According to Kepler’s law , the planets in our solar system move in elliptical orbits around the Sun. If a planet’s closest approach to the Sun occurs at time t = 0 , then the distance r from the center of the planet to the center of the Sun at some later time t can be determined from the equation r = a 1 − e cos ϕ where a is the average distance between centers, e is a positive constant that measures the “flatnessâ€� of the elliptical orbit, and ϕ is the solution of Kepler’s equation 2 π t T = ϕ − e sin ϕ in which T is the time it takes for one complete orbit of the planet. Estimate the distance from the Earth to the Sun when t = 90 days. [First find ϕ from Kepler’s equation, and then use this value of ϕ to find the distance. Use a = 150 × 10 6 km , e = 0.0167 , and T = 365 days.]
According to Kepler’s law , the planets in our solar system move in elliptical orbits around the Sun. If a planet’s closest approach to the Sun occurs at time t = 0 , then the distance r from the center of the planet to the center of the Sun at some later time t can be determined from the equation r = a 1 − e cos ϕ where a is the average distance between centers, e is a positive constant that measures the “flatnessâ€� of the elliptical orbit, and ϕ is the solution of Kepler’s equation 2 π t T = ϕ − e sin ϕ in which T is the time it takes for one complete orbit of the planet. Estimate the distance from the Earth to the Sun when t = 90 days. [First find ϕ from Kepler’s equation, and then use this value of ϕ to find the distance. Use a = 150 × 10 6 km , e = 0.0167 , and T = 365 days.]
According to Kepler’s law, the planets in our solar system move in elliptical orbits around the Sun. If a planet’s closest approach to the Sun occurs at time
t
=
0
,
then the distance
r
from the center of the planet to the center of the Sun at some later time
t
can be determined from the equation
r
=
a
1
−
e
cos
ϕ
where
a
is the average distance between centers,
e
is a positive constant that measures the “flatness� of the elliptical orbit, and
ϕ
is the solution of Kepler’s equation
2
π
t
T
=
ϕ
−
e
sin
ϕ
in which
T
is the time it takes for one complete orbit of the planet. Estimate the distance from the Earth to the Sun when
t
=
90
days. [First find
ϕ
from Kepler’s equation, and then use this value of
ϕ
to find the distance. Use
a
=
150
×
10
6
km
,
e
=
0.0167
,
and
T
=
365
days.]
A tornado can be represented in polar cords by the velocity 7 =4 +ig. Show that
streamline from logarithmic A = Ce.
020
Do part c,d,e
A pendulum is release data point 5 meters to the right of its position at rest. Graph a cosine function that
represents the pendulum's horizontal displacement relative to its position at rest if it completes one back-and-forth
swing every π seconds.
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