# Is there life on mars? Questions Flashcards

Show that, with a surface gravity of 3.7 N/kg and a mass of 6.4 x 10²³ kg, Mars has a radius of about 3400km

G = 6.67 * 10^-11 Nm²/kg²

g = (-) GM/r² so r² = GM/g = 6.67 x 10⁻¹¹ x 6.4 x 10²³ / 3.7 = 1.15 x 10¹³ r = 3397 km r ≈ 3400 km

Calculate the gravitational potential at the surface of Mars, taking the radius to be 3390 km

M = 6.4 x 10²³ kg

V = (-) GM/r

= 6.67 x 10⁻¹¹ x 6.4 x 10²³/(3390 x 10³)

= 1.259233…x 10⁷

= 1.26 x 10⁷ J/kg

Calculate the gravitational potential energy needed to lift a 2500 kg Mars lander back into orbit at 280 km

G = 6.67 * 10^-11 Nm²/kg²

M = 6.4 x 10²³ kg

E = (-) GmM/r²

= 6.67 x 10⁻¹¹ x 6.4 x 10²³ x 2500/(280 x 10³)²

= 1.3612… x 10⁶

= 1.36 x 10⁶

Calculate the kinetic energy needed to lift a 2500 kg Mars lander back into orbit at 280 km

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A day on Mars is 24 hours 40 minutes. Show that the altitude of an areostationary orbit is about 17,000 km

r = (h + rₘ) mv²/r = GmM/r² r = GM/v² v=s/t s = 2rπ v = 2rπ / (24*60*60 + 40*60) 2r²π = GMt r² = 6.03 x 10¹⁷ r = 7.77 x 10 ⁸ h = 7.77 x 10 ⁸ - 3390 x 10³ ????????

Assuming the image of Mars is 500 x 500 pixels at 24 bit per pixel:

Calculate the resolution of the image

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Assuming the image of Mars is 500 x 500 pixels at 24 bit per pixel:

Calculate the amount of information in the image

500 x 500 x 24 = 6 Mbits

Assuming the image of Mars is 500 x 500 pixels at 24 bit per pixel:

Calculate the number of alternative colours that the image can contain

2^24 = 16,777,216

= 16,800,000 alternatives

(??)

Assuming the image of Mars is 500 x 500 pixels at 24 bit per pixel:

Calculate the data transfer rate needed to transmit the image in 2 1/2 minutes

500 x 500 x 24 = 6 Mbits

6,000,000/(2.5*60)

= 40,000 bits/s

Assuming the image of Mars is 500 x 500 pixels at 24 bit per pixel:

Describe how each of the following image processing techniques could improve the image of Mars:

Very brightness

Very contrast

Reduce noise

Detect edges

False colour

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The orbital radius of Mars’ orbit is 2.3×10¹¹ m and that of earth is 1.5×10¹¹ m:

Use Kepler’s 3rd law T² ∝ r³ to show that the time for Mars to orbit the Sun is about 687 Earth days

(2.3×10¹¹ / 1.5×10¹¹)³/² = T / 365

1.89869… x 365 = T

T = 693.02… days

T ≈ 687 days (??)

The orbital radius of miles is orbit is 2.3×10¹¹ m and that of earth is 1.5×10¹¹ m:

Calculate i) The orbital velocity and ii)The centripetal acceleration due to Mars’s orbit around the Sun

v²= GM/r v² = 6.67 x 10⁻¹¹ x 6.4 x 10²³ / (3390 x 10³) v² = 12.6 x 10⁶ v = 3549 m/s = 3500 m/s (2sf)

a = v²/r = 12.6 x 10⁶ / (3390 x 10³)

= 3.71455…m/s²

= 3.7 m/s² (2sf)

The orbital radius of miles is orbit is 2.3×10¹¹ m and that of earth is 1.5×10¹¹ m:

Calculate the maximum and minimum times for a radio signal to travel from Earth to Mars and back

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The mean surface temperature on Mars is 210 K:

Show that the root mean square speed of a gas molecule of mass m is given by cᵣₘₛ = √(3kT/m)

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The mean surface temperature on Mars is 210 K:

Calculate the root mean square speed of i) CO₂ molecules ii) N₂ molecules

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