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.)
Show that the values vA and vP of the speed of an earth satellite at the apogee A and the perigee P of an elliptic orbit are defined by the relationswhere M is the mass of the earth, and rA and rP represent, respectively, the maximum and minimum distances of the orbit to the center of the earth.
A satellite orbits the Earth in an elliptic orbit with eccentricity 0,3. Itspericentric height is 150 km. What is its velocity at a height of 300 km?If its speed at perigee is decreased by 10%, still perpendicular to theradius, determine if if it will stay in an orbit or hit the Earth.
Show that the period of orbit for two masses, m1 and m2 , in circular orbits of radii r1 and r2 , respectively, about their common center-of-mass, is given by T = 2π √(r3 / (G(m1 + m2))) where r = r1 + r2 . (Hint: The masses orbit at radii r1 and r2 , respectively where r = r1 + r2 . 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 expressions for the kinetic energy.)
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