reason why option B was chosen as the most appropriate choice.
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A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of λ, and the cylinder has a net charge per unit length of 2λ . From this information, use Gauss's law to find (c) the electric field outside the cylinder a distance r from the axis.
The electric field outside the cylinder a distance r from the axis. E=6k/λr [k= 1/4πε1]
The electric force per unit charge is referred to as the electric field. It is assumed that the field's direction corresponds to the force it would apply to a positive test charge. From a positive point charge, the electric field radiates outward, and from a negative point charge, it radiates in.
From the point charge, the electric field radiates outward in all directions. Spherical equipotential surfaces are represented by the circles. The vector sum of the individual fields can be used to calculate the electric field from any number of point charges.
E outside of the cylinder is given by:
E(2rL) = L+2rL
q out =3λL
E=0 2rL /3rL
E=6k/λr [k= 1/4πε1]
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eska answer batado please
Answer:
01110111 01101000 01111001 0100000 01110100 00100000
5. Suppose you and a friend are test driving a new car. You drive out of the car dealership and go
10 miles east, and then 8 miles south. Then, your friend drives 8 miles west, and 6 miles north.
If you had the dealer's homing pigeon in the car, how far do you think it would have to fly to
get back to the dealership? Use the simulation to test ideas.
• The distance that the bird must fly represents the sum of the 4 displacement vectors. Use the
simulation to test ideas you have about vector addition. After your tests, describe how you can
use the simulation to add vectors.
The displacement of the dealer's homing pigeon in the car is 12.81 miles.
What is displacement?
The displacement of an object is the change in position of an object.
Displacement is a vector quantity because it can be described by both magnitude and direction.
The displacement of the dealer's homing pigeon in the car is calculated as follows;
initial position = 10 miles east
final position = 8 miles south
displacement = √(10² + 8²)
displacement = 12.81 miles
Thus, the displacement of the dealer's homing pigeon in the car is 12.81 miles.
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How can you create an equivalent resistance of 8 ohms from only 10 ohms resistors and 3 ohm resistors?
You should connect two 10 Ohms resistors in parallel and then connect it in series with a 3 Ohms resistors.
How to achieve the desired resistance under these circumstances?In order to achieve the desired resistance under the given circumstances, we would connect two 10 Ohms resistors in parallel and then connect it in series with a 3 Ohms resistors.
Mathematically, the total equivalence resistance of two resistors that are connected in parallel is given by:
1/Rt = 1/R₁ + 1/R₂
1/Rt = 1/10 + 1/10
1/Rt = 2/10
1/Rt = 1/5
Rt = 5 Ohms.
Next, we would connect this 5 Ohms resistor in series with the 3 Ohms resistor:
R₃ = 3 + Rt
R₃ = 3 + 5
R₃ = 8 Ohms.
In conclusion, you can create an equivalent resistance of 8 ohms from only 10 ohms resistors and 3 ohm resistors by connecting two 10 Ohms resistors in parallel and then connect it in series with a 3 Ohms resistors.
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A particle is moving at a speed less than c / 2 . If the speed of the particle is doubled, what happens to its momentum?
If the particle's speed is doubled. The momentum's value is then increased by twice.
What is momentum?In Newton's equations of motion, an object's linear momentum, translational momentum, or simply momentum is the product of its speed and mass. Given that it has a dual magnitude and its direction, it is a vector quantity. kg-m/s is the SI unit for momentum.
Let m be the item's mass and v be its speed. Then the momentum is given as,
P = mv kg-m / s
A particle is traveling less quickly than c / 2. if the particle's speed is twice.
P = m(2v)
P = 2mv
If the particle's speed is twice. The momentum's value is then increased by a factor of two.
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Consider (a) an electron (b) a photon, and (c) a proton, all moving in vacuum. Choose all correct answers for each question. (v) Which move at the speed of light?
Photon move at the speed of light which is option (b)
An electron is a solid negatively charged factor of an atom. Electrons exist outdoor of and surrounding the atom nucleus. Each electron includes one unit of bad charge (1.602 x 10^-19 coulomb)A proton is a subatomic particle discovered with inside the nucleus of each atom. The particle has a advantageous electric charge, identical and contrary to that of the electron. A photon is a subatomic particle, having strength and momentum however no mass or electric powered charge, this is the quantum unit of electromagnetic radiation, together with light.As electrons and protons are particles of the atoms and posses mass so they do not move at the speed of light even in vaccum.
Photon is a light energy so it moves with the speed of light .
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rearrange equations for the said varibles
The given equations of motion are rearranged for the said variables.
In the given equations of motion, the variables used represents:
[tex]v_{f}[/tex] = Final velocity
[tex]v_{i}[/tex] = Initial velocity
Δx = Displacement
a = Acceleration
t = Time
The given equations that are rearranged for said variables are as follows.
t = 2 Δx / ( [tex]v_{i} +v_{f}[/tex] )[tex]v_{f}[/tex] = ( 2 Δx / t ) - [tex]v_{i}[/tex][tex]v_{i}[/tex] = ( Δx / t ) - ( a t / 2 )a = ( 2 Δx / t² ) - ( 2 [tex]v_{i}[/tex] / t )[tex]v_{i}[/tex] = √ ( [tex]v_{f}[/tex]² - 2 a Δx )Δx = ( [tex]v_{f}[/tex]² - [tex]v_{i}[/tex]² ) / 2 a[tex]v_{f}[/tex] = ( Δx / t ) + ( a t / 2 )Therefore, the given equations of motion are rearranged above for the said variables.
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A car drives a total of 10 miles along Waukegan Road. Along the road the speed limit is 35 mph but there are many stop lights along the drive. The average speed of driving the 10 miles would be:
a: Lower than 35 mph
b: Exactly 35 mph
c: Some speed that cannot be calculated
d: Greater than 35 mph
The average speed of driving the 10 miles would be lower than 35 mph.
What is average speed?
The average speed of an object is the ratio of the total distance to the total time of motion of an object.
Mathematically, average speed of an object is given as;
v(average) = total distance / total time
The average speed of a car decreases with increase in the total time of motion.
Due to the many stop lights along the drive, the total of motion of the car will increase will the total distance traveled by the car (10 miles) will be constant.
Also, since the speed limit is 35 mph, the average speed of the car will lower than the 35 mph speed limit.
Thus, the average speed of driving the 10 miles would be lower than 35 mph.
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what is motor effect ? class-10
Answer:
a wire carrying a currents creates a magnetic field this can interact with another magnetic field causing a force that pushes the wire at right angles. This is called the motor effect
In 1962 , measurements of the magnetic field of a large tornado were made at the Geophysical Observatory in Tulsa, Oklahoma. If the magnitude of the tornado's field was B=1.50×10⁻⁸ T pointing north when the tornado was 9.00 km east of the observatory, what current was carried up or down the funnel of the tornado? Model the vortex as a long, straight wire carrying a current.
B = μ₀i/2πr
i = 2πrB/μ₀
∵ 16.50 nano Tesla = 1.65×10⁻⁸ Tesla
∵8.10Km = 8100 m
i = 2(3.14)(8100)(1.65×10⁻⁸)/4×3.14×10⁻⁷
i = 668.25 A
So the current carried up or down the funnel of the tornado is 668.25 A.
What is a tornado?A tornado is a fast spinning column of air that occasionally strikes the base of a cumulonimbus cloud as well as the Earth's surface.
A tornado is a narrow, violently rotating column of air that extends from the ground to a thunderstorm.
Tornadoes are difficult to notice since wind is invisible unless they build a condensation funnel of water droplets, dust, and debris.
Some tornadoes increase and become powerful or destructive. Strong tornadoes can last for twenty minutes or more and have winds of up to 200 miles per hour, whereas severe tornadoes can persist for more than an hour and have winds of 200 to 300 miles per hour!
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explain why cooking food with pressure pot is faster than cooking with an ordinary pot
Answer:
Pressure forces heat into food, which triggers the chemical reaction of food. Also entire pot has same temp and pressure. Also successful pressure cooking much like an autoclave requires three things: sustained time, pressure and temperature to be effective.
a model house that runs completely on renewable energy uses 222 windmills and 333 solar panels. each windmill generates mmm kilowatt-hours (kwh) of energy per year, and each solar panel generates sss kwh per year. which expressions can we use to describe how many kwh of energy the model house will output in 101010 years? choose 2 answers: choose 2 answers:
The total energy output in 1010 years is therefore equal to (22M + 33S) 1010 kWh.
Energy output in 1010 years will be equal to (22M + 33S) 1010 kWh.
22 windmills make up the model home. M kWh of energy are produced by one wind turbine year. 22 windmills generate 22 M kWh of energy each year. 33 solar panels make up the model home. S kWh of energy is produced by one solar panel annually. Energy produced by 33 solar panels annually equals 33 S kWh.
Now, the total amount of energy produced by 22 windmills and 33 solar panels in a year is equal to (22 M + 33 S) kWh.
Why is clean energy so essential?One of the most crucial steps you can take to lessen your influence on the environment is to use renewable energy. More than all of our driving and flying put together, electricity production is our main source of greenhouse gases. Clean energy also lessens damaging smog, toxic buildup in our air and water, and the effects of coal mining and gas extraction. It will take time to replace our fossil fuel infrastructure, and clean energy demand from consumers and companies, as well as strong, continuous support from state and federal mandates to create renewable energy generation.
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(a) what is the wavelength of a 2.4 ghz sine wave in inches? (b) what is the most efficient length in inches of a monopole antenna transmitting at 2.4 ghz? 2. calculate the frequency of an electromagnetic wave in free space having a wavelength of 12 cm.
The wavelength of a 2.4 ghz sine wave is 0.5 inches.
What is wavelength?In physical science, the frequency is the spatial time of an occasional wave the distance over which the wave's shape rehashes. Albeit X-beams have numerous advantageous applications, utilizing them requires alert since openness can cause visual deficiency, malignant growth and different wounds. Frequency and recurrence are conversely related so that more drawn out waves have lower frequencies, and more limited waves have higher frequencies. Frequency addresses the distance between two successive recurrence wave tops and is normally used to portray the electromagnetic range.
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a pupil with a mass of 55kg swinging back on a chair and falling off at a speed of 0.6 m/s
The Kinetic energy of the pupil with mass of 55kg swinging back on a chair and falling off at a speed of 0.6 m/s is "9.9 J".
Kinetic energy is defined as the energy possessed by a body due to the virtue of velocity.
the S.I. unit of Kinetic energy is joule .
Kinetic energy is conserved.
velocity is defined as the displacement per unit time.
S.I unit of velocity is m/s.
given:
Mass (m) = 55 kg
velocity (v) = 0.6 m/s
Kinetic energy(K)=1/2×mv²
Kinetic energy (K)=1/2×55×0.36
Kinetic energy (K)= 9.9 joule
therefore,
The Kinetic energy of the pupil with mass of 55kg swinging back on a chair and falling off at a speed of 0.6 m/s is "9.9 J".
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which of statements about the skateboarder's energy is true? as he travels from the top of the ramp to the bottom, ke turns into pe. as he travels from the bottom of the pipe to the top, ke turns into pe. if friction is present, mechanical energy will be conserved. the pe is the greatest at the bottom of the ramp.
The statements about the skateboarder's energy is true option C which is if friction is present, mechanical energy will be conserved. the pe is the greatest at the bottom of the ramp.
What is energy?
Energy is the ability to perform a task or do work. Energy can be potential or kinetic energy. Potential energy is the energy posses by a body in a state of rest while kinetic energy is the energy in motion.
As the skateboarder travels the ramp, potential energy turn to kinetic energy and if friction is present some of the energy in the system is converted to heat energy.
Therefore, The statements about the skateboarder's energy is true option C which is if friction is present, mechanical energy will be conserved. the pe is the greatest at the bottom of the ramp.
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M A family ice show is held at an enclosed arena. The skaters perform to music with level 80.0 dB . This level is too loud for your baby, who yells at 75.0 dB. (b) What is the combined sound level?
A family ice show is held at an enclosed arena. The skaters perform to music with level 80.0 db. This level is too loud for your baby, who yells at 75.0 db. 155 db. is the combined sound level.
What is intensity?In physical science, the force or motion of brilliant energy is the power moved per unit region, where the region is estimated on the plane opposite to the heading of spread of the energy. Light force assumes an essential part. With expanded light the fish' s vision improves, and they will turn out to be more careful about hunters.
The formula for intensity is given by, I = P A. Where I am the intensity, P is the power and A is the area of cross section.
The sun' s point decides how much light entering the water. As would be normal, the most elevated measure of sun-based force happens on the globe right where the sun is above and as the point of the sun brings down, the sun-oriented power declines.
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if the second floor and the top floor of a building are separated by a distance of 100 m, what is the approximate difference between the air pressures of the two levels? (note: air density
The difference in air pressure between the second floor and the top floor of a building is about equal to (1.2)(10)(100) = 1200 N/m2, where air density is equal to 1.2 kg/m3 and gravity acceleration is equal to 10 m/s2.
What is a gravitational acceleration?In physics, gravitational acceleration refers to the speed at which a body falls freely in a vacuum (and thus without experiencing drag). This is the constant acceleration brought on just by the gravitational pull. Gravimetry is the measurement and analysis of these rates. All bodies accelerate at the same rate in vacuum, independent of their masses or compositions.
The combined effects of gravity and the centrifugal force from Earth's rotation cause the Earth's gravity to be as great as it is at a given location on the surface. Depending on height, latitude, and longitude, the free fall acceleration varies at various locations on the surface of the Earth from 9.764 to 9.834 m/s2 (32.03 to 32.26 ft/s2). The exact definition of a conventional standard value is 9.80665 m/s2 (32.1740 ft/s2). Gravity anomalies are areas where this value differs significantly. Other effects like buoyancy or drag are not included in this.
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A pion at rest (mπ = 273 me) decays to a muon (mµ = 207 me) and an antineutrino (m-v≈0) . The reaction is written π-→ µ- + v-. Find (a) the kinetic energy of the muon
The kinetic energy of the muon is 4.08 MeV
Given that:
A pion (mπ = 273 me)
muon (mµ= 207me)
Neutrino (mv=0)
(Let’s assume that c =1, and that me= 0.511MeV)
Since the pion is at rest conversation of momentum dictates that the momenta of the muon and the neutrino be equal in magnitude,
P_μ=P_v (1)
Since the pion is at rest its energy equals its mass, E_π=m_π. Since the neutrino is massless its energy equals its momentum E_v=P_v . By conservation of energy,
E_π=E_μ+E_v, so
E_μ=m_π-P_v (2)
Substituting the right sides of (1) and (2) into the left side of the fundamental kinematic equation for the muon E_μ^2-P_μ^2=m_μ^2 yields
〖(m_π-P_v)〗^2-P_μ^2=m_μ^2
Solving for P_v gives (the magnitudes of) the momenta of the decay particles and the kinetic energy (equal to the total energy) of the massless neutrino,
P_v (〖=P〗_u=E_v )=((m_π^2-m_μ^2))/(2m_π )
P_v=(〖273〗^2-〖207〗^2)/(2× 273)=29.65 MeV
The kinetic energy of the muon equals its total energy minus its mass which, using (2), is
〖(m〗_π-P_v)-m_μ=4.08 MeV
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1. why did aristarchus choose the time of a half (quarter) moon to make his measurements for calculating the earth-sun distance?
In order to make his measurements for determining the Earth-Sun distance, Aristarchus waited for the Moon's phase to be exactly half full while the Sun was still visible in the sky. For this reason, he chose the time of a half (quarter) moon.
How did Aristarchus calculate the distance to the Sun?It was now possible for another Greek astronomer, Aristarchus, to attempt to determine the Earth's distance from the Sun after learning the distance to the Moon. Aristarchus discovered that the Moon, the Earth, and the Sun formed a right triangle when they were all equally illuminated. Now that he was aware of the distance between the Earth and the Moon, all he needed to know to calculate the Sun's distance was the current angle between the Moon and the Sun. It was a wonderful argument that was weakened by scant evidence. Aristarchus calculated this angle to be 87 degrees using only his eyes, which was not far off from the actual number of 89.83 degrees. But when there are significant distances involved, even slight inaccuracies might suddenly become significant. His outcome was more than a thousand times off.
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