Falling around Earth forever

Science · Space Systems & Earth's History · ages 17-18

Name ______________________ Date ____________

A satellite climbs to a higher orbit. What happens to its speed?
- It drifts slower
- It races faster
- It stays exactly level
What defines a geostationary orbit?
- Above the equator, 24 hour period, fixed spot
- Above the pole, 12 hour period
- Low orbit, 90 minute period
For circular orbits, period squared is proportional to radius cubed.
Circle one: True False
Which equation gives orbital speed for a circular orbit?
- G M m over r equals m v over r
- G M m over r squared equals m v squared over r
- m v squared over r equals m g h
A moon moves out to 4 times its old radius. By what factor does its period grow?
Answer: ______________
About how far is a geostationary slot from Earth's centre?
- 6,400 km
- 384,000 km
- 42,000 km
Nina parks a geostationary satellite over the North Pole. What fails?
- Nothing, poles work too
- It cannot hang over one spot from there
- The period becomes 12 hours
Moon A circles with period 2 hours. Moon B orbits the same planet at 4 times the radius. What is B's period in hours?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

It drifts slower · Speed follows root G M over r, so bigger r means a smaller root.
Above the equator, 24 hour period, fixed spot · It circles the equator once per day, turning with Earth over one spot.
True · That is Kepler's third law, straight from gravity feeding circular demand.
G M m over r squared equals m v squared over r · Gravity feeds circular demand term for term, then the small mass cancels.
8 · Period tracks the square root of r cubed: 4 cubed is 64, whose root is 8.
42,000 km · The 24 hour circle sits about 42,000 km out from the centre.
It cannot hang over one spot from there · Only an equatorial circle turns with the ground below, so a polar slot drifts away.
16 · Period grows 8 times for 4 times the radius: 2 times 8 is 16 hours.