Show that the period of orbit for two masses, m 1 and m 2 , in circular orbits of radii r 1 and r 2 , respectively, about their common center-of −mass, is given by T = 2 π r 3 G ( m 1 + m 2 ) where r = r 1 + r 2 . ( Hint: The masses orbit at radii r 1 and r 2 , respectively where r = r 1 + r 2 . Use the expression for the center-of-mass to relate the two radii and note that the two masses must have equal but opposite momenta. Start with the relationship of the period to the circumference and speed of orbit for one of the masses. Use the result of the previous problem using momenta in the expression for the kinetic energy.)
Show that the period of orbit for two masses, m 1 and m 2 , in circular orbits of radii r 1 and r 2 , respectively, about their common center-of −mass, is given by T = 2 π r 3 G ( m 1 + m 2 ) where r = r 1 + r 2 . ( Hint: The masses orbit at radii r 1 and r 2 , respectively where r = r 1 + r 2 . Use the expression for the center-of-mass to relate the two radii and note that the two masses must have equal but opposite momenta. Start with the relationship of the period to the circumference and speed of orbit for one of the masses. Use the result of the previous problem using momenta in the expression for the kinetic energy.)
Show that the period of orbit for two masses,
m
1
and
m
2
, in circular orbits of radii
r
1
and
r
2
, respectively, about their common center-of −mass, is given by
T
=
2
π
r
3
G
(
m
1
+
m
2
)
where
r
=
r
1
+
r
2
. (Hint: The masses orbit at radii
r
1
and
r
2
, respectively where
r
=
r
1
+
r
2
. Use the expression for the center-of-mass to relate the two radii and note that the two masses must have equal but opposite momenta. Start with the relationship of the period to the circumference and speed of orbit for one of the masses. Use the result of the previous problem using momenta in the expression for the kinetic energy.)
Synchronous or stationary communications satellites are put into an orbit whose radius is r= 3.5x10^7m. The orbit is in the plane of the equator, and two adjacent satellites have an angular separation of theta= 3.9 degrees. Find the arc lenght in m that separates the satellites. Express answer in whole number.
A satellite describes an elliptic orbit of minimum altitude 606 km above the surface of the earth. The semimajor and semiminor axes are 17 440 km and 13 950 km, respectively. Knowing that the speed of the satellite at point C is 4.78 km/s, determine (a) the speed at point A, the perigee, (b) the speed at point B, the apogee.
Consider an earth satellite moving with a speed 8200 m/s at perigee which is 340 km
above the earth’s surface. Calculate distance to the satellite from the earth's surface when
it is at apogee. (Radius of earth is 6.4×10° m ).
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