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Using your deductive reasoning skills, can you figure out what each variable in our formula stands for?
\( v=\sqrt{{\frac{{G\times M}}{R}}}\)
V


G


M


R


Are there any values which are not part of this question which you found surprising? (Hint: the mass of Earth is included, but no other mass)
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Alright, let’s figure out how fast our rocket has to travel in order to hook up with the international space station.
We will use our formula for the velocity of objects in orbit formula.
\( v=\sqrt{{\frac{{G\times M}}{R}}}\)
G is the Universal Gravitational Constant, a standard value used in most formulas involving gravity. It is equal to \( 6.67\times {{10}^{{11}}}N{{m}^{2}}/k{{g}^{2}}\).
M is the mass of the Earth. Search online and find the mass of the Earth in kg.
R is the distance from the center of mass (center of Earth) to the object in orbit. Search online for the radius of Earth (in meters) and the height of the space station above Earth (in meters), and combine these values to find R (in meters).
Make sure to write each of these values down in your notebook before moving on, you’re going to need them again.
Using these values, calculate the velocity our rocket will have in orbit when it meets up with the International Space Station. (You will need to use your scientific calculator to input values like \( 6.67\times {{10}^{{11}}} \)
Round your answer to the nearest 100 meters per second. Ex. 5632~5700
How long does it take our rocket to complete a full orbit of the earth? Remember, Distance=Velocity x Time. (Hint: Use the formula for circumference of a circle and the R from the last problem)
Since the velocity we found in the last problem is in meters per second, go ahead and just calculate the number of seconds it takes to orbit the Earth.
Can you convert the number of seconds it takes into minutes? How many minutes does it take the space station to orbit Earth? (Round to the nearest minute)
Writing Assignment: Alright Math Commanders, it’s time to put your understanding to the test, and to share this new knowledge with someone in your family. Below, write 23 paragraphs about what you learned today. Make sure you specifically address issues like:
When you’re finished, share what you learned with a family member. You may be surprised that even adults you know think there is no gravity in space and have never learned the truth you discovered today!
When you’re finished writing, come back and we’re going to learn about another amazing aspect of space travel.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.