כבידה
✦ בנוי על ידי פהד גאנם ✦
العربية
☀ מצב בהיר
7.1
▾
✕
r =
a(1 − e²)
1 + e·cosθ
|
ΔA
Δt
=
π·a·b
T
= const |
T²
a³
= const
1.50 AU
0.50
0
0
0
0
0
0
T²
0
a³
0
0
a = 4.0 AU | a
E
= 1.0 AU | T
E
= 1.0 yr
T²
a³
=
T
E
²
a
E
³
T²
(4.0)³
=
(1.0)²
(1.0)³
T² = 64 yr²
T = √64 = 8.0 yr
7.2
▾
✕
F = G ·
m₁ · m₂
r²
| G = 6.674 · 10⁻¹¹ N·m²/kg²
5.97·10²⁴ kg
7.35·10²² kg
3.84·10⁸ m
0
0
0
0
F = G ·
m₁ · m₂
r²
= 6.674·10⁻¹¹ ·
5.97·10²⁴ · 7.35·10²²
(3.84·10⁸)²
F = 1.99·10²⁰ N
a₂ =
F
m₂
=
1.99·10²⁰
7.35·10²²
= 2.70·10⁻³ m/s²
a₁ =
F
m₁
= 3.33·10⁻⁵ m/s²
7.2
▾
✕
G ·
M · m
r²
=
m · v²
r
→ v =
√
G · M
r
| M =
4π² · r³
G · T²
35864 km
5.97·10²⁴ kg
6371 km
24.0 h
0
0
0
0
0
G ·
M · m
r²
= m ·
4π² · r
T²
r³ =
G · M · T²
4π²
T = 24 h = 86400 s , G·M = 3.984·10¹⁴
r = 4.224·10⁷ m = 42235 km
h = r − R = 42235 − 6371 = 35864 km
v =
2π · r
T
=
2π · 4.224·10⁷
86400
= 3071 m/s
7.3
▾
✕
g =
F
m
= G ·
M
r²
6.40·10²³ kg
3400 km
1.0 R
0
0
0
0
g = G ·
M
R²
= 6.674·10⁻¹¹ ·
6.4·10²³
(3.4·10⁶)²
g = 3.69 m/s²
r = R + R = 2R = 6.8·10⁶ m
g₂ = G ·
M
(2R)²
=
g
4
= 0.92 m/s²
7.3
▾
✕
E
p
= − G ·
M · m
r
| v
מילוט
=
√
2 · G · M
R
5.0 km/s
5.97·10²⁴ kg
6370 km
0
0
0
0
0
0
½·v² −
G·M
R
= 0 → v =
√
2·G·M
R
v =
√
2 · 6.674·10⁻¹¹ · 5.97·10²⁴
6.37·10⁶
= 1.12·10⁴ m/s = 11.2 km/s
5.0 km/s < 11.2 km/s
½·v₀² −
G·M
R
= −
G·M
r
r = 7.96·10⁶ m → h = r − R = 1.59·10⁶ m ≈ 1591 km
→
🏠
♿