Studied by 3 peopleAll the Maths Skill you need for GCSE Edexcel Astronomy Paper 1
The Moon’s equatorial radii is 1738km & its polar radii is 1736km. Calculate the mean radius of the Moon. Give your answer to an appropriate number of significant figures.
(1738km + 1736km) / 2 = 1737km
A planetary scientist obtained the following dimensions for the radius of the asteroid Hector:
185km x 133km x 102km
Calculate the mean diameter of Hector.
(185km + 133km +102km) / 3 = 140km x 2 = 280km
Note: It has asked you to find the diameter, when you have been given the radius, which is why we times by 2 at the end!
The Sun’s diameter is roughly —- times bigger than the Moon’s, & the same goes for their relative —-. This is why the Sun & the Moon —- —- —- —- in the sky.
The Sun’s diameter is roughly 400 times bigger than the Moon’s, & the same goes for their relative distances. This is why the Sun & the Moon subtend the same angle in the sky.
The diameters of the Earth & the Moon are 13000km & 3500km respectively
What is the ratio of the diameter of Earth : diameter of Moon?
13000km / 3500km = 3.7
Felix made a scale model of the Solar System in which the Sun was 4×10² times further away from the Earth than the Moon was.
The model representing the Sun was 2.00m from Earth.
How many mm away was the model representing the Moon?
We first need to calculate how many m the Moon was from earth in the Model, so we do 2.00m / 4×10² = 0.005m
Then we convert m into mm by multiplying by 1000, so 0.005m x 1000 = 5mm
Eratosthenes determined the distance from Alexandria to Syene to be 5000 stadia.
If one stadium is 185m, calculate the distance in km between Alexandria & Syene.
Note: Stadia is the plural of stadium!
185m x 5000stadia = 925000m / 1000 = 925km
A straight flagpole casts a shadow from the Sun onto horizontal ground. The Sun makes an angle of 31° with the vertical.
Calculate the value of the angle between the Sun & the horizon.
Angle from the flagpole to the horizontal ground = 90°
90° - 31° = 59°
What is the equation that Eratosthenes used to calculate the circumference of the Earth?
circumference of the Earth / distance from Alexandria to Syene = 360° / 7°
Two students live at different locations in the southern hemisphere & conduct an experiment to measure the circumference of the Earth.
Student 1 measure the angle from the Earth to the Sun to be 60°
Student 2 measure the angle from the Earth to the Sun to be 44°
They live 1720km apart. Using the student’s data, determine the circumference of the Earth, correct to 2 significant figures.
The angle of the Sun between the two students is 60° - 44° = 16° & we know that the distance between the two is 1720km
Substitute into the equation we get circumference of the Earth / 1720km = 360° / 16°, and rearranging this we get circumference of the Earth = (360° / 16°) x 1720km = 38700km
Put into 2s.f., we get 39000km
1° = —-’
1° = 60’ a.k.a. 60arcmins
Calculate the difference between 54°52’ & 38°38’
16°14’
Calculate the difference between 44°12’ & 23°49’
20°23’
Two students live at different locations in the southern hemisphere & conduct an experiment to measure the circumference of the Earth.
Student 1 measure the angle from the Earth to the Sun to be 48°17’
Student 2 measure the angle from the Earth to the Sun to be 31°53’
They live 1860km apart. Using the student’s data, determine the circumference of the Earth, correct to 3 significant figures.
The difference between 48°17’ & 31°53’ is 16°24
To be able to use this number in our equation, we need to covert into decimal. This equals to 16.4
Substituting & rearranging, we get (360 / 16.4) x 1860km = 40829.26829
To 3s.f. we get 40800km
Two astronomers observe the north-western from different sites at the same longitude.
At the same time, they measured the altitude at their locations to be 17°’30 & 8°50’. If the circumference of the Earth is 40800km, calculate the distance between the two astronomers. Give your answer to 3 significant figures.
The difference between 17°30’ & 8°50’ is 8°40
To be able to use this number in our equation, we need to covert into decimal. This equals to 8.6666666…
Substituting & rearranging, we get 40800 / (360 / 8.666) = 982.2222222…
To 3s.f. we get 982km
What is the equation that Aristarchus of Samos used to determine the diameter of the Moon & the Earth?
diameter of Moon / diameter of Earth = time interval from U1 to U2 / time interval from U2 to U4
Calculate the time interval between 11:41 & 13:28
1hr 47mins
Calculate the time interval between 22:56 & 00:18
1hr 22mins
An astronomer obtained the following times of umbral contacts:
U1 - 18:06
U2 - 19:38
U3 - 22:45
U4 - 00:16
Using this data, calculate the ratio of Earth’s diameter : Moon’s diameter to the nearest whole number.
Find the time interval between U1 & U2, which is 1hr 32mins
Turn this into a decimal, which is 1.53
Do the same for the time interval between U2 & U4, so you should get 4.63
Because we want it in the ratio Earth : Moon, we do 4.63 / 1.53
Round to the nearest whole number, you get 3
What is the equation that links the diameter & distance of the Sun & Moon?
diameter of Sun / diameter of Moon = distance to Sun / distance to Moon
What is the Earth’s precession rate per century?
1.4°
Precession
The slight wobbling of the Earth’s axis that causes it to move its position in Ursa Minor
How many years does it take for the Earth to precess 1°?
(1.0 / 1.4) x 100 = 71 years to the nearest whole number
Note
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