Physics 400
Practice Orbits
Mr. Youker |
Planet
Venus
Earth
Mars
(Sun)
Mass (kg)
4.87 x1024
5.97 x1024
6.42 x1023
1.99 x1030
Radius (m)
6.05 x106
6.38 x106
3.40 x106
6.96 x108
Orbital Radius (m)
1.08 x1011
1.50 x1011
2.28 x1011
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1. What is the size of the gravitational force of attraction between the Earth and the Sun?
(Hint: r = the orbital radius of the Earth.)
Fg = GMm/r2
Fg = (6.67 x10-11)(1.99 x1030)(5.97 x1024)
(1.50 x1011)2
Fg = 7.924 x1044
2.25 x1022
Fg = 3.52 x1022 N
Why do we ignore the actual radius of the Sun and Earth in this calculation?
The additional separation produced by adding the radii
of the Earth and Sun only contributes 0.5% to the distance.
2. What is the size of the gravitational force of attraction between the Earth and a 1000 kg
satellite with an altitude of 2000 km (2.00 x106 m above the Earth’s surface)?
Fg = GMm/r2
Fg = (6.67 x10-11)(5.97 x1024)(1000)
(6.38 x106 + 2.00 x106)2
Fg = 3.98 x1017
7.02 x1013
Fg = 5668 N
Why do we not ignore the actual radius of the Earth in this calculation?
The altitude of the satellite is 24% of the total separation.
3. What would be the weight of a 600 kg rock on the surface of Mars?
Fg = GMm/r2
Fg = (6.67 x10-11)(6.42 x1023)(600)
(3.40 x106)2
Fg = 2.57 x1016
1.156 x1013
Fg = 2,223 N
4. If you wished to fly your spaceship to Mars and place it in orbit at an altitude of 2000 km
above the Martian surface, then what tangential velocity must you give to your
spaceship?
vorbit2 = GM/r
vorbit2 = (6.67 x10-11)(6.42 x1023)
(2.0 x106 + 3.40 x106)
2
vorbit = 7.93 x106
vorbit = 2816 m/s
5.
How frequently (in Earth years) do the planets Venus and Mars align with one another
during their orbits around the Sun?
Venus
Torbit2 = 42r3/GM
Torbit2 = (42)(1.08 x1011)3
(6.67 x10-11)(1.99 x1030)
2
Torbit = 3.75 x1014
Torbit = 1.94 x107 s
Mars
Torbit2 = 42r3/GM
Torbit2 = (42)(2.28 x1011)3
(6.67 x10-11)(1.99 x1030)
2
Torbit = 3.53 x1015
Torbit = 5.94 x107 s
∆t = TmarsT venus/(T mars – Tvenus)
∆t = (5.94 x107)( 1.94 x107)
(5.94 x107 – 1.94 x107)
∆t = 2.99 x107 s
∆t = 8002.5 hr
∆t = 333 days
6.
A geosynchronous satellite is one that possesses an orbital period equivalent to the
rotational period of the planet around which it orbits. At what altitude must an Earth
satellite be placed in order to be geosynchronous?
Torbit2 = 42r3/GM
86,4002 = (42)(r)3
(6.67 x10-11)(5.97 x1024)
3
r = 7.53 x1022
rorbit = 4.22x107 m
-6.38 x106 m
alt.orbit = 3.58 x107 m
alt.orbit = 35,800 km
7.
In an attempt to determine the mass of Venus, NASA officials send a probe into orbit
around the planet. This probe has a mass of 5000 kg and orbits in a 14,000 km diameter
circular orbit. The satellite completes one revolution in two hours. What is the mass of
Venus that can be determined from this data?
Torbit2 = 42r3/GM
72002 = (42)(7 x106)3
(6.67 x10-11)(M)
M = 3.92 x1024 kg