Check Your Understanding There is another consideration to this last calculation of ME. We derived Equation 13.8 assuming that the satellite orbits around the center of the astronomical body at the same radius used in the expression for the gravitational force between them. What assumption is made to justify this? Earth is about 81 times more massive than the Moon. Does the Moon orbit about the exact center of Earth? Which is about 17,000 mph. Using Equation 13.8, the period is T = 2 π r 3 G M E = 2 π ( 6.37 × 10 6 + 4.00 × 10 5 m ) 3 ( 6.67 × 10 − 11 N ⋅ m 2 /kg 2 ) ( 5.96 × 10 24 kg ) = 5.55 × 10 3 s
Check Your Understanding There is another consideration to this last calculation of ME. We derived Equation 13.8 assuming that the satellite orbits around the center of the astronomical body at the same radius used in the expression for the gravitational force between them. What assumption is made to justify this? Earth is about 81 times more massive than the Moon. Does the Moon orbit about the exact center of Earth? Which is about 17,000 mph. Using Equation 13.8, the period is T = 2 π r 3 G M E = 2 π ( 6.37 × 10 6 + 4.00 × 10 5 m ) 3 ( 6.67 × 10 − 11 N ⋅ m 2 /kg 2 ) ( 5.96 × 10 24 kg ) = 5.55 × 10 3 s
Check Your Understanding There is another consideration to this last calculation of ME. We derived Equation 13.8 assuming that the satellite orbits around the center of the astronomical body at the same radius used in the expression for the gravitational force between them. What assumption is made to justify this? Earth is about 81 times more massive than the Moon. Does the Moon orbit about the exact center of Earth?
Which is about 17,000 mph. Using Equation 13.8, the period is
T
=
2
π
r
3
G
M
E
=
2
π
(
6.37
×
10
6
+
4.00
×
10
5
m
)
3
(
6.67
×
10
−
11
N
⋅
m
2
/kg
2
)
(
5.96
×
10
24
kg
)
=
5.55
×
10
3
s
Using canonical units, What is the circular velocity of a satellite orbiting the earth at a radius of 1.50? (Answer: 0.816). What is the radius and altitude of a satellite orbiting the earth with a period of 10.0? (Answer: radius = 1.363, altitude = 0.363)
Mars has a Known radius of 3390 Km. Somebody threw a baseball at 990 Km/hr and it orbited the planer succesfuly.
a) determine the period of orbit in secords
b) Determine the gravitational field strength on Mars in N/Kg (how can I do that if I don´t have the mass of Mars)
Neptune orbits the Sun with an orbital radius of 4.495 x 10^12 m. If the earth to sun distance 1A.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 x10^30 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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