Find the Hohmann transfer velocities, Δ v E l l i p s e E a r t h and Δ v E l l i p s e M a r s ,needed for a trip to Mars. Use Equation 13.7 to find the circular orbital velocities for Earth and Mars. Using Equation 13.4 and the total energy of the ellips (with semi-major asix a ), given by E = − G m M s 2 a , find the velocities at Earth (perihelion) and at Mars (aphelion) required to be on the transfer ellipse. The difference, Δ v , at each point is the velocity boost or transfer velocity needed.
Find the Hohmann transfer velocities, Δ v E l l i p s e E a r t h and Δ v E l l i p s e M a r s ,needed for a trip to Mars. Use Equation 13.7 to find the circular orbital velocities for Earth and Mars. Using Equation 13.4 and the total energy of the ellips (with semi-major asix a ), given by E = − G m M s 2 a , find the velocities at Earth (perihelion) and at Mars (aphelion) required to be on the transfer ellipse. The difference, Δ v , at each point is the velocity boost or transfer velocity needed.
Find the Hohmann transfer velocities,
Δ
v
E
l
l
i
p
s
e
E
a
r
t
h
and
Δ
v
E
l
l
i
p
s
e
M
a
r
s
,needed for a trip to Mars. Use Equation 13.7 to find the circular orbital velocities for Earth and Mars. Using Equation 13.4 and the total energy of the ellips (with semi-major asix a), given by
E
=
−
G
m
M
s
2
a
, find the velocities at Earth (perihelion) and at Mars (aphelion) required to be on the transfer ellipse. The difference,
Δ
v
, at each point is the velocity boost or transfer velocity needed.
O Jupiter's third-largest natural satellite, lo, follows an
orbit with a semimajor axis of 422,000 km (4.22 × 105
km) and a period of 1.77 Earth days (Plo = 1.77 d). To
use Kepler's Third Law, we first must convert lo's orbital
semimajor axis to astronomical units. One AU equals
150 million km (1 AU = 1.50 x 108 km). Convert lo's a
value to AU and record the result.
alo =
AU
Two celestial bodies whose masses are m1 and m2 are revolving around their common center of mass and the distance between them is L. Assuming that they are both point masses, Find the angular speed, tangential speeds of the masses m1 and m2, and period of the motion.
Universal Gravitational Constant, G=6,6742867E-11 m3 kg / s2(Note that the exponent is negative)Radius of Earth, RE: 6,3781366E+06 mMass of Earth, ME: 5,9721426E+24 kg
m1=10^12kg
m2=10^11kg
L=10^8m
7,27210E+00 m1
3,85280E+00 m2
6,16500E+00 L
Neptune orbits the Sun with an orbital radius of 4.495 x 10^12 m. If the earth to sun distance 1 A.U. = 1.5 x 10^11 m, a) Determine how many A.U.'s is Neptune's orbital radius (Round to the nearest tenth). b) Given the Sun's mass is 1.99 x 10^30 kg , use Newton's modified version of Kepler's formula T^2 = (4pi^2/Gm(star)) x d^3 to find the period in seconds using scientific notation. (Round to the nearest thousandth). c) Convert the period in part b) to years(Round to the nearest tenth).
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