Download SPH4U: Forces

SPH4U: Orbits
Consider an object (mo) like a satellite or a
moon travelling in a circular orbit around the
earth.
Recorder: __________________
Manager: __________________
Speaker: _________________
mE = 5.98x1024 kg
rE = 6.38 x 106 m
G = 6.67x10-11 Nm2/kg2
0 1 2 3 4 5
1.
Represent. Label the altitude (h), the radius of the circular orbit (r), the radius of Earth (rE), matching them with the
letters X, Y, and Z.
2.
Reason. Which quantity, X, Y, or Z, does r in the expression for universal
gravitation represent? Explain.
Gm1 m 2
Fg 
r2
mA
Y
X
3.
Reason. Which quantity, X, Y, or Z, does r in the expression for the centripetal
acceleration represent? Explain.
4 2 r
ac  2
T
4.
Represent. Draw a force diagram for the object at the moment shown.
5.
Solve. Use Newton’s 2nd Law, universal gravitation and an expression for centripetal
acceleration to create an equation that relates the radius of the orbit and the period of the
orbit. Solve this for T2. Be careful with the labels for the masses!(Don’t memorize this
equation.)
Z
mB
FD
This result is known as Kepler’s law, named after the brilliant mathematician who spent 25 years working out this result.
How long did it take you? (Thanks, Newton!)
6.
Solve. Complete the chart below which compares orbital velocities, altitude, radii and periods.
Location
Space Shuttle Orbit
Geostationary Orbit (satellite
stationary above Earth’s
surface)
Moon’s Orbit
Altitude
r (m)
T (s)
600 km
24 h =
27 d =
Earth’s Orbit around Sun
(msun = 1.98 x 1030 kg)
©
37