Kepler's 1st Law
What is the shape of an orbit with an eccentricity of 0?
A circle.
A planet is hit by an asteroid, causing its trajectory to change. Its semi-major axis changed from 3.4 AU to 2.9 AU. How would this change affect its average orbital velocity?
The average orbital velocity would increase.
State Kepler's 3rd Law.
As the distance between two planets increases, what happens to the gravitational force between them?
It decreases.
Think back to the activity where we drew orbital trajectories using a string and push pins.
As the distance between the foci (push pins) increased, what happened to the eccentricity?
It also increased.
At what point on an elliptical orbit would a planet/comet experience the greatest orbital velocity?
(you need to give the specific vocabulary term)
perihelion
If you decrease the semi-major axis of a comet's orbit, what would you expect to happen to its orbital period?
It would also decrease.
The Moon orbits at an average distance of 384,400 km from Earth, and has a mass of 7.35 x 1022 kg. Earth's mass is 5.97 x 1024 kg. Calculate the gravitational force between Earth and the Moon. (G= 6.67 x 10-17)
-1.98 x 1020 N
Cathy attempted to calculate the eccentricity of an orbit. Her answer was 2.41.
How do you know her answer is incorrect?
The eccentricity of an orbit cannot be greater than 1.
At what point on an elliptical orbit would a planet/comet experience the smallest orbital velocity?
(you need to give the specific vocabulary term)
aphelion
Venus has an orbital period of 0.615 years and a semi-major axis of 0.723 AU. If Mars has a semi-major axis of 1.52 AU, what is its orbital period?
1.87 years
The Moon orbits at an average distance of 384,400 km from Earth, and has a mass of 7.35 x 1022 kg. Earth's mass is 5.97 x 1024 kg. What is the acceleration of the moon towards Earth? (G= 6.67 x 10-17)
-0.0027 m/s2
What is the eccentricity of a comet whose foci are 34 AU apart and whose semi-major axis is 17.8 AU
0.955
As gravitational force decreases, what happens to an orbiting planet's velocity?
It also decreases.
A comet orbits the sun with a semi-major axis of 2.7 x 1010 km and an orbital period of 2400 years. During its orbit around the Sun, it comes into close proximity with Jupiter and scientists measure a new semi-major axis of 2.2 x 1010. What is its new orbital period?
1765 years
Suppose Earth's mass was increased by a factor of four, and its distance from the Sun was doubled. What would happen to the gravitational force between the Sun and Earth?
It would stay the same.
A comet has an eccentricity of 0.78 and a semi-major axis of 2.6 AU. What is the distance between its foci?
4.06 AU
Compare the orbits of two planets, Planet 1 and Planet 2.
Planet 2 is twice the mass of Planet 1, and is also twice the distance from the sun.
Which planet will have the faster orbital velocity?
Planet 1.
The Moon orbits the earth with a semi-major axis of 384,400 km and an orbital period of approximately 27 days. Suppose that scientists wanted to change the orbital period of the Moon to 30 days. How much farther would its semi-major axis need to be?
27,971 km
The gravitational force between Earth and the Sun is -3.55 x 1022 N. If the Earth has a mass of 5.97 x 1024 kg and the Sun has a mass of 2 x 1030 kg, what is the distance between them? (G = 6.67 x 10-17 N km2/kg2)