Lesson test: Orbits

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Orbits

1.[3p]
A probe circles Mars at an altitude of 400 km. Taking $G M_{M} = 4.283 \times 10^{13}$ m³ s⁻² and a Martian radius of $3.390 \times 10^{6}$ m, what is its orbital speed in metres per second?

CorrectNot quite: 3362

2.[3p]
A satellite in low orbit is slowed by the thin atmosphere it passes through. What happens over the following weeks?

It loses total energy, so its radius falls and its orbital speed rises

Correct

It loses speed steadily while staying at the same radius

The answer is: It loses total energy, so its radius falls and its orbital speed rises

It picks up energy from the atmosphere and climbs to a higher orbit

The answer is: It loses total energy, so its radius falls and its orbital speed rises

Its speed falls and its period lengthens, leaving the orbit otherwise unchanged

The answer is: It loses total energy, so its radius falls and its orbital speed rises

3.[2p]
Two orbits around the same star with the same semi-major axis but very different eccentricities have the same total energy.

True

Correct

False

The answer is: True

4.[2p]
A transfer orbit has a perigee radius of $7.0 \times 10^{6}$ m and an apogee radius of $4.2 \times 10^{7}$ m. What is its eccentricity?

CorrectNot quite: 0.714

5.[3p]
For that same orbit, what is the speed at perigee in metres per second, with $G M_{E} = 3.986 \times 10^{14}$ m³ s⁻²?

CorrectNot quite: 9880

6.[3p]
Match each total energy to the shape of the resulting path.

Negative total energy
Zero total energy
Positive total energy
Negative total energy with zero eccentricity

a circle
a closed ellipse
a parabola, reaching infinity with no speed left
a hyperbola, escaping with speed to spare

Show the answer

Negative total energy: a closed ellipse Zero total energy: a parabola, reaching infinity with no speed left Positive total energy: a hyperbola, escaping with speed to spare Negative total energy with zero eccentricity: a circle

7.[3p]
Which of these are true of the vis viva equation $v^{2} = G M (2 / r - 1 / a)$ ?

Select all that apply

Setting $r = a$ recovers the circular orbit speed

Correct

Letting $a$ grow without bound gives the escape speed at radius $r$

Correct

It gives the speed at any radius without needing the eccentricity

Correct

It gives the direction of the velocity as well as its size

The answer is: Setting $r = a$ recovers the circular orbit speed, Letting $a$ grow without bound gives the escape speed at radius $r$, It gives the speed at any radius without needing the eccentricity

8.[2p]
Put the stages of a Hohmann transfer between two circular orbits in order.

Burn in the low circular orbit, raising the far point of the path to the target radius
Burn again on arrival, raising the near point so the orbit is circular
Coast half an ellipse out to the target radius

Show the answer

b, a, c

9.[3p]
What is the 43 arcseconds per century in Mercury's perihelion advance?

What is left of the observed advance once the equinoxes and the other planets are subtracted, which Newtonian gravity cannot account for

Correct

The whole observed advance of Mercury's perihelion

The answer is: What is left of the observed advance once the equinoxes and the other planets are subtracted, which Newtonian gravity cannot account for

The uncertainty in the nineteenth century measurements of Mercury's orbit

The answer is: What is left of the observed advance once the equinoxes and the other planets are subtracted, which Newtonian gravity cannot account for

The part of the advance caused by Venus and Jupiter

The answer is: What is left of the observed advance once the equinoxes and the other planets are subtracted, which Newtonian gravity cannot account for

1.[3p] A probe circles Mars at an altitude of 400 km. Taking GMM=4.283×1013 m³ s⁻² and a Martian radius of 3.390×106 m, what is its orbital speed in metres per second?

2.[3p] A satellite in low orbit is slowed by the thin atmosphere it passes through. What happens over the following weeks?

3.[2p] Two orbits around the same star with the same semi-major axis but very different eccentricities have the same total energy.

4.[2p] A transfer orbit has a perigee radius of 7.0×106 m and an apogee radius of 4.2×107 m. What is its eccentricity?

5.[3p] For that same orbit, what is the speed at perigee in metres per second, with GME=3.986×1014 m³ s⁻²?

6.[3p] Match each total energy to the shape of the resulting path.

7.[3p] Which of these are true of the vis viva equation v2=GM(2/r-1/a)?

8.[2p] Put the stages of a Hohmann transfer between two circular orbits in order.

9.[3p] What is the 43 arcseconds per century in Mercury's perihelion advance?

1.[3p]
A probe circles Mars at an altitude of 400 km. Taking $G M_{M} = 4.283 \times 10^{13}$ m³ s⁻² and a Martian radius of $3.390 \times 10^{6}$ m, what is its orbital speed in metres per second?

2.[3p]
A satellite in low orbit is slowed by the thin atmosphere it passes through. What happens over the following weeks?

3.[2p]
Two orbits around the same star with the same semi-major axis but very different eccentricities have the same total energy.

4.[2p]
A transfer orbit has a perigee radius of $7.0 \times 10^{6}$ m and an apogee radius of $4.2 \times 10^{7}$ m. What is its eccentricity?

5.[3p]
For that same orbit, what is the speed at perigee in metres per second, with $G M_{E} = 3.986 \times 10^{14}$ m³ s⁻²?

6.[3p]
Match each total energy to the shape of the resulting path.

7.[3p]
Which of these are true of the vis viva equation $v^{2} = G M (2 / r - 1 / a)$ ?

8.[2p]
Put the stages of a Hohmann transfer between two circular orbits in order.

9.[3p]
What is the 43 arcseconds per century in Mercury's perihelion advance?