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Name _____________________________________ Date ________________________ Period _______ Advanced Physics How Fast Are We Moving? How fast are you moving right now? You may think you’re not moving at all, but that’s only your relative motion compared to the Earth. The Earth itself is moving, and since you’re on it, you’re moving too. We can calculate how fast we’re moving with some knowledge of time and circles, the value of G, and the following data: Mass of Earth = 5.9736 x 1024 kg Mass of Sun = 1.9891 x 1030 kg Radius of Earth’s orbit = 1.4960 x 1011 m Radius of planet Earth = 6.37 x 106 m First let’s calculate how fast we’re moving due to the rotation of the Earth. For simplicity, let’s pretend Earth is spherical and we’re standing on the equator. 1) Use the radius of planet earth and definition of circumference to calculate the distance we would travel in one day. 2) Do some unit conversions to calculate the number of seconds in one day. 3) Use your answers from problems 1 and 2 to calculate our speed (in m/s) due to Earth’s rotation. Earth is also revolving around the sun. Let’s calculate how fast we’re moving due to that motion. We’ll pretend that Earth’s orbit is circular. 4) Calculate the force of gravity between the sun and the Earth. 5) What is the centripetal force acting on Earth? Name _____________________________________ Date ________________________ Period _______ Advanced Physics 6) Calculate the centripetal acceleration of Earth using Earth’s mass and the centripetal force. 7) Calculate the speed at which the Earth is moving around the sun using the centripetal acceleration and the radius of Earth’s orbit. Once a day, our motion due to rotation and revolution are in the exact same direction. When two vectors are in the same direction, we can add their magnitudes. 8) Add your answers from problems 3 and 7 to calculate the maximum speed of a person due to Earth’s rotation and revolution around the sun. 9) If we’re moving so fast, why don’t we feel it? Newton’s third law tells us that the force of gravity that keeps Earth revolving around the Sun is equal in magnitude to the force of gravity from the Earth pulling on the sun. This force causes the Sun to travel in a small circle. Let’s pretend Earth is the only planet in the solar system. 10) Calculate the centripetal acceleration of the sun. 11) The formulas 𝑣 = 𝑑 𝑡 = 2𝜋𝑟 𝑡 and 𝑎𝑐 = 𝑣2 𝑟 2𝜋 2 can be combined into 𝑎𝑐 = ( 𝑡 ) 𝑟 where 𝑡 is the number of seconds in a year and 𝑟 is the radius of the circle around which the sun moves. Calculate 𝑟. 12) Calculate the velocity at which the sun moves due to Earth’s gravitational pull.