Physics Challenge Question 1: Solutions
Physics Challenge Question 15: Solutions
Part 1
The Earth orbits the Sun in a circle of radius 149,600,000 km. One orbit takes 365.25 days. (The 0.25 is what gives us a leap year every 4 years.)
The speed is:
[pic]
[pic]
[pic]
So the Earth orbits around the sun, traveling about 29.8 km (18.5 miles) every second!
Part 2
To stay in a circle, the resulting force must be
[pic]
This force is supplied by gravity. Therefore,
[pic]
We can now cancel the Earth mass and one r to get
[pic]
Solving for the Sun’s mass, we get
[pic]
Notice how you don’t need to know the mass of the Earth; you could have looked at any planet or satellite orbiting the Sun to determine its mass! This technique is actually used by astronomers to find the mass of other stars in our galaxy. If you can measure the speed and distance of an orbiting planet, you know the mass of its star.
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2.pð.r
v
r
π.r
v
r
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